Past MAS seminars
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Past Seminars ( 2004 | 2005 | 2006 | 2007 | 2008 | 2009 | 2010 | 2011)
Spring 2004
Date: 13 Jan 2004
Time: 10:30-12:30
Room: M279
Speakers:
- Daniela Vasileva, MAS2, "On a local refinement solver for computer simulation of flow through oil filters"
- JF Williams, MAS1, "r-adaptivity and equidistribution in arbitrary dimension"
Date: 3 Feb 2004
Time: 10:30-12:30
Room: M279
Speakers:
- Ismail Rafatov, MAS3, "Numerical investigation of spatio-temporal patterns in planar glow discharges"
- Marc van Raalte, MAS2, "Two-level Fourier analysis of the convection-diffusion equation discretized by discontinuous Galerkin methods"
Date: 24 Feb 2004
Time: 10:30-12:30
Room: M279
Speakers:
- Ingrid Lepot, U. Liege, "A parallel high-order finite volume method for three-dimensional inviscid compressible flows on deforming unstructured meshes"
- Carolynne Montijn, MAS3, "Numerical simulation of the minimal streamer model using local grid refinements"
Date: 16 Mar 2004
Time: 10:30-12:30
Room: M279
Speakers:
- Johannes Krottje, MAS1, "Solving diffusion equations with small moving sources and flexible domains"
- Jason Frank, MAS1, "Symplectic Integration of Atmospheric Fluids"
Date: 6 Apr 2004
Time: 10:30-12:30
Room: M279
Speakers:
- Jelmer Cnossen, TU Delft, "Adjoint based model adaptation for a linear problem"
- Gilbert Duivesteijn, TU Delft, "Comparison of two adjoint equation approaches with respect to boundary-condition treatments for the quasi-1D Euler equations"
Date: 27 Apr 2004
Time: 10:30-12:30
Room: M279
Speakers:
- Jeroen Witteveen, TU Delft, "The 1D and 2D simple-wave shock wave approximation and a new numerical method for hyperbolic flow problems"
- Willem Hundsdorfer, MAS3, "TVD and TVB multistep methods"
Date: 18 May 2004
Time: 10:30-12:30
Room: M279
Speakers:
- David Echeverria, MAS2, "Optimization in electromagnetics with the space-mapping technique"
- Joost Batenburg, MAS2, "Discrete tomography and its application to the reconstruction of crystal lattices"
Date: 1 June 2004
Time: 10:30-12:30
Room: M279
Speakers:
- Roelof de Groot, Wijnand Hoitinga and Marc Gerritsma, TUD, "Direct minimisation of residual in the least squares spectral element method"
- Anton Kuut, MAS2, "Adaptive refinement criteria for discontinuous Galerkin methods"
Date: 15 Jun 2004
Time: 10:30-12:30
Room: M279
Speakers:
- Blair Perot, U. Massachusetts, Amherst, "Mimetic discretization methods for incompressible flow problems on moving meshes"
- Jan Verwer, MAS1, "Stability of the Runge-Kutta-Chebyshev method for advection-diffusion-reaction problems"
Fall 2004
Date: 24 Aug 2004
Time: 10:30-12:30
Room: M279
Speakers:
- A.S. Vasudeva Murthy, Bangalore, "Asymptotic and numerical analysis of a simple model for the Ramdas layer"
- Barry Koren, MAS2, "Five-equation model for compressible two-fluid flow"
Date: 7 Sep 2004
Time: 10:30-12:30
Room: M279
Speakers:
- Bruno Dubroca, U. Bordeaux I, "Mathematical and numerical modelling for radiative transfer and coupling with hydrodynamics"
- Herman te Riele, MAS2, "Finding prime values of a polynomial of which the positive values represent the primes"
Date: 28 Sep 2004
Time: 10:30-12:30
Room: M279
Speakers:
- Jan Brandts, UvA, "Simplicial Finite Elements in R^n for n >= 4"
- Jens Lang, TU Darmstadt, "Adaptive FEM for radiative heat transfer"
Date: 19 Oct 2004
Time: 10:30-12:30
Room: M279
Speakers:
- Domenico Lahaye, MAS2, "Design Optimization of Electromagnetic Linear Actuators"
- Francois Henrotte Aachen, "Guidelines for the computation of electromechanical problems"
Date: 9 Nov 2004
Time: 10:30-12:30
Room: M279
Speakers:
- Ben Sommeijer, MAS1, "Extensions to the Runge-Kutta-Chebyshev scheme"
- Anton Tijhuis, TU/e, "Stability Problems in Solving Integral Equations for Transient Electromagnetic Fields"
Date: Friday(!) 3 Dec 2004
Time: 11:00-12:00
Room: M279
Speaker:
- Kevin Burrage, U. Queensland, "Modelling and simulation issues in computational cell biology"
Abstract: A cell is a wonderously complex object. In this talk I will give an overview of some of the mathematical frameworks that are needed in order to make progress towards understanding the complex dynamics of a cell. The talk will consist of a directed random walk through discrete Markov processes, stochastic differential equations, anomalous diffusion and fractional differential equations.
Date: 14 Dec 2004
Time: 10:30-12:30
Room: M279
Speakers:
- Danijela Šijačić, MAS3, "Spatio-temporal pattern formation in a semiconductor-gas-discharge system"
- Domenico Lahaye, MAS2
Date: 11 Jan 2005
Time: 10:30-12:30
Room: M279
Speakers:
- Marc van Raalte, MAS2, "Embedded boundary conditions for Discontinuous Galerkin discretization"
- Willem Hundsdorfer, MAS3, "Limiting for diffusion discretizations"
Date: 1 Feb 2005
Time: 10:30-12:30
Room: M279
Speakers:
- Kees Oosterlee, TU Delft, "Evaluation of European and American options with grid stretching and accurate discretization."
- Johannes Krottje, MAS1, "Time Integration Aspects of Generalized Parabolic-Gradient Systems."
Date: 22 Feb 2005
Time: 10:30-12:30
Room: M279
Speakers:
- Nga Pham Thi, MAS1, TBA
- Sander van Zuijlen, TU Delft, Simulation of fluid-structure interaction
Date: 15 Mar 2005
Time: 10:30-12:30
Room: M279
Speakers:
- Sander van der Pijl, TU Delft, "Modeling of multi-phase flow with a mass-conserving level-set method."
- Domenico Lahaye, MAS2, "Space-mapping applied to a one-dimensional voice-coil actuator problem."
Date: 5 Apr 2005
Time: 10:30-12:30
Room: M279
Speakers:
- Harald van Brummelen, TU Delft, "Interface-GMRES(R) for Fluid-Structure Interaction"
- Joost Batenburg, PNA5, "On the reconstruction of crystals through discrete tomography"
Date: 26 Apr 2005
Time: 10:30-12:30
Room: M279
Speakers:
- Luca Ferracina, U. Leiden, TVD Runge-Kutta processes
- Carolynne Montijn, MAS3, Propagation and branching of negative streamers: a numerical investigation using local uniform grid refinements
Date: 10 May 2005
Time: 10:30-12:30
Room: M279
Speakers:
- Anton Kuut, MAS2, An hp-adaptive multigrid strategy with discontinuous Galerkin
- Piet Hemker, MAS2, Space mapping optimization
Date: 31 May 2005
Cancelled (MAS outing)
Date: 15 Jun 2005
Time: 11:30-12:15
Room: M279
Speaker:
- Theo Gerkema, NIOZ (Texel), Internal waves in the ocean: a 'non-traditional' view
Date: 21 Jun 2005
Time: 10:30-12:30
Room: M279
Speakers:
- Valeriu Savcenco, MAS3, A multirate time-stepping strategy for PDEs
- Johannes Krottje, MAS1, Time integration aspects of generalized parabolic-gradient systems
Date: 12 Jul 2005
Time: 10:30-12:30
Room: M280 (!)
Speakers:
- Sander van Veldhuizen, TU Delft, Efficient methods for solving advection diffusion reaction equations. Abstract.
- Edwin Vollebregt, VORtech Computing (Delft), Domain Decomposition for Shallow Water Models. Abstract.
Fall 2005
Date: 30 Aug 2005
Time: 10:30-12:30
Room: M279
Speakers:
- Xander Tielrooy, TU Delft, Numerical Analysis of the Aerodynamic Characteristics of the Spyker C8 Spyder
- Arno Swart, Utrecht, Numerical Approximation of the Poincaré Equation
Date: 20 Sep 2005
Time: 10:30-12:30
Room: M279
Speakers:
- Bastiaan Braams, Emory U. Atlanta (MAS2 guest), "Use of computational invariant theory in molecular modelling."
- Alejandro Luque, MAS3, "Trapped particle modes and their role in the stability of current-carrying plasmas"
Date: 11 Oct 2005
Time: 10:30-12:30
Room: M279
Speakers:
- Bram van Leer, U. Michigan (MAS2 guest), "Discontinuous Galerkin for Diffusion"
Date: 27 October 2005 (date changed!)
Time: 10:30-12:30
Room: M279
Speakers:
- Laura Portero, Navarra (MAS3 guest), Fractional Step Runge--Kutta methods and some of their applications
- Maciej Dobrzynski, MAS1, On modelling of multiscale and noisy life systems
Date: 8 November 2005 (extra seminar)
Time: 10:30-12:30
Room: M279
Speakers:
- Henk van der Vorst, MAS, Jacobi's ideas on eigenvalue computation in a modern context
- Jan Verwer, MAS1, A brief introduction to MAS
Date: 22 Nov 2005
Time: 10:30-12:30
Room: M279
Speakers:
- Anke Mourik, VU, Determining stochastic dynamics in biological systems
- Maksat Ashyraliyev, MAS1, On the Numerical Solution of Diffusion-Reaction Equations with Singular Source Terms.
Date: 13 Dec 2005
Time: 10:30-12:30
Room: M279
Speakers:
- Arie Verhoeven, TUe/Philips, Multirate Time Integration Methods in Circuit Simulation Problems
Date: 19 Dec 2005
Time: 15:00--16:00 (!)
Room: M279
Speakers:
- Jean-Pierre Boeuf & Gerjan Hagelaar, U. Toulouse, Low temperature plasmas and applications: some modeling problems
Date: 10 Jan 2006
Time: 10:30-12:30
Room: M279
Speakers:
- Pieter Collins, MAS2, Continuity and computability in partial differential equations
- Jorick Naber, MAS2, A Runge-Kutta discontinuous Galerkin level-set method for unsteady compressible two-fluid flow
Date: 31 Jan 2006
Time: 10:30-12:30
Room: M279
Speakers:
- Reinout vander Meulen, MAS2/TU Delft,
- Alex Loeven, MAS2/TU Delft, Efficient uncertainty quantification in computational fluid-structure interaction, Overview and comparison
Date: 21 Feb 2006
Time: 10:30-12:30
Room: M279
Speakers:
- Pieter Collins, MAS2, Continuity and computability in partial differential equations (Part 2)
- Jan Verwer, MAS1, On global error estimation and control for initial value problems
Date: 14 Mar 2006
Time: 10:30-12:30
Room: M279
Speakers:
- G. Carpentieri, MAS2/T.U. Delft, Improving the efficiency of aerodynamic shape optimization on unstructured meshes
- Antonios Zagaris, MAS1, Linear Stability Analysis of Phytoplankton Blooming
Date: 4 Apr 2006
Time: 10:30-12:30
Room: M279
Speakers:
- Bernard Meulenbroek, MAS3, Conformal mapping applied to streamer branching
- Steve Ruuth, Simon Fraser University, MAS3 guest, A simple technique for solving partial differential equations on surfaces
Date: 25 Apr 2006
Time: Cancelled.
Date: 27 Apr 2006 (Extra seminar)
Time: 16:00-17:00
Room: M280(!)
Speaker:
- Jaideep Ray, Sandia National Laboratories, Algorithmic challenges in the high fidelity simulation of flames
Date: 1 June 2006
Time: 10:30-12:30
Room: M280 (!)
Speakers:
- G. R. W. Quispel, La Trobe University, Australia (MAS1 guest), Integral-preserving integrators
- Brett Ryland, Massey University, New Zealand (MAS1 guest), Explicit, high order multisymplectic discretizations for Hamiltonian wave equations
Date: 6 Jun 2006
Time: 10:30-12:30
Room: M279
Speakers:
- Geertje Hek, UvA (MAS1 guest), Algebraically decaying pulses in a Ginzburg-Landau system with a neutrally stable mode
- Maciek Dobrzynski and Jordi Vidal Rodriguez, MAS1, Jordi: Stochastic and Spatial Modelling of Biochemical Networks;
Maciek: Mesoscopic methods for noisy biochemical processes
Date: 27 Jun 2006
Time: 11:30-12:30
Room: M279
Speaker:
- Daniele Corona MAS2, Optimal control of linear affine hybrid automata
Fall 2006
Date: 29 Aug 2006
Time: 10:30-12:30
Room: M279
Speakers:
- Nico Temme, MAS1, Exact solution approach of model problems in singular perturbations
- Jason Frank, MAS1, Local conservation and multisymplectic discretizations for Hamiltonian PDEs
Date: 19 Sep 2006
Time: 10:30-12:30
Room: M279
Speakers:
- Arjen Doelman, MAS1, Interacting pulses and the renormalization group method
- Jens Rademacher, MAS, Dissipationless shocks and modulated wave trains in FPU lattices
Date: 10 Oct 2006
Time: 10:30-12:30
Room: M279
Speakers:
- Domenico Lahaye, MAS2, An hp-adaptive strategy for computing the current induced in thin wire antennas
After a brief introduction into the mathematical modelling of electromagnetic scattering by thin wire antennas, we will present an hp-adaptive strategy for solving the resulting integro-differential equation along with some numerical results.
- Vivien Mallet, MAS1 guest, Data assimilation and ensemble forecast with a chemistry-transport model for air quality.
Date: 31 Oct 2006
Time: 10:30-12:30
Room: M279
Speakers:
- Li Chao, MAS3, Particle versus density models and hybrid computations for ionization fronts
To understand ionization fronts and the growth of streamer channels, both density and particle models have been developed. The streamer channel consists of an ionized interior with many charged particles that is efficiently approximated by continuous particle densities, and a pulled ionization front where the statistics of few single particles can create velocity fluctuation and might trigger inherent instabilities. The goal of the project is therefore to develop a computation scheme that is hybrid in space. We explain concepts and implementations of the kinetic Monte Carlo model and of the spatially coupled one-dimensional hybrid model. We compare results for planar ionization fronts which have been carried out within the PDE model, the Monte Carlo model, and the hybrid model.
- Jeroen Wackers, MAS2, Local grid refinement for water flow around ships
This talk concerns work that I have done this summer, while staying at the National Maritime Research Institute, Japan. I discuss the cause of the errors made by a CFD code for ship flow. Then I show a technique for unstructured grid generation that is tailor-made for these problems.
Date: 14 Nov 2006
Time: 10:30-12:30
Room: M279
Speakers:
- Erik Wagenaars, TU Eindhoven, Electric field measurements in moving ionization fronts during plasma breakdown
Plasma breakdown, or plasma ignition, is a highly transient process marking the transition from a gas to a plasma. Some aspects of plasma breakdown are reasonably well understood, but many details remain unknown, mainly because of a lack of direct measurements of plasma properties. Most of the important processes in low-pressure breakdown, such as electron multiplication in avalanches and propagation of ionization fronts, are controlled by the electric field distribution in the discharge region. We have developed an experimental laser technique capable of measuring spatially and temporally resolved electric field distributions in both plasma and neutral gas. The technique is based on detecting the Stark shift and mixing of high-lying Rydberg levels of xenon atoms, using a 2+1 photon excitation scheme with fluorescence-dip detection. With this experimental arrangement, we measured absolute, time-resolved electric field strengths during the breakdown phase of a low-pressure plasma between parabolic electrodes. Characteristic features of breakdown, such as a moving ionization front with electric field enhancement and the formation of a plasma sheath, were observed.
- Antonios Zagaris, CWI MAS1, An Asymptotic Analysis of the Constrained Runs Algorithm
Detailed macroscopic modelling often yields high-dimensional systems whose dynamics take place in more than one time scales. The same is true of microscopic modelling, where the microscopic dynamics evolve in time scales much shorter than the macroscopic ones. Multiscale reduction methods exploit such time scale disparities to obtain simplified descriptions of these systems, which are valid after the fast initial transients have been exhausted. In this way, numerical stiffness is effectively removed and simulations become much less time intensive, hence opening the road to time-efficient simulation of many complex systems.
A class of reduction methods was proposed recently with the explicit aim of enabling efficient, equation-free implementations of the projective integration schemes developed by C.W. Gear and I.G. Kevrekidis. The first method in this class has also been used in hybrid modelling - namely, to couple the state variables that are used in different spatial regions across the interface. In this talk, I will present the principle on which these methods are based, and I will examine its accuracy in the context of geometric singular perturbation theory. Subsequently, I will present the simplest algorithmic implementations of these methods and derive their stability properties analytically. I will conclude the talk with a short discussion of possible stabilization schemes, the implementation of which which will be the topic of future research.
Extra date
Date: 8 Dec 2006
Time: 11:30-12:30
Room: M279
Speaker:
- Martin Berzins, University of Utah, Mesh Quality and Global Error Estimation in Anisotropic Fluid Flow Problems.
Date: 12 Dec 2006
Time: 10:30-12:30
Room: M279
Speakers:
- Peter van Heijster, MAS1, Pulse dynamics in a 3 component system
In my research we analyse a three component reaction diffusion system and look for so-called pulse solutions. With standard singular perturbation analysis and Evans function theory we proved existence and stability of standing pulses, traveling pulses and double pulses in certain parameter domains. In my presentation I will give an overview of the results obtained so far and explain some of the techniques used.
- Jan Verwer: Coffee, cake and MAS announcements
- Scott McLachlan, T.U. Delft, Improving robustness in algebraic multigrid
Date: 9 Jan 2007
Time: 10:30-12:30
Room: M279
Speakers:
- Alexander Panfilov, Univ. Utrecht (Biology), Vortex dynamics in reaction-diffusion equations with applications to electrophysiology.
Cardiac arrhythmias and sudden cardiac death is the leading cause of death accounting for about 1 death in 10 in industrialized countries. Although cardiac arrhythmias has been studied for well over a century, their underlying mechanisms remain largely unknown. One of the main problems in studies of cardiac arrhythmias is that they occur at the level of the whole organ only, while in most of the cases only single cell experiments can be performed. Due to these limitations alternative approaches such as mathematical modeling are of great interest. From mathematical point of view excitation of the heart is described by a system of non-linear parabolic PDEs of the reaction diffusion type with anisotropic diffusion operator. Cardiac arrhythmias correspond to the solutions of these equations in form of 2D or 3D vortices characterized by their filaments. full abstract.
- Daan Crommelin, CWI MAS1, Reconstruction of effective stochastic dynamics from data.
Construction of stochastic models that describe the effective dynamics of observables of interest is an useful instrument in various fields of application, such as physics, climate science, and finance. I will discuss a new technique for the construction of such effective models from timeseries. The approach centers on the minimization of an object function that measures the difference between the eigenspectrum of the generator of the stochastic process (for example, the Fokker-Planck operator) and a reference eigenspectrum obtained from the data.
Date: 30 Jan 2007
Time: 10:30-12:30
Room: M279
Speakers:
- no first speaker, Mike will start at 11.30h.
- Mike Botchev, TU Twente, Time integration schemes with matrix functions for finite element space-discretized Maxwell's equations
Extra seminar with introductory talk by Kees:
Date: 13 Feb 2007
Time: 10:30-11:20
Room: M279
Speaker: Kees Oosterlee , CWI MAS2, "The Delft Experience"
With this presentation I intend to introduce myself and my work to the colleagues at CWI. So, ?this talk will give an overview of some of the projects I have worked on in the last 5 years in Delft. The projects vary from numerical methods for the Helmholtz equation to fast numerical methods for option pricing. If there is time, the numerical treatment of the poroelasticity equations is also adressed. Most of the research is driven by applications originating from industry.
Date: 20 Feb 2007
Time: 10:30-12:30
Room: M279
Speakers:
- Ale Jan Homburg, UvA, Global bifurcations in systems with symmetry
It is well known that in generic systems of differential equations a homoclinic bifurcation can give rise to a blue sky catastrophe: a periodic orbit develops unbounded period and disappears. I will discuss just this bifurcation but now in contexts where some structure is preserved, either time reversibility or symmetry (under the action of a finite group). This changes the picture dramatically; a common theme is the occurrence of infinite recurrent sets (suspended horseshoes). This talk reviews joint work with Alice Jukes, Juergen Knobloch and Jeroen Lamb.
Literature: A.J. Homburg, J. Knobloch. Multiple homoclinic orbits in conservative and reversible systems. Transactions Amer. Math. Soc. 358 (2006), 1715-1740; A.J. Homburg, J.S.W. Lamb. Symmetric homoclinic tangles in reversible systems. Ergod. Th. and Dynam. Sys. 26 (2006), 1769-1789; A.J. Homburg, A.C. Jukes, J. Knobloch , J.S.W. Lamb. Bifurcation from codimension one relative homoclinic cycles. preprint - Luca Ferracina, CWI MAS3, An adaptive finite element method of lines approach for coupled reaction-diffusion equations in Ω-∂Ω
A numerical study of an Adaptive Finite Element Method Of Lines (AFEMOL) approach is presented for the approximation of the solution of a system of reaction-diffusion equations coupling species defined on a 2-dimensional domain and species confined to the boundary of the domain. In order to bound the energy norm of the space discretization error, in the AFEMOL the spatial mesh changes automatically at selected times when the underlying triangulation is refined in areas where it is needed. The decision of when and where to modify the mesh is based on the estimation of the space discretization error. The adaptive process and the a-posteriori explicit error estimation exploited in this talk are a modification of the pioneer work developed by Bieterman and Babuska in [Numer. Math. 40 (1982), 339], [Numer. Math. 40 (1982), 373], [J. Comput. Phys. 63 (1986), 33]. The primary interest is the effect of the coupling Ω-∂Ω on the performance of the error estimator and the successive adaptive process. Our numerical results indicate that the global error estimators are accurate, the local error indicators are reliable and that the adaptive strategy successfully controls the space discretization error.
Date: 20 Mar 2007
Time: 10:30-12:30
Room: M279
Speakers:
- Jan Bouwe van den Berg, VU, Bubbling in the harmonic map heat flow
The harmonic map heat flow is a model for nematic liquid crystals and also has origins in geometry. We will introduce the model and discuss some of its mathematical properties. In particular, we will focus on the possibility that singularities may develop. The rate at which singularities develop is investigated in settings with certain symmetries. We use the method of matched asymptotic expansions and identify different scenarios for singularity formation. More specifically, we distinguish between singularities that develop in a finite amount of time and those that need infinite time to form. Finally, we discuss which results can be proven rigorously and what can be said about stability (ongoing work).
- Bram van Leer, University of Michigan, USA, CFD by first-order PDE's.
Over the past dozen years we have developed in our CFD Lab the view that flow physics would be best expressed in PDEs of the first order. Such PDEs only contain flux derivatives and local, possibly stiff source terms; these are called hyperbolic-relaxation (HR) equations. The flux terms represent advection and wave propagation, the source terms are responsible for damping, traditionally the role of second- or higher-order dissipation terms. A hierarchy of equation systems can be derived by taking successively higher moments of the collisional Boltzmann equation and using a BGK approximation of the collision terms. Best known is the 10-moment system, which describes viscous, nonconducting flow and is valid up to intermediate Knudsen numbers. A validation study based on a MEMS flow will be presented.
Discretizations of HR systems have a host of advantages, among which:
* stencil size is minimal;
* stiffness is only local;
* convergence is faster than for NS;
* accuracy problems on adaptive grids are minimized;
* suited for decomposition by equations;
* suited for flow at intermediate Knudsen numbers, reacting flow, radiative hydrodynamics.
A grand numerical challenge is to develop algorithms for HR systems that remain accurate whether or not the relaxation time-scale is resolved; this property is called "Asymptotic Preserving" (AP). It requires strong coupling between flux and source terms. We have chosen to pursue the AP property with Discontinuous Galerkin methods, since these achieve maximum compactness of the computational stencil for any order of accuracy, and therefore are a good match to the PDE's chosen. I will describe the development of DG methods for HR systems and illustrate it with numerical results.
A second challenge lies in the detailed physical modeling of shock waves, in particular, steady shocks in supersonic flow. Viscous shock structures obtained with HR systems for most Mach numbers show an incorrect embedded inviscid-like discontinuity. I shall explain the nature of such discontinuities, and present an example of how to prevent their appearance.
Date: 3 Apr 2007
Time: 10:30-12:30
Room: M279
Speakers:
- Gianne Derks, Univ. Surrey, UK (Gianne is spending a sabbatical at the CWI for three months).
Stability of semi-fluxons and pinned fluxons in Josephson junctionsThis talk considers a spatially non-autonomous sine-Gordon equation with constant forcing to model a Josephson junction with an applied bias current. The non-autonomous character is due to the presence of discontinuity points. Two types of discontinuities will be considered.
First a jump of~$\pi$ in the sine-Gordon phase is considered, this models a so-called $0$-$\pi$ Josephson junction. The model admits static solitary waves which are called semi-fluxons and are attached to the discontinuity point. For small forcing, there are three types of semi-fluxons. One of these is stable and the others are unstable. There is a critical value of the forcing beyond all static semi-fluxons fail to exist. Up to this value, the (in)stability of the semi-fluxons can be established analytically.
The second type of discontinuity is due to magnetic impurities in the material, socalled defects. It does not induce a phase-jump, but travelling fluxons can be trapped or pinned by a defect. A start of the analysis of existence and stability of static pinned fluxons will be given.
This talk discusses joint work with Arjen Doelman, Stephan van Gils and Hadi Susanto. - Valeriu Savcenco, CWI MAS3, Analysis of a multirate time stepping scheme for ODEs
To solve ODE systems with different time scales which are localized over the components, multirate time stepping can be used. We present a study of a simple multirate scheme, consisting of the theta-method with one level of temporal local refinement. The results are illustrated by numerical experiments, including results for higher order methods and more levels of refinement with automatic partitioning.
Date: 24 Apr 2007
Time: 10:30-12:30
Room: M279
Speakers:
- Fabian Brau, CWI MAS3, Moving boundary approach for ionization fronts
- Arnd Scheel, University of Minnesota, USA, Pulses and fronts at the boundary of excitability
Extra seminar
Date: 4 May 2007
Time: 11:00-12:00
Room: M279
Speaker: Iuliu Sorin Pop, TU Eindhoven, Crystal dissolution and precipitation in porous media: analysis and simulations at the pore scale
We discuss a pore scale model for crystal dissolution and precipitation in porous media. The underlying model is a parabolic problem that is coupled through the boundary conditions to an ordinary differential inclusion defined on the boundary of the domain. We consider first general domains, for which existence and uniqueness of a weak solution is proven. For the particular case of strips we show that free boundaries occur in the form of dissolution/precipitation fronts. The final part is devoted to the numerics: we present some simulation results, and show that the numerical scheme used is convergent. This is a joint work with C.J. van Duijn and T.L. van Noorden (Eindhoven), V. Devigne (Lyon) and M. Roeger (Leipzig).
Date: 15 May 2007
Time: 10:30-12:30
Room: M279
Speakers:
- Jeroen Wackers, CWI MAS2, Efficient computation of steady water waves
In this talk I present an overview of my Ph.D. work, that will be completed next month. A model for steady water flow with surface waves is presented that can be solved very efficiently. The model contains a high-accuracy water surface discretisation and turbulence; it is solved with a novel linear multigrid technique and defect correction. I will show results that confirm the accuracy of the model and the fast convergence of the solver.
- Johan Grasman, Wageningen University and Research Centre, Testing a method for analyzing the effect of parameter change in climate driven ecological systems
In high dimensional systems with many parameters, like global circulation systems in meteorology, no systematic method exists to detect the most sensitive parameters of the system. Specially in climate modelling there is the additional problem that for these systems exremely long runs have to be made to cover extreme conditions that rarely occur. From the error growth near the (strange) attractor parameter changes can be selected that are likely to be effective. For this emperical method a good mathematical explanation is still lacking.
Date: 5 Jun 2007
Time: 10:30-12:30
Room: M279
Speakers:
- Karel in't Hout, Universiteit Antwerpen, ADI schemes for convection-diffusion equations modelling option prices
Contemporary option pricing models are frequently formulated as initial-boundary value problems for convection-diffusion equations, constituting extensions of the famous Black-Scholes partial differential equation (PDE). These convection-diffusion equations often possess spatial dimensions that are greater than one and closed-form analytic formulas for their exact solutions are usually not at hand.
This talk deals with numerical methods for solving multi-dimensional PDEs arising in finance. For the numerical solution we consider the well-known method-of-lines approach, whereby the PDE is first discretized in the spatial variables, yielding a large system of ordinary differential equations (ODEs), which is subsequently solved by a numerical time-discretization method. In general, the obtained systems of ODEs are very large and stiff and standard time-discretization methods are not effective. Accordingly, tailored numerical time-stepping methods are required. In the past decades operator splitting schemes of the Alternating Direction Implicit (ADI) type have proven to be a successful tool for efficiently dealing with many of such systems. However, PDEs modelling option prices often contain mixed-derivative terms, stemming from correlations between the driving Brownian motions, and ADI schemes were not originally developed to deal with such terms.
In this talk we shall consider the popular Heston stochastic volatility model, which is a time-dependent two-dimensional convection-diffusion equation containing a mixed derivative term. After discussing its semi-discretization by finite differences, we show how three known ADI schemes can be adapted to the numerical solution of the obtained ODE systems. We next discuss several recent theoretical results on the stability of these schemes. Finally we present numerical experiments, revealing their convergence behaviour and actual performance. - Alfons Hoekstra, UvA, Complex Automata as a paradigm for modeling and Simulation of multi-scale complex systems.
We introduce Complex Automata, a generic methodology to model multi-scale complex systems. A Complex Automaton is a scalable hierarchical aggregation of Cellular Automata and agent-based models, each modeling components of the Complex System. The components represent a sub-system operating on its typical spatial and temporal scales. The concept of a scale map is introduced to identify components and to define appropriate couplings. Five classes of scale separation are identified, each potentially giving rise to a specific multi-scale modeling paradigm. A number of canonical examples are briefly discussed. Finally a challenging case study from biomedicine, dealing with coronary vascular disease will be introduced and first results in defining a Complex Automaton for this case will discussed.
Extra seminar
Date: 7 Jun 2007
Time: 11-12 !
Room: M279
Speaker: Gretar Tryggvason, Worcester Polytechnic Institute, Computational studies of disperse multiphase flows
Date: 26 Jun 2007
Time: 10:30-12:30
Room: M279
Speakers:
- Menno Genseberger, Delft Hydraulics, Parallel Performance of two different applications of a Domain Decomposition technique to the Jacobi-Davidson method
The Jacobi-Davidson method is an iterative method suitable for computing solutions of large eigenvalue problems. Most computational work of Jacobi-Davidson is due to a so-called correction equation at the intermediate level. In previous research a strategy for the computation of (approximate) solutions of the correction equation was proposed. The strategy is based on a domain decomposition technique in order to reduce wall clock time and local memory requirements.
This talk discusses the aspect that the original strategy can be improved by taking into account the relation of the intermediate level with the top level of the Jacobi-Davidson method. This results in a different application of the domain decomposition technique to the Jacobi-Davidson method. Although the two approaches look similar, there are subtle differences in implementation and the consequences in terms of computational time for large scale eigenvalue problems are nontrivial. Therefore, the parallel performance of the two approaches has been investigated with scaling experiments. - Paulien van Slingerland, Delft Hydraulics / TU Delft An accurate and robust finite volume method for the advection diffusion equation.
Delft3D-WAQ, a program that has been developed by WL | Delft Hydraulics, simulates water quality by computing a finite volume approximation of the advection diffusion reaction equation. Roughly speaking, there are two types of numerical schemes in Delft3D-WAQ. On the one hand, there are robust implicit first order linear schemes, that are inaccurate due to numerical diffusion. On the other hand, there are accurate explicit higher order FCT (Flux Correcting Transport) schemes, that are not robust due to a restriction on the time step. We have investigated if a combination of the two types yields a scheme that is both accurate and robust.
Starting point of this research was the first-order upwind theta-scheme. Kuzmin et al. have shown that this scheme is positivity preserving, provided that theta is sufficiently large. The main disadvantage of this scheme is the aforementioned numerical diffusion, which grows with theta. The idea is to make theta space- and time-dependent, and ensure stable, positive and non-oscillatory behavior with a lower bound for the local theta-coefficients, rather than with a low upper bound for the time step. Moreover, the flux corrected transport algorithm is used to improve the accuracy even more. During the presentation the performance of the local theta scheme will be illustrated by means of the Molenkamp test and real-life applications for estuaries near Hong Kong.
Summer 2007
Date: 3 July 2007
Time: 11-12
Room: M279
Speaker:
Edriss Titi, Weizman Institute, Israel and Univ. Calif. Irvine, Global Regularity for Three-dimensional Navier-Stokes Equations and Other Relevant Geophysical Models
The basic problem faced in geophysical fluid dynamics is that a mathematical description based only on fundamental physical principles, the so-called the ``Primitive Equations'', is often prohibitively expensive computationally, and hard to study analytically. In this talk I will survey the main obstacles in proving the global regularity for the three-dimensional Navier--Stokes equations and their geophysical counterparts. Even though the Primitive Equations look as if they are more difficult to study analytically than the three-dimensional Navier--Stokes equations I will show in this talk that they have a unique global (in time) regular solution for all initial data.
This is a joint work with Chongshen Cao.
Date: 10 July 2007
Time: 11-12
Room: M279
Speaker:
Martin Krupa, Univ. Twente and New Mexiko State Univ., Dynamics near a folded-node singularity
A folded node is characterized by the presence of oscillatory dynamics and multiple canard solutions. The so-called primary canards (the weak canard and the strong canard) play an important role in organizing the dynamics. The weak canard is the center of the oscillations and the strong canard separates purely spiking solutions from solutions which make small oscillations before they spike. Secondary canards separate solutions with different rotational properties. In this talk the overall picture of the dynamics, based partly on rigorous results and partly on conjectures, will be presented.
Date: 21 August 2007
Time: 10.30-12.30
Room: M279
Speakers:
- Tasso Kaper, Boston University, USA, Traveling waves in reaction-diffusion equations with cut-offs
- Martin Krupa, Univ. Twente and New Mexiko State Univ., Folded saddle-node type II
Folded singularities occur in sow fast systems in association with the loss of normal hyperbolicity of a slow manifold. Typical folded singularities are folded node, folded saddle and folded focus. A point of transition between folded saddle and folded node is a folded saddle node. Folded saddle node is connected to the onset of small amplitude oscillations in the Hodgkin Huxley equation and other well known models. An integral part of the description of a folded saddle node II is slow passage through a Hopf bifurcation. In this talk we focus on the introduction to folded saddle node II and the analysis of the slow passage.
Fall 2007
Date: 11 September 2007
Time: 10.30-12.30
Room: M280
Speakers:
- Jens Rademacher, CWI MAS, Computing essential and absolute spectra using continuation
A continuation approach to the computation of essential and absolute spectra of differential operators on the real line is presented. The advantage of this approach, compared with direct eigenvalue computations for the discretized operator, are the efficient and accurate computation of selected parts of the spectrum (typically those near the imaginary axis) and the option to compute nonlinear travelling waves and selected eigenvalues or other stability indicators simultaneously in order to locate accurately the onset to instability. We present example computations for the linearization in steady states and wave trains of various dissipative pdes.
- Jan Verwer, CWI MAS, On the numerical integration of Maxwell's equations
The lecture is based on current research with Mike Botchev, University of Twente, directed at numerically solving Maxwell equations which contain a conduction term for the electric field. Especially the derivation of efficient methods with temporal order beyond the standard two has our interest. In this respect, a conduction term, which introduces damping in the system, leads to interesting questions akin to those for higher order IMEX (IMplicit EXplicit) methods. The lecture will start with an overview of a general semi-discrete system covering most common spatial discretizations. Then we will rehearse existing second-order methods based on a combination of the explicit leapfrog rule for the wave terms and the implicit trapezoidal rule for the conduction term. In the third part we will address the question how to efficiently raise the temporal order of these leapfrog-trapezoidal methods, while maintaining their ease of use and simplicity. The lecture will close with comments on a numerically related damped wave equation system, viz., the coupled sound and heat flow problem.
Date: 2 October 2007
Time: 10.30-12.30
Room: M279
Speakers:
- Michael Herrmann, Humboldt University Berlin, Two-scale reduction for Hamiltonian structures
Considering a microscopic Hamiltonian system (PDE or ODE) it is a challenging problem to derive macroscopic evolution equations that govern the effective dynamics on large spatial and temporal scales. A natural and non-trivial question in this context concerns the behavior of the underlying Hamiltonian structure. In this talk I present a general framework for Hamiltonian two-scale reduction that relies on suitable chosen non-canonic Hamiltonian structures, and allows for moving frames and/or oscillatory micro-structures. To illustrate this method I consider simple chain models (FPU and Klein-Gordon) and derive the effective Hamiltonian structures for various macroscopic limits including the nonlinear wave equation, the KdV equation, and the nonlinear Schroedinger equation.
- Svetlana Dubinkina, CWI MAS1, Statistical mechanics of Arakawas discretizations
The results of statistical analysis of simulation data obtained from long time integrations of geophysical fluid models greatly depend on the conservation properties of the numerical discretization chosen. This is illustrated for quasi-geostrophic flow with topographic forcing, for which a well established statistical mechanics exists. Statistical mechanical theories are constructed for the discrete dynamical systems arising from three discretizations due to Arakawa (1966) which conserve energy, enstrophy or both. Numerical experiments with conservative and projected time integrators show that the statistical theories accurately explain the differences observed in statistics derived from the discretizations.
Date: 18 October 2007 (Thursday!)
Time: 11.00-12.00
Room: M279
Speaker:
- Witold Rudnicki, Interdisciplinary Centre for Mathematical and Computational Modelling, Warsaw University, Poland Modeling phase transitions in cocoa butter
Cocoa butter is a main ingredient of chocolate, responsible for its thermal properties. It is a complex mixture of several tri-glycerides, as well as trace quantities of other lipids. It exhibits polymorphic behaviour with six distinct crystalline phases. Processes that contribute to formation of the related spatial structure are highly non-linear and exhibit multi-scale nature. Multi-scale modelling approach to phase transitions in cocoa butter will be exposed. Three classes of processes: microscopic nucleation, mesoscopic crystal growth/melting and macroscopic heat transfer, are described with three separate models, which can be hierarchically combined into single multi-scale model. In particular the connection between nucleation phase and crystal growth will be explored.
Date: 30 October 2007
Time: 10.30-12.30
Room: M279
Speakers:
- Jeroen Hazewinkel , CWI MAS1 and NIOZ, Observations on the wave number spectrum and evolution of an internal wave attractor in a two-dimensional domain
- Alfonso Caiazzo , UvA, Asymptotic Analysis of lattice Boltzmann Method
Date: 8 November 2007 (Thursday!)
Time: 14.00-16.00 !!
Room: M279
Speakers:
- Peter Forsyth, Waterloo, Canada (guest of Kees), A Numerical Scheme for the Impulse Control Formulation for Pricing Variable Annuities with a Guaranteed Minimum Withdrawal Benefit (GMWB)
There is a growing trend away from Defined Benefit pension plans to Defined Contribution (DC) plans. DC plans shift the risk to the pension plan holder. Since retirees are living longer, it is conventional wisdom that retirement funds should be at least partially invested in risky assets. A Guaranteed Minimum Withdrawal Benefit (GMWB) contract shields retirees from poor market performance in the early years of retirement.
In this talk, we outline an impulse stochastic control formulation for pricing variable annuities with a GMWB benefit assuming the policyholder is allowed to withdraw funds continuously. We develop a single numerical scheme for solving the Hamilton-Jacobi-Bellman (HJB) variational inequality corresponding to the impulse control problem, and for pricing realistic discrete withdrawal contracts. It can be shown that this scheme converges to the viscosity solution of the continuous withdrawal problem, provided a strong comparison result holds.
Numerical experiments are conducted, which show a region where the optimal control appears to be non-unique. It also seems that insurance companies are undercharging for this benefit. Typical fees charged will not cover the cost of hedging.
This is joint work with Zhuliang Chen. - Jan van Schuppen, CWI MAS2, Control of piecewise-affine hybrid systems
Date: 20 November 2007
Time: 10.30-12.30
Room: M279
Speakers:
- Ute Ebert, CWI, MAS3, The multiscale nature of streamers
In this talk I will review the multiscale and multidisciplinary problems of streamer discharges. Particular emphasis is on recent experimental results in Eindhoven (Ph.D. theses Briels, Winands etc.) and on moving boundary approximations (work with Brau, Luque, Meulenbroek, Schaefer, Tanveer, Derks).
- Martin van der Schans, Universiteit Leiden, Stability of blow-up solutions of the Ginzburg-Landau equation
Date: 4 December 2007
Time: 10.30-12.30
Room: M280
Speakers:
- Bob Rink, Vrije Universiteit Amsterdam, Branching patterns of resonant wave trains in a Hamiltonian lattice
Wave trains in a Hamiltonian lattice are found by solving an advance-delay equation on a loop space. This equation inherits the Hamiltonian structure, reversibility and symmetries of the equations of motion of the lattice. In this talk I will use these geometric properties to describe the branching pattern of resonant wave trains in the Fermi-Pasta-Ulam lattice. Using invariant theory, we find that the nonlinearity of the lattice selects families of resonant wave trains by imposing a phase condition.
- M.N. Spijker, Universiteit Leiden, Monotonicity in the numerical solution of initial value problems
This talk is about numerical methods for solving (large) systems of ordinary differential equations, which arise e.g. when partial differential equations are solved via semi-discretization.
First, a brief introduction is given to monotonicity properties of such methods.
Next, a new theorem is presented which yields the optimal stepsize condition guaranteeing monotonicity. The theorem is applied to answer some natural open questions.
Date: 11 December 2007
Time: 10.30-11.30
Room: M279
Speaker: Alexandre Goldsztejn, l'Universite de Nantes, A new containment method for rigorous shadowing
A reliable simulation usually refers to a simulation that presents a small global error, that is to a simulation which remains close to the exact trajectory it simulates. This study of reliability is called forward error analysis. However, this kind of analysis is useless when one studies chaotic systems, because such systems will present exponential growth global (forward) errors no matter how small is the local error. In this context, where the forward error analysis does not provide any interesting information, the backward error analysis may allow extracting information from simulations that diverge exponentially.
The backward error analysis consists of finding a modified problem for which the simulation is a good approximation of the exact solution. Among other backward error analysis techniques, shadowing allows modifying the problem by changing its initial condition. Therefore, the question asked by shadowing error analysis is "Given a dynamical system, an initial condition and a simulation of this system (simulation which certainly diverges exponentially), can we find a different initial condition for which our simulation is accurate?"
This talk will introduce the shadowing backward analysis. We will present our new algorithm for the rigorous proof of the existence of a shadow. Because the backward error analysis relates the simulation to the exact solution of a different problem, its use is not as easy as the use of forward error analysis. One potential application of shadowing is to provide a rigorous proof of the presence of chaos in a system. Some promising experimentations will be presented on the H?on and Gingerbread-man strange attractors.
Date: 20 December 2007 (Thursday!)
Time: 11.30-12.30 (second slot!)
Room: M279
Speaker: Martin Berzins, Center for the Simulation of Accidental Fires and Explosions CSAFE, School of Computing and Scientific Computing and Imaging Institute University of Utah,
Multiscale Parallel Adaptive Engineering Simulations of Fires and Explosions
The multidisciplinary C-SAFE project at Utah has been concerned with developing algorithms and software to model a wide variety of challenging physical problems related to fluid structure interaction. Some of these problems arise from the transport of hazardous materials. For example, in 2005, a truck carrying 36,000 pounds of high explosives on U.S. Route 6 in Spanish Fork Canyon, Utah, rolled over, caught fire, and within three minutes, detonated in a devastating explosion. The detonation produced a crater approximately 70 feet across by 30 feet deep, and hot metal shards from the trailer set fire to the surrounding hillsides up to a quarter mile away.
Simulations, such as those undertaken by the multidisciplinary C-SAFE team, play an important role in prevention of such accidents and involve the use of multiscale multi-physics models and innovative computational techniques on large-scale parallel computers. An over view of the key physical insights used to reduce complexity and computational techniques will be given as well as results on a number of challenging physical problems. An analysis of the particle method used will be provided in outline. A key feature of such simulations is the need to vary the grid resolution to capture the different space and time scales in the simulation. The parallel implementation of such algorithms will be shown. The results obtained are counter-intuitive and challenging with regard to the transportation of hazardous materials.
Date: 22 January 2008
Time: 10.30-12.30
Room: M279
Speakers:
- Willem Hundsdorfer, CWI MAS3, IMEX Methods for Stiff Hyperbolic Relaxation Systems
For solving hyperbolic systems with stiff sources or relaxation terms, time stepping methods should combine favourable monotonicity properties (for shocks and steep solution gradients) with good stability properties for stiff terms. This can be achieved with implicit-explicit (IMEX) multistep methods. We will discuss the construction of suitable methods, based on explicit methods with favourable monotonicity and boundedness properties (such as the TVD and TVB properties) for hyperbolic equations. Comparisons will be made with several implicit-explicit Runge-Kutta methods. The material for this talk is based on joint research with Steve Ruuth (SFU, Canada).
- Maksat Ashyraliyev, CWI MAS3, On parameter estimation and determinability
Mathematical modelling of real-life processes often requires the estimation of unknown parameters. Once the parameters are found by means of optimization, it is important to asses the quality of the parameter estimates. In this talk I will describe how the quality of these estimates can be analyzed. This methodology is applied for the large-scale biological problem.
Date: 12 February 2008
Time: 10.30-12.30
Room: M279
Speakers:
- Joost Batenburg, Univ. Antwerpen, Tomography at all scales
Transmission tomography is a powerful technique for noninvasive imaging of physical objects. It can be applied in scenarios where projection images of the object can be recorded (e.g., X-ray photos) from several angles. A reconstruction algorithm combines the information from these projection images into a three-dimensional image of the scanned object. The most common practical example of tomography can be found in the medical CT-scanner, which consists of an assembly of one or more X-ray sources and one or more cameras that rotate around the patient to acquire a series of projection images. The resulting three-dimensional reconstructions of a patient's body can be highly accurate. Less known is the fact that tomography has many important applications outside the field of medical imaging as well. In fact, tomography can be used, and is being used, at all imaginable scales. It reaches from the reconstruction of individual atom positions in nanocrystals at sub-?gstrom resolution, to the determination of galaxy locations in astronomy. The entire spectrum of scales between these two extremes is covered fairly well by a range of other applications. Mathematically speaking, the tomographic reconstruction problem is an inverse problem, involving a rather huge system of linear equations (both the number of unknowns and the number of equations may well exceed 10^9). In this talk various problems will be discussed that one encounters in setting up these equations (i.e., the modeling step) and subsequently solving them. A range of algorithms can be used, depending on whether or not the system is underdetermined and the amount of prior knowledge available on the solution. Particular attention will be given to discrete tomography, which deals with highly underdetermined reconstruction problems, under the assumption that the scanned object consists of only a few different materials.
- Frank Bruggeman, CWI, Regulatory networks in living cells
Cellular behavior derives from the functioning of networks of interacting biomolecules. The understanding of those networks using experiment and theory is the aim of systems biology. In this presentation I will illustrate a number of modeling and theoretical approaches currently being applied in systems biology.
Date: 26 February 2008
Time: 10.30-12.30
Room: M279
Speakers:
- Jennifer K. Ryan, TU Delft, Local Smoothness Increasing Accuracy-Conserving Post-Processing for discontinuous Galerkin methods
In this presentation an overview of aspects of post-processing for discontinuous Galerkin (DG) methods will be given. Specifically, we will examine extensions to non-uniform meshes and one-sided post-processing. This discussion will be presented through the application to filtering for streamline visualization. Improving the accuracy in the solution and its' derivatives is important for many scientific applications in such areas as fluid mechanics and chemistry. The specific technique that we will examine was shown to improve the order of accuracy from k+1 of the DG approximation to 2k+1 for the post-processed solution over a uniform mesh where k is the highest degree polynomial used in the approximation. We will explore one-sided post-processing as well as two techniques for extending the applications to smoothly varying and non-uniform mesh structures. Lastly, we will discuss using this technique for one-dimensional filtering of multi-dimensional data to aid in calculation of streamlines.
- Boris Levant, Weizman Institute, CANCELLED
Date: 27 March 2008 (moved from March 11, NOTE DAY CHANGED, WAS 26th!)
Time: 11.30-12.30
Room: M279
Speaker: Oliver Buhler, Courant Institute, NYU, Internal waves in the deep ocean: focusing, saturation, and mixing
Date: 8 April 2008
Time: 10.30-12.30
Room: M280
Speaker:
- Bert Peletier, Univ. Leiden, Dynamical Systems in Pharmaceutical Science
In recent years, mathematical modelling in Pharmacokinetics and Pharmacodynamics (PK/PD) has become increasingly important. In this lecture we review a few classical and more recent models designed to capture critical features of data sets obtained from {\em in vivo} experiments. Thus, we consider a classical family of turnover models, a recent model for Selective Serotonin Reuptake Inhibitors (SSRI's) and a recent model designed to capture the characteristic properties of the circadian rhythm exhibited by data sets of blood pressure and heart rate.
- Henk Broer , Univ. Groningen, On parametrized KAM Theory
Kolmogorov-Arnold-Moser Theory (or KAM-Theory) deals with persistent occurrence of multi- (mostly quasi-) periodic dynamics. Classically kam Theory was committed mainly in Hamiltonian systems and linked to questions like the stability of the Solar system or of plasma dynamics inside Tokamaks. It was already known that the theory extends to other classes of dynamical systems, for example leading to the persistent occurrence of quasi-periodic attractors that generically occur in families. These families are smoothly parametrized over a Cantor set of positive measure, in the sense of Whitney. Such quasi-periodic attractors are of interest in the Ruelle-Takens scenario regarding the onset of turbulence, where they serve as an intermediate state in the transition to chaos. In the talk I will sketch a systematic approach to parametrized kam Theory, based on the notion of transversality. One application of this is the quasi-periodic Hopf bifurcation both in the Hamiltonian and in the reversible setting. Here the dynamical models can have a quite high dimensional phase space, where resonances may obscure the scenery. The theory leads to a marriage between KAM- and Singularity Theory, yielding a Cantorisation of the semi-algebraic, stratified sets like Folds, Cusps, etc., so well-known from classical Bifurcation Theory.
Date: 17 April 2008 (Thursday CANCELLED!! due to illness)
Time: 11.30-12.30
Room: M280
Speaker: Jacques Vanneste, University of Edinburgh, Passive-scalar decay in smooth random flows
Date: 22 April 2008 (newly added)
Time: 10.30-11.30
Room: M280
Speaker: Orencio Duran, Univ. Twente, A continuous model for Aeolian sand dunes and its application to barchan dune fields and vegetated "parabolic" dunes
The existence of a minimal size for Aeolian dunes of about 10m long, and thus, the impossibility of generate them in wind tunnel experiments, has led to an enormous emphasis in numerical simulations as the simplest, and sometimes the only, tool to get insight into dune emergence and evolution under controlled conditions. In this talk, I'm going to present a continuous sand transport model developed in successive contributions by the H.J. Herrmann's group, and I'll focus into two main applications: first, the emergence of barchan dune fields from a "beach" as a result of the coupling of a longitudinal and transversal instability. Second, by including the vegetation dynamics into the model, we were able to study the emergence of inactive parabolic dunes from active barchan ones, and hence, to uncover the mechanisms underlying the stabilization of dunes induced by the vegetation growth.
Date: 28 April 2008 (Monday! Newly added)
Time: 10.30-11.30
Room: M279
Speaker: Thorsten Riess, TU Illmenau, Finding and following connecting orbits between equilibria and periodic orbits.
We introduce a numerical adaption of Lin's method to find and continue (in parameter space) connecting orbits between hyperbolic equilibria and hyperbolic periodic orbits. We demonstrate our method with an ODE in R^3 with a heteroclinic cycle that consists of a codimension-zero connection from an equilibrium to a periodic orbit and a codimension-one connection from the periodic orbit back to the equilibrium.
Date: 13 May 2008
Time: 10.30-12.30
Room: M280
Speakers:
- Kees Vuik, DIAM Delft, Spectral analysis of complex shifted-Laplace preconditioners for the Helmholtz equation
Abstract (pdf)
- Wim Vanroose, University of Antwerpen, An application of the Helmholtz-equation: ionization and breakup of molecules
We give an introduction to the numerical methods that solve ionization and breakup problems in molecules. These processes are described by the time-independent Schrodinger equation which is a Helmholtz equation with a space dependent wavenumber. The solutions are similar to acoustic problems and exhibit amongst other evanescent waves. We discuss a six dimensional breakup problem known as the double ionization problem. It is solved with absorbing boundary conditions and preconditioned iterative methods. These calculations explain for the first time experimental observations in physics. We discuss the computational challenges that need to be solved before more complex systems treated.
Reference: Vanroose, Martin, Rescigno and McCurdy, Science, 310 p 1787-1789 (2005)
Date: 15 May 2008 (Thursday! Newly added)
Time: 11.30-12.30
Room: M279
Speaker: Marcel Oliver, Jacobs University, Bremen, Hamiltonian particle methods for barotropic flow
We present recent results on the convergence of the Hamiltonian Particle-Mesh (HPM) method of Frank, Gottwald, and Reich. In particular, we show that the method can be interpreted as a "fast local summation" approach to traditional smoothed particle hydrodynamics (SPH).
In the second part of the talk, we give an outlook on potential new higher order particle methods for rotating barotropic flow which still preserve the Hamiltonian structure.
Date: 20 May 2008 (newly added)
Time: 11.30-12.30
Room: M280
Speaker: Boris Levant, Weizman Institute, Shell models as phenomenological models of turbulence
Date: 27 May 2008 (newly added)
Time: 10.30-12.30
Room: M280
Speakers:
- Ivan Zapreev, CWI MAS 2, Model Checking Markov Chains: Techniques and Tools.
In this talk I will discuss the results obtained during my PhD study at the University of Twente. More specifically I will talk about four important aspects of model checking Markov chains: the development of efficient model-checking tools, the improvement of model-checking algorithms, the efficiency of the state-space reduction techniques, and the development of simulation-based model-checking procedures. After providing background information I will introduce MRMC, a model checker for DMRMs and CMRMs, that supports reward extensions of PCTL and CSL. Then we will study the efficiency of this tool in comparison with probabilistic model checkers such as ETMCC, PRISM, YMER and VESTA, focusing on fully probabilistic systems. Further, we discuss a precise procedure of steady-state detection for time-bounded reachability on CTMCs. Next, we concentrate on studying the effect of bisimulation minimization in model checking of monolithic DTMCs, CTMCs and the variants thereof with rewards. In conclusion we will talk about new discrete-event simulation and sequential confidence-intervals based techniques for model checking CSL properties on CTMCs.
- Greg Pavliotis Imperial College, London, Amplitude equations for stochastic PDEs
In this talk we will present some results on the rigorous derivation of amplitude equations for stochastic PDEs. In the first part we will discuss about amplitude equations for stochastic PDEs with quadratic nonlinearities, under the assumption that the noise acts only on the stable modes and for an appropriate scaling between the distance from bifurcation and the strength of the noise. In the second part of the talk we will show that the amplitude equation for the stochastic Swift-Hohenberg equation in a large domain is the stochastic Ginzburg-Landau equation.
Date: 3 June 2008 (newly added)
Time: 10.30-12.30
Room: M280
Speakers:
- Heiko Berninger, Free University Berlin, Nonlinear domain decomposition for saturated-unsaturated flow through heterogeneous porous media
We present a numerical solution technique for the Richards equation in heterogeneous soil without linearizing the problem. Our approach is based on Kirchhoff transformation which can be carried out in case of a homogeneous porous medium. As a result convex minimization problems are obtained to which monotone multigrid methods can be applied. We assume that different homogeneous soils are located in different subdomains while the coupling condition imposes continuity of the pressure and the water flux across the interfaces between the subdomains. This heterogeneity is addressed via nonlinear nonoverlapping domain decomposition. More concretely, a Dirichlet-Neumann or, alternatively, a Robin method provides for an iteration of the coupled homogenous problems. Gravity is discretized explicitly in time using an upwind technique given by a viscosity term within our finite element discretization. Our solver determines both the free boundary separating the saturated from the unsaturated regime and the free boundary of the seepage face around surface water coupled with the Richards equation.
In the talk we give a presentation of our solution method and mention some analytical results in 1D. Furthermore, we present various numerical results in 2D which show the concrete behaviour of the domain decomposition methods in different situations and demonstrate the applicability of our technique for usual soil parameters. Joint work with: M. Discacciati (EPFL Lausanne), R. Kornhuber and O. Sander (FU Berlin) - Scott MacLachlan, Tufts University, USA, A comparison of two-level preconditioning strategies
In recent years, significant effort has been put into the design of effective and efficient preconditioners for the linear systems that arise from discretizations of PDEs. In many cases, these preconditioners take the form of two-level (or multi-level) preconditioners, where a coarser, auxiliary problem is used to improve the approximation at a given fine scale. In this talk, I will discuss the motivation for these methods, as well as theoretical results comparing the performance of deflation, balancing, and multigrid preconditioners. A numerical comparison of deflation and multigrid algorithms for problems arising from two-phase, bubbly, flows will also be presented. This project is joint work with Jok Tang and Kees Vuik from TU-Delft and Reinhard Nabben from TU-Berlin.'
Date: 10 June 2008
Time: 10.30-12.30
Room: M280
Speakers:
- Fred Vermolen, DIAM TU Delft, A Mathematical model for wound closure, (invited by Kees)
Abstract [pdf]
- Jacques Huyghe, TU/E, Cellular and tissue mechanics: ionisation, multiphysics and localisation (invited by Kees)
Considerable experimental evidence exists that living cells sense tissue stress as a full 3D tensor. The nature of living cells and of many tissues is one of an ionised 3D skeleton saturated with a fluid with opposite charge, resulting in a genuinely multiphysics, multicomponent environment. The mathematical chalenges associated with the description of intricate electro-chemo-mechanical behaviour of this highly deformable medium will be discussed.
Date: 17 June 2008 (newly added)
Time: 10.30-12.30
Room: M280
Speakers:
- Jan ten Thije Boonkkamp, TU/E, A flamelet model for premixed stretched flames, (invited by Jens)
A premixed flame can be considered as a thin region, where all chemical reactions and heat production take place, separating the burned and unburned gas mixtures. Variations of most variables (velocity, temperature, species mass fractions, etc.) across the flame are typically much larger than variations in the directions aligned with the flame. This feature allows us to reformulate the conservation laws of premixed flames as a quasi-one- dimensional system of differential equations, describing the internal structure of the flame and the propagation velocity normal to itself. This one-dimensional system is based on a curvilinear, moving coordinate system attached to the flame. More precisely, coordinate surfaces coincide with flame surfaces for some suitable progress variable (e.g. the temperature or fuel mass fraction). Parameters in the equations are the area element and the stretch rate K, which describes strain and curvature of flame surfaces. These equations are referred to as the strongly stretched flamelet equations (SSFE). The SSFE can be used as a model for numerical simulations as well as to analyse the impact of stretch on the propagation speed of flames. In particular, integrating the SSFE across the flame we can derive several models for the laminar burning speed. The SSFE has proven to be succesful in many studies to analyse flame behaviour, however, a rigorous analysis is still lacking. (pdf of abstract.)
- Saleh Tanveer, Ohio State University, USA, Divergent series, Borel Summation and 3-D Navier-Stokes Problem, (invited by Ute)
Divergent series occur naturally in asymptotic expansions of solutions to differential systems and can typically be calculated through an algorithmic process to any order desired. Borel summation provides a one-one correspondence between such divergent series expansion and actual functions they represent such that this correspondence is maintained under a whole range of algebraic operations, including addition, multiplication, composition, differentiation, etc. This so-called isomorphism is similar to that between convergent series and analytic functions. Borel summability of a formal asymptotic series therefore provides an actual solution to the differential equations that gave rise to the formal expansion.
While the ideas are more generally applicable, we use Borel Transforms and Borel Summability to cast the 3-D Navier-Stokes equation into an integral equation on a half-line for which a unique solution is shown to exist, within a certain class of functions. In this reformulation of Navier-Stokes, the question of global existence can be posed as a question of asymptotics of a known solution. If the solution on the half-line is subexponential at $\infty$, then global existence of classical solution would follow.
The Borel based methods are also constructive and provide precise asymptotics with error-bounds for small time for analytic initial data. Further, there it has consequences in numerical calculations.
Date: 19 June 2008 (Thursday!)
Time: 10.30-11.30
Room: M280
Speaker: Jacques Vanneste, University of Edinburgh, Passive-scalar decay in smooth random flows, (invited by Jason)
Date: 24 June 2008
Time: 10.30-11.30
Room: M280
Speaker: Marielba Rojas, Technical University of Denmark, LSTRS: Matlab software for large-scale trust-region subproblems and regularization, (invited by Kees)
We describe the features of a MATLAB implementation of the method LSTRS from: M. Rojas, S.A. Santos and D.C. Sorensen. A new matrix-free method for the large-scale trust-region subproblem, SIAM J. Optim. 11(3): 611-646, 2000. LSTRS is designed for large quadratic problems with one quadratic constraint. These problems arise in trust-region methods for optimization and in the regularization of discrete forms of ill-posed problems. The method is a limited-memory, iterative procedure that requires the solution of a large eigenvalue problem at each step. In the software, the eigensolver can be chosen from several options, and can also be supplied by the user. The Hessian matrix can be provided explicitly, or as a matrix-vector multiplication routine. Therefore, the software preserves the matrix-free nature of the original algorithm.
We describe the method and the software, and present examples to illustrate the use of the package. We also present comparisons with other state-of-the-art methods for large trust-region subproblems.
Joint work with: Sandra A. Santos and Danny C. Sorensen
Date: 15 July 2008 (Newly added)
Time: 11.30-12.30
Room: M280
Speaker: Jacco Snoijer, Universiteit Twente, Dynamics of liquid film deposition: the Landau-Levich problem, (invited by Jens)
Date: 17 July 2008 (Thursday! Newly added)
Time: 11.30-12.30
Room: M280
Speaker: Jonathan Sherratt, Heriot-Watt University, Edinburgh, UK, Periodic Travelling Waves in Ecology, (invited by Jens)
Many ecological populations undergo large-amplitude multi-year cycles in abundance. A number of recent field studies on such cyclic populations have found that the oscillations are spatially organised into periodic travelling waves (wavetrains). I will discuss the use of mathematical models to understand the mechanisms responsible for this spatial organisation. The periodic wave pattern is selected from a one-parameter family of such waves, and I will discuss established results and some open problems associated with this wave selection mechanism. In some cases the selected wave is actually unstable as a solution of the governing partial differential equations, in which case the long term behaviour is highly disordered spatiotemporal oscillations. I will discuss the use of numerical continuation to determine wave stability, via computation of the essential spectrum. This enables prediction of whether a given set of parameter values result in regular or disordered behaviour in the long term. As a specific case study, I will discuss the example of field voles in Kielder Forest (UK), which is one of the best-studied example of a population exhibiting periodic travelling waves. I will end by discussing the more general ecological implications of the work, and the key challenges for future mathematical research.
Fall 2008
Date: 9 September 2008
Time: 10.30-11.30 , tea starting at 10.00
Room: M279
Speaker: Marco Veneroni, TU/E, Variational methods for pattern formation in diblock copolymers
Abstract [pdf]
Date: 16 September 2008
Time: 10.30-11.30 , tea starting at 10.00
Room: M279
Speaker:
Date: 23 September 2008
Time: 10.30-11.30 , tea starting at 10.00
Room: M279
Speaker: Barry Koren, CWI MAS 2, Immersed-boundary methods
Date: 29 September 2008 (Monday!!)
Time: 10.30-11.30 , tea starting at 10.00
Room: M279
Speaker: Gunnar Klau, CWI, Functional Modules in Protein-Protein Interaction Networks Via Prize-collecting Steiner Trees
An important topic in systems biology is the identification of functional modules in protein-protein interaction networks. These modules might help, for example, to better understand the underlying biological mechanisms of different tumor subtypes. In this talk, I report on results of a cooperation with statisticians and medical researchers from the University of Wuerzburg. In particular, I will present an exact integer linear programming solution for this problem, which is based on its connection to the well-known prize-collecting Steiner tree problem from Operations Research. If the remaining time allows, I will give a brief overview of a couple of life science-related projects I am involved in.
Date: 7 October 2008
Time: 10.30-11.30 , tea starting at 10.00
Room: M279
Speaker: Bob Planque, UvA, Flexible house hunting strategies in social insects
The study of decentralized decision making in social insects and other groups of social animals has revealed a number of prominent mechanisms such as positive feedback, inhibition of behaviours and response thresholds. One of the prime examples in which many of these behaviours are employed to form collective decisions is house hunting by colonies of ants. When their old nest is destroyed, scouts go looking for potential new nests, recruit other ants to these nests through a process called tandem-running, and switch from recruitment to carrying by monitoring if a quorum of ants has been reached inside a new nest. Using these different behaviours allows the ants to efficiently trade speed for accuracy when deciding which nest to emigrate to. One of the behaviours commonly observed during colony emigrations has sparked much speculation, and does not fit the above emigration paradigm: reverse tandem running from the new to the old nest.
Although ants are usually regarded as simple automatons obeying innate rules, close scrutiny reveals that they are capable of rich individual behaviour, including learning and even teaching others. In this talk I will highlight the challenges to model such behaviour in order to understand collective decision making in these ants. Then, using a number of models, we will explore different hypotheses that might explain the role of reverse tandem running.
Date: 14 October 2008 - two speaker session
Time: 10.30-12.30, tea starting at 10.00
Room: M279
Speakers:
- Illia Horenko, Free University Berlin (guest of Daan), Finite element techniques in computational time series analysis and clustering
In recent years there has been considerable increase of interest in the mathematical modeling and analysis of complex systems that undergo transitions between several phases or regimes. Such systems can be found, e.g., in weather forecast (transitions between weather conditions), climate research (ice and warm ages), computational drug design (conformational transitions) and in econometrics (e.g., transitions between different phases of the market). In all cases, the accumulation of sufficiently detailed time series has led to the formation of huge databases, containing enormous but still undiscovered treasures of information. However, the extraction of essential dynamics and identification of the phases is usually hindered by the multidimensional nature of the signal, i.e., the information is "hidden" in the time series. The standard filtering approaches (like f.~e. wavelets-based spectral methods) have in general unfeasible numerical complexity in high-dimensions, other standard methods (like f.~e. Kalman-filter, MVAR, ARCH/GARCH etc.) impose some strong assumptions about the type of the underlying dynamics.
Approach based on optimization of the specially constructed regularized functional (describing the quality of data description in terms of the certain amount of specified models) will be introduced. Based on this approach, several new adaptive mathematical methods for simultaneous data-based dimension reduction and identification of hidden phases in high-dimensional time series will be presented. The methods exploit the topological structure of the analysed data an do not impose severe assumptions on the underlying dynamics. Special emphasis will be done on the mathematical assumptions and numerical cost of the constructed methods.
The application of the presented methods will be first demonstrated on a toy example and the results will be compared with the ones obtained by standard approaches. The importance of accounting for the mathematical assumptions used in the analysis will be pointed up in this example. Finally, applications to analysis of meteorological and financial data will be presented. - Richard Dwight, DLR and TU Delft, A posteriori estimation of error due to stabilizing dissipation for compressible Navier-Stokes
Date: 21 October 2008 -- two speaker session
Time: 10.30-12.30, tea starting at 10.00
Room: M279
Speakers:
- Svetlana Dubinkina, CWI MAS 1, Statistical mechanics of a Hamiltonian particle-mesh method for incompressible flow over topography
A Hamiltonian particle-mesh method for quasi-geostrophic potential vorticity flow is proposed. The microscopic vorticity field at any time is an area- and energy-conserving rearrangement of the initial field. We construct a statistical mechanics theory to explain the long-time behavior of the numerical solution. The statistical theory correctly predicts the spatial distribution of particles as a function of their point vorticity. A nonlinear relation between the coarse grained mean stream function and mean vorticity fields is predicted, consistent with the preservation of higher moments of potential vorticity reported in [R. V. Abramov, A. J. Majda 2003, PNAS 100 3841--3846].
- James Glazier, University of Indiana Bloomington, Multi-Cell Modeling of Biological Development using the GGH Model and CompuCell3D --TALK HAS BEEN CANCELLED!--
Date: 28 October 2008
Time: 10.30-11.30, tea starting at 10.00
Room: M279
Speaker: Peter Sonneveld, TU Delft, A history of Krylov Product Methods - A case of serendipity,
In about 1976, the author was preparing a renovation of the elementary course on numerical analysis in Delft University. In relation to the problem of solving a single nonlinear equation iteratively, he wondered whether the so-called `secant method' could be generalized to systems of N nonlinear equations with N unknowns.
Before starting to read everything on the subject, the author always tries to think about it unbiased, and so he started (probably) with inventing the wheel again. Would he have seen the book by Ortega and Rheinboldt at that time, CGS, BiCGSTAB and IDR(s) probably wouldn't exist today.
In this presentation a brief reconstruction is given of the strange history of the so-called `Krylov Product Methods'.
Date: 4 November 2008
Time: 10.30-11.30, tea starting at 10.00
Room: M279
Speaker: Onno Bokhove, Universiteit Twente, Dynamics of fluid-filled gelatin cracks,
I will present preliminary laboratory experiments and mathematical modeling results on fluid-rock-tunnel interactions, with the aim to understand key physical processes in geological and industrial applications. A hierarchy of idealized laboratory and numerical experiments will be investigated, using gelatine as proxy for rock and water(/glycerine) as a proxy for magma. The mathematical model consists of a (known) coupled model with linear elasticity equations for the rock and width averaged and simplified Stokesâ€™ equations for the fluid, with fixed, free surface and inflow boundary conditions. Associated advanced two- and three-dimensional finite element methods will be sketched. The laboratory experiments are used to validate the (numerical) models by systematically measuring the dependence on the dike shape (along the major axis and in the vertical) and â€œmagmaâ€ discharge in the steady state situation, as function of hydrostatic head (â€œoverpressureâ€) and fluid (â€œmagmaâ€) viscosity. In addition we have determined the elastic modulus and fracture toughness of the gelatine in compression and pressure tests to fix the parameters in the coupled model.
Date: 11 November 2008 - two speaker session
Time: 10.30-12.30, tea starting at 10.00
Room: M279
Speakers:
- Herbert de Gersem, Katholieke Universiteit Leuven, Electromagnetic Field Simulation of Electrotechnical Models with Symmetries,
The increasing complexity of electrotechnical devices is tackled by modelling techniques with higher flexibility and efficiency. Modern 3D finite-element models account for translationally or cylindrically symmetric parts by dedicated discretization techniques and by that, reduce the model size. For discrete symmetries, generalized fast Fourier algorithms are applied. In the case of a continuous symmetry along which a smooth variation of the field quantities may be expected, an optimal resolution is achieved by orthogonal polynomials. The resulting hybrid system of equations and the use of Lagrange multipliers necessitate the introduction of appropriate iterative solving techniques. Some technically relevant examples from electrical engineering and accelerator technology are used to illustrate the numerical techniques.
- Sergey Pancheshnyi, Toulouse, Filamentary gas discharges: what we expect from numerical simulation,
The results of direct numerical simulation of pulsed atmospheric pressure gas discharges (streamers, sparks, microdischarges) and comparison with experimental measurements are presented. Usually, a simple hydrodynamic model based on balance equation for charged species coupled with Poissonâ€™s equation for electric field determination is sufficient for such kind of simulations. However, some questions cannot be easily analyzed within this approach and a stochastic or hybrid modeling is required.
Date: 18 November 2008
Time: 10.30-11.30, tea starting at 10.00
Room: M279
Speaker: Jan van Dijk, TU/E, Plasma Modelling at Eindhoven University --- The LinSys Framework
With the advent of cheap, yet powerful computers, self-consistent modelling has become a vi- able tool for understanding, designing and improving technological and scientiï¬c plasma sources. Nowadays multi-dimensional models which are capable of simulating time-dependent discharge behaviour are in use at various universities and research institutes. One such computer code is Plasimo, the PLasma SImulation MOdel which is being developed at Eindhoven University of Technology1 . Plasimo provides sub-models for kinetic (Monte Carlo), hybrid, Maxwellian and thermal equilibrium plasma.
In this presentation, we will brieï¬‚y introduce Plasimo, and demonstrate some of its capa- bilities. In the second part, we will take a look under the hood and present Plasimoâ€™s â€˜LinSysâ€™ framework. LinSys provides code for representing such concepts as tensor values, tensor ï¬elds and systems of equations involving such ï¬elds. These ï¬elds can be deï¬ned on distinct, user- deï¬ned domains. LinSys also provides (C++) code that facilitates the task of discretizing sets of (coupled) linearised equations.
In the presentation we will demonstrate LinSys by discussing its application to the discretisa- tion of the equations that govern transport and electromagnetic phenomena in plasma science on ortho-curvilinear meshes. We will critically assess the quality of the generated stencils, discuss the eï¬ƒciency of LinSys and provide ideas for future work.
Date: 25 November 2008
Time: 10.30-11.30, tea starting at 10.00
Room: M279
Speaker: Jeroen Wackers, Ecole Centrale de Nantes, Adaptive grid refinement for ship flow calculation
The computation of the water flow around ships is very challenging. On one side, this is caused by the need to model the water surface and its interaction with the ship hull. Also, the high Reynolds numbers of these flows require fine grids and thus high computational power.
ISIS-CFD, the ship flow code developed at Ecole Centrale de Nantes, has evolved over the years from an academic research code to a mature method that is able to compute realistic flow scenarios for industrial applications. In the first part of my talk, I will present ISIS-CFD and its ability to compute steady wave patterns, unsteady ship-wave interaction, and ship motion.
In the second part, I present my own work: the inclusion of automatic adaptive grid refinement in ISIS-CFD. Necessarily, the method is parallelised and based on unstructured grids. Test cases show its great potential for improving the accuracy of flow calculations.
Date: 2 December 2008
Time: 10.30-11.30, tea starting at 10.00
Room: M279
Speaker: Cars Hommes, Center for nonlinear dynamics in economics and finance at UvA, Complex Evolutionary Systems in Behavioral Finance
Traditional finance is built on the rationality paradigm. In this talk we discuss simple models from an alternative approach in which financial markets are viewed as complex evolutionary systems. Agents are boundedly rational and base their investment decisions upon market forecasting heuristics. Prices and beliefs about future prices co-evolve over time with mutual feedback. Strategy choice is driven by evolutionary selection, so that agents tend to adopt strategies that were successful in the past. Calibration of ``simple complexity models'' with heterogeneous expectations to real financial market data and laboratory experiments with human subjects are also discussed.
Date: 9 December 2008
Time: 10.30-11.30, tea starting at 10.00
Room: M279
Speaker: Peter van Heijster , CWI, Front Interactions by the Renormalization Group Method
During this presentation, I will give an overview of how to analyze the interactions of pulses or fronts for reaction-diffusion equations. The renormalization group method I use is general applicable for slow-fast systems, however, I will apply it to a particular paradigm system. Using this RG method, we derive an ODE system describing the leading order motion of interacting fronts and pulses. After the derivation, I will study the derived ODEs.
Date: 11 December 2008
Time: 10.30-11.30
Room: M376
Speaker: Martin Berzins, University of Utah, Positivity Preservation and Error Estimation for Time Dependent PDEs
The solution of differential equations in which the numerical solution should stay positive is considered for conservation laws. Provably positive high-order space discretisations are described. The application of positivity preservation to variable-step, variable-order time integrations is considered and an algorithm is proposed. Finally, the estimation of global error in the same variable-order, variable-step algorithms is considered and results are shown.
Date: 16 December 2008
Time: 10.30-11.30, tea starting at 10.00
Room: M279
Speaker: David Lentink, Wageningen University, How swifts control their glide performance with morphing wings
Gliding birds continually change the shape and size of their wings, presumably to exploit the profound effect of wing morphology on aerodynamic performance. That birds should adjust wing sweep to suit glide speed has been predicted qualitatively by analytical glide models, which extrapolated the wing's performance envelope from aerodynamic theory. Here, we describe the aerodynamic and structural performance of actual swift wings, as measured in a wind tunnel, and on this basis build a semi-empirical glide model. By measuring inside and outside swifts' behavioural envelope, we show that choosing the most suitable sweep can halve sink speed or triple turning rate. Extended wings are superior for slow glides and turns; swept wings are superior for fast glides and turns. This superiority is due to better aerodynamic performance - with the exception of fast turns. Swept wings are less effective at generating lift while turning at high speeds, but can bear the extreme loads. Finally, our glide model predicts that cost-effective gliding occurs at speeds of 8-10 m/s, whereas agility-related figures of merit peak at 15 to 25 m/s. Swifts in fact roost at 8-10 m/s, thus our model can explain this choice for a resting behaviour. Morphing not only adjusts birds' wing performance to the task at hand, but could also control the flight of future aircraft. To demonstrate this we designed a morphing micro air vehicle inspired by gliding swifts together with a group of students. This micro air vehicle, RoboSwift, with a span of 50cm and a weight of 100 grams, has been flight-tested to show such morphing vehicles are feasible.
Spring 2009
Date: 27 January 2009
Time: 10.30-11.30h, tea starting at 10h
Room: M279
Speaker: Roeland Merks, CWI
Title: Modeling de novo and sprouting blood vessel growth: role of contact-inhibited chemotaxis
Abstract: Blood vessels form either when dispersed endothelial cells (the cells lining the inner walls of fully-formed blood vessels) organize into a vessel network (vasculogenesis), or by sprouting or splitting of existing blood vessels (angiogenesis). Although these mechanisms are closely related biologically, no current model explains both phenomena with a single biophysical mechanism. Most computational models describe sprouting at the level of the blood vessel, ignoring how cell behavior drives branch splitting during sprouting. We present a cell-based simulation based on plausible behaviors of endothelial cells. The endothelial cells secrete a chemoattractant, which attracts other endothelial cells. As in the classic Keller-Segel model, chemotaxis causes cells to aggregate into isolated clusters. However, adding adhesion-driven contact inhibition of chemotaxis causes cells to organize into networks and cell aggregates to sprout, reproducing aspects of both de novo and sprouting blood-vessel growth. We discuss two branching instabilities responsible for our results. Cells at the surface of the cell clusters attempting to migrate to the center of the clusters, produce a buckling-type instability. In a model variant that eliminates the surface normal force, a dissipative mechanism drives sprouting, with the secreted chemical acting both as a chemoattrant and as an inhibitor of pseudopod extension. The branching instabilities responsible for our results, which result from contact inhibition of chemotaxis, are both generic developmental mechanisms and interesting examples of unusual types of patterning instabilities.
Date: 3 February 2009
Time: 10.30-11.30h, tea starting at 10h
Room: M279
Speaker: Li Chao, CWI, MAS
Title: Joining particle and fluid aspects in streamer simulationsAbstract: Streamers are used in industrial applications such as lightning, gas and water purification or combustion control, and they occur in natural processes as well such as lightning or transient luminous events in the upper atmosphere. Both fluid and particle models have been developed for streamer simulations. The particle model is suited to study physical phenomena related to the dynamics of individual electrons, such as the precise electron energy distribution, the generation of run-away electrons, the branching triggered by particle fluctuations, or streamer inception from few electrons. But it demands an enormous computational power and storage to simulate a full long streamer while so-called super-particle methods create numerical artifacts. Fluid models, on the other hand, approximate the electrons and ions as continuous densities. They are computationally efficient in regions with large particle densities like the interior of a streamer finger. To study the physics phenomena related with individual electron dynamics in an evolving streamer, a hybrid model that couples fluid and particle model in suitable regions, has been developed in a systematical way. We present the algorithms and the simulation results of the 3D hybrid model. The 3D hybrid model can simulate long streamers while following the real electron motion at the most active region of the streamer head. We also investigate the generation of run-away electrons and present how keV electrons are produced in a growing streamer.
Date: 17 February 2009
Time: 10.30-12.30h, tea starting at 10h
Room: M279
Speaker: Mart Borsboom , Deltares
Title: The free-surface flow/wave model ComFLOW at Deltares
Speaker: Peter Wellens, Deltares
Title: Development of a Generating-Absorbing Boundary Condition (GABC) for ComFLOW and other wave models
Date: 24 February 2009
Time: 10.30-11.30h, tea starting at 10h
Room: M279
Speaker: n.n., tba
Date: 3 March 2009
Time: 10.30-14.30h, tea starting at 10h
Room: M280
Speakers: Sander vd Pijl (CWI - MAS), Ulrike Laeuferts-Mau (NRG Petten), Lech Grzelak (TU Delft), Bowen Zhang (TU Delft).
An extended MAS colloquium at CWI, with 4 presentations about Investment under Uncertainty.
Date: 10 March 2009
Time: 10.30-11.30h, tea starting at 10h
Room: M280
Speaker: n.n., tba
Date: 17 March 2009
Time: 10.30-11.30h, tea starting at 10h
Room: M279
Speaker: Huib de Swart, IMAU, Utrecht University
Title: Do Wadden Sea basins have multiple morphodynamic equilibria?
Date: 24 March 2009
Time: 10.30-11.30h, tea starting at 10h
Room: M280Speaker: Willem Haverkort, CWI and FOM-Rijnhuizen
Title: Magnetic Drug Targeting: Analytical and Computational Analysis in Simplified and Realistic Arterial Geometries.
Date: 31 March 2009
Time: 10.30-12.30h, tea starting at 10h
Room: M279
Speaker: Jeroen Witteveen, TU Delft
Title: Uncertainty Quantification in Computational Fluid Dynamics and Fluid-Structure InteractionSpeaker: Max Rietkerk, Universiteit Utrecht
Title: Turing patterns in ecology
Date: 6 April 2009
Time: 15.00-16.00h
Room: M279
Speaker: Xavier Vasseur, Cerfacs, Toulouse, France.
Title: A two-grid method used as a preconditioner for the solution of Helmholtz problems
Date: 7 April 2009
Time: 10.30-11.30h, tea starting at 10h
Room: M279
Speaker: Rachel Kuske, University of British Columbia
Title: Transients + instabilities + noise = structure?
Abstract:
Transient or unstable behavior is often ignored in considering long time dynamics in
the deterministic world. However, stochastic effects can change the picture dramatically, so that the transients can dominate the long range behavior.
Coherence resonance is one relatively simple example of this transformation,
and we consider others such as noise-driven synchronization in networks,
recurrence of diseases, and stochastic stabilization in systems with delay.
The challenge is to identify common features in these phenomena, leading to new
approaches for other systems of this type. Some recurring themes include the influence of multiple time scales, cooperation of both discrete and continuous aspects in the dynamics, and the remnants of underlying bifurcation structure visible through the noise.
Date: 14 April 2009
Time: 10.30-11.30h, tea starting at 10h
Room: M279
Speaker: Stephan van Gils
Title: Some aspects of dynamics within the basal ganglia
Abstract: Networks of excitatory and inhibitory neurons are responsible for
the generation of rhythms. An example is the basal ganglia, a group of
nuclei that play a key role in the organization of movement. Under
pathological conditions, for instance a lack of Dopamine, dysfunction of
basal ganglia is associated with movement disorders such as Parkinson's
disease. We consider a computational model for a thalamic relay neuron in
relation to pathological input. The effect of Deep Brain Stimulation is
explained in a reduced model. As a first step toward integration of
measurements into our modeling, we show results of micro recordings in the
subthalamic nucleus in patients undergoing deep brain surgery.
Date: 21 April 2009
Time: 10.30-11.30h, tea starting at 10h
Room: M279
Speaker: Eric de Sturler (Virginia Tech)
Title: Simulating photosynthesis, optimization, evolution, and challenges for
mathematics
Abstract: Photosynthesis is arguably the most important biological process on earth
as the prime provider of energy to all other biological processes. We have
developed an extensive model of (leaf) photosynthesis inside the
chloroplast based on a system of coupled ordinary differential equations.
Simulation of this process can help answer many important biological
questions. We can optimize carbon fixation (more biofuel) or starch
production (more food), and we can analyze questions from evolutionary
biology and the influence of climate change. As the differential equations
describing photosynthesis are highly nonlinear and very stiff, the
analysis and optimization of this dynamical system are mathematically
challenging. Another important topic is to estimate the many parameters
that govern the photosynthesis process, that cannot be measured directly
inside a cell, and that may vary considerably among different plants.
We will describe these challenges, some of our results, and future plans.
This is a collaboration with:
Xinguang Zhu and Danny Tholen (Plant Systems Biology Group, Chinese
Academy of Sciences/Max Planck Society Partner Institute for Computational
Biology, Shanghai), and Stephen Long (Plant Biology and Crop Science, University of Illinois at Urbana-Champaign
Date: 28 April 2009
Time: 10.30-11.30h, tea starting at 10h
Room: M279Speaker:
Lennaert van Veen (Concordia University, Montreal)
Title:
The computation of 2D unstable manifolds of cycles in turbulent shear flow.
Abstract:
Since the publication of a landmark paper by Kawahara and Kida on the relevance of unstable periodic solutions to shear flow in 2001, the cale of dynamical systems-type computations in turbulence research has ncreased spectacularly. Equilibrium and periodic solutions have been computed in great spatial detail for Couette flow, pipe flow and many
other geometries. One of the main goals of these computations is to explain the process of turbulent bursting in shear flows. Often, this transition occurs in the presence of a asymptotically stable laminar low, so ordinary bifurcation scenarios cannot explain them. Instead, he current focus is on so-called "edge states", i.e. saddle-type equilibria or periodic solutions that appear to live on a boundary between turbulent and laminar behaviour in phase space. In principle, we should be able to clarify the bursting process if we know the geometry of the (un)stable manifolds of such states. However, the systematic computation of these manifolds is a hard task. I will present a recently eveloped algorithm for the computation of unstable manifolds and its application to shear flow, both in a toy model and in a full-scale simulation of turbulent Couette flow.
Date: 5 May 2009
Time: 10.30-11.30h, tea starting at 10h
Room: M279
Speaker: n.n., tba
Date: 12 May 2009
Time: 10.30-11.30h, tea starting at 10h
Room: M279
Speaker: n.n., tba
Date: 19 May 2009
Today is the first "Computational Science Seminar" of the CWI, hence no
regular MAS seminar.
Date: 26 May 2009
Time: 10.30-12.30h, tea starting at 10h
Room: M279
Speaker: Marc Gerritsma (TU Delft)
Title: Mimetic Spectral Element MethodsSpeaker: Benjamin Sanderse (CWI)
Title: CFD of wind farms
Read more about this seminar...
Date: 9 June 2009
Time: 10.30-11.30h, tea starting at 10h
Room: M279
Speaker: Ed Komen (NRG)
Title: Computational fluid Dynamics at NRGAbstract: In this presentation, the following three items will be shortly introduced
first: the Nuclear Research and Consultancy Group NRG; NRG's CFD team; Overview of activities within this team. Subsequently, the application of Large Eddy Simulation to the assessment of the following two nuclear reactor safety topics will be explained: thermal fatigue in a reactor cooling system; pressurized thermal shock in a reactor pressure vessel. Finally, the application of CFD to assist the assessment of storage of
nuclear waste will be explained. The three considered examples refer to current projects. The status of these projects will be discussed, but also the open issues that have to be resolved.
Date: 11 June 2009
Time: 10.30-11.30h, tea starting at 10h
Room: M279
Speaker: David Echeverria Ciaurri (Stanford University)
Title: A Robust Scheme for Inversion of Production and Seismic Data in Reservoir Facies Modeling
Date: 16 June 2009
Time: 10.30-11.30h, tea starting at 10h
Room: M279
Speaker: n.n., tba
Date: 23 June 2009
Time: 10.30-11.30h, tea starting at 10h
Room: M279
Speaker: n.n., tba
Date: 30 June 2009
Time: 10.30-11.30h, tea starting at 10h
Room: M279
Speaker: n.n., tba
Date: 7 July 2009
Time: 10.30-11.30h, tea starting at 10h
Room: M279
Speaker: Margaret Insley and Tony Wirjanto (University of Waterloo, Canada)
Title: Contrasting two approaches in real options valuation: contingent claims versus dynamic programminggAbstract: This paper compares two well-known approaches for valuing a risky investment using real options theory: contingent claims (CC) with risk neutral valuation and dynamic programming (DP) using a risk adjusted discount rate. In theory, the correct risk adjusted discount rate will depend on the value and volatility of an investment and hence will not in general be constant. In practice, however, many researchers choose a constant risk adjusted discount rate for simplicity. A proof is presented which shows that, except under certain restrictive assumptions, DP using a constant discount rate and CC will not yield the same solutions for investment value. A few special cases are considered for which CC and DP with a constant discount rate are consistent with each other. An optimal timber harvesting example is presented to illustrate that the values obtained using the two approaches can differ significantly particularly when timber price is assumed to be mean reverting. Further, the implied risk adjusted discount rate calculated from CC is found to vary with the stochastic state variable and stand age. We conclude that for real options problems the CC approach should be used, since use of the correct stochastic discount rate results in unnecessarily complex pricing equations.
Fall 2009
Date: 22 September 2009
Time: 11.30-12.30h !
Room: Nikhef H220
Speaker: Antonios Zagaris, UTwente
Title: Phytoplankton-nutrient dynamics in oligotrophic envirnoments
Date: 13 October 2009
Time: 10.30-11.30h
Room: Nikhef H220
Speaker: Matthias Sommer, FU Berlin (Visiting Jason)
Title: Energy, potential enstrophy and phase space volume conservation properties of the shallow-water equations on a staggered geodesic grid.
Abstract: A spatial semi-discretization scheme for the shallow-water equations on a geodesic grid with C-type staggering obeying conservation laws for total energy, potential enstrophy and mass is presented. The method of construction of this scheme relies on Nambu representation, a generalization of Hamiltonian representation for dynamical systems. The main idea of this method, which can be applied to a wide range of atmospheric dynamical equations, is to discretize the phase space structure of a given partial differential equation rather than the occurring operators. Results of numerical experiments with this scheme are compared to those of a standard implementation emphasizing the role of classical and phase space volume conservation laws. /p
pDate: strong10 November 2009/strongbr Time: strong10.30-11.30h/strongbr Room: strongNikhef H220/strongbrbr Speaker: strongPieter Collins,/strong CWIbr Title: em Computational Analysis of Nonlinear Hybrid Systems/embrbr strongAbstract:/strong In this talk I will give an overview of my work on the tool Ariadne for rigorous computational analysis of nonlinear hybrid systems. Amongst other issues, I will discuss the data structures for system description and storing reachable sets, the main computational sub-problems and the algorithms used for each one, and give a brief history of the development process and the successes and failures along the way./p
pDate: strong17 November 2009/strongbr Time: strong10.30-11.30h/strongbr Room: strongNikhef N328 !/strongbrbr Speaker: strongCarmen Rodrigo, /strong University of Zaragoza, Spain (Visiting Kees)br Title: emDesign of efficient multigrid finite element methods on semi-structured triangular grids/embr brstrongAbstract:/strong We are interested in the design of efficient geometric multigrid methods on hierarchical triangular grids for problems in two dimensions. Assuming that the coarsest grid is rough enough to fit the geometry of the domain, a hierarchy of globally unstructured grids, which is suitable for use with geometric multigrid, is generated. To discretize problems with constants coefficients on this type of meshes, explicit assembly of the global stiffness matrix for the finite element method is not necessary and its implementation can be done by using stencils, being enough four stencils to represent the discrete operator on each coarse triangle, reducing drastically the memory required. On the other hand, local Fourier analysis is a well-known useful tool in multigrid for the prediction of two-grid convergence rates. So, for the efficient design of geometric multigrid algorithms, we will use the local Fourier Analysis on triangular grids, which was recently introduced. /p
pDate: strong24 November 2009/strongbr Time: strong10.30-11.30h/strongbr Room: strongNikhef H220/strongbrbr Speaker: strongJens Rottmann-Matthes, /strong University of Bielefeld (Visiting Jens)br Title: emAsymptotic stability and approximation of traveling waves in hyperbolic-parabolic systems/embrbr strongAbstract:/strong In this talk I will first explain the method of freezing traveling waves for general evolution equations. The method is particularly useful for the simulation of the long time behavior of traveling waves. A convergence result for rather general coupled hyperbolic-parabolic systems will be presented which shows the nonlinear stability under certain spectral assumptions. In the second part I will indicate the main ideas of the proof. Finally we present some numerical results for the FitzHugh-Nagumo system and a one-dimensional version of Barkley's problem. Both systems satisfy the assumptions from the theoretical result and they can be seen as a numerically validation of the theory. /p
pDate: strong1 December 2009/strongbr Time: strong10.30-11.30h/strongbr Room: strongNikhef H220/strongbrbr Speaker: strongAnna Mozartova,/strong CWI MAS3br Title: emMonotonicity and boundedness properties of general linear methods/embrbr strongAbstract:/strong In this work an analysis of monotonicity and boundedness properties is provided for the class of general linear methods which includes Runge-Kutta methods and linear multistep methods. We present a framework for deriving optimal stepsize conditions which guarantee boundedness. General results are presented for linear multistep methods. Several numerical illustrations will be given to verify the theory./p
pDate: strong8 December 2009/strongbr Time: strong10.30-11.30h/strongbr Room: strongNikhef H220/strongbrbr Speaker: strong Asuka Hatano, /strong Tokyo University (visiting Kees)br Title: emHeart Simulator - multiscale and multiphysics simulation/embrbr strongAbstract:/strong The heart is an essential organ for maintaining human life by propelling blood throughout the circulatory system. Although recent studies in cellular and molecular biology have greatly promoted our understanding of the structure and function of the heart at the microscopic level, these approaches have contributed little to the understanding of the integrated function of this organ as a pump. We approach this problem with integration based on computational sciences. To construct a comprehensive model of the heart that can accurately simulate the series of events during cardiac cycle, microscopic as well as macroscopic mechanisms should be taken into consideration (multiscale simulation). Furthermore, description of each event involves the coupling of various disciplines such as electricity, physical chemistry, solid mechanics, and fluid dynamics (multiphysics simulation). In my talk, first I want to show how our heart simulator is modeled and how it is applied to clinical problems. And then move on to my own research scoping more microscopic dynamics inside of the heart cell, to be integrated into the heart simulator through my PhD study. /p
pDate: strong17 December 2009/strongbr Time: strong16.00-17.00h (!)/strongbr Room: strongNikhef H220/strongbr Speaker: strong Martin Berzins/strong, School of Computing and SCI Institute. University of Utah, Salt Lake City (visiting Jan)br Title: emPetascale Computing and Beyond for Simulation Science/em/p
pemnbsp;/emstrongAbstract:/strong Two present trends are the use of ever-larger computers to solve increasingly complex physical problems, often with procedures such as uncertainty quantification, and ever more complex multicore and GPU architectures. The present focus of a number of US research programs is on making use of present and near-future petascale architectures with peak performance of one or more petaflops (10**15 flops). In this talk we will look at such architectures and explain how programs such as the the NSF Petaflops program are exploiting them. One computational approach uses asynchronous task-based parallelism. We will discuss how this is being used in linear algebra as well as in adaptive p.d.e. calculations and show performance results for adaptive algorithms on (hopefully) as many as 100,000 cores. Finally we will consider present discussions led by DARPA on exascale (10**18 flops) computing and explain how todays approaches will have to evolve to address the challenges of such architectures. /p
p
a name=spring2010/a/p
h3Spring 2010/h3
hr
pDate: strong6 January 2010/strongbrTime: strong11.30-12.30h/strongbrRoom: strongZ009 /strongbrbrSpeaker: strongThomas Christen, ABB Corporate Research, Theoretical Physics, Baden, Switzerland (visiting Ute), /strongbrTitle: emEntropy production principles for Electric Arc Modeling/embrbrstrongAbstract:/strong
It is shown how various aspects of electric arc physics in high voltage
gas circuit breakers can be modeled in the framework of entropy
production rate optimization. First, the working principle of a
self-blast circuit breaker is introduced. Secondly, various optimization
principles are critically discussed. Finally, it is shown how arc
radiation and radiation induced material ablation can be described in
the framework of entropy production./p
hr
pDate: strong2 February 2010/strongbrTime: strong10.30-11.30h/strongbrRoom: strongL120/strongbrbrSpeaker: strongBert Kappen, RU Nijmegen/strongbrTitle: emKL control theory and decision making under uncertainty/embrbrstrongAbstract:/strong
KL control theory consists of a class of control problems for which the
control computation can be solved as a graphical model inference
problem. In this talk, we show how to apply this theory in the context
of a delayed choice task and for collaborating agents. We first
introduce the KL control framework. Then we show that in a delayed
reward task when the future is uncertain it is optimal to delay the
timing of your decision. We show preliminary results on human subjects
that confirm this prediction. Subsequently, we discuss two player games,
such as the stag-hunt game, where collaboration can improve or worsten
as a result of recursive reasoning about the opponents actions. The Nash
equilibria appear as local minima of the optimal cost to go, but may
disappear when monetary gain decreases. This behaviour is in agreement
with experimental findings in humans. We subsequently extend the setting
to delayed rewards and show how cooperation develops as a result of
recursive reasoning. Suboptimal cooperation arise as local minima of the
objective function./p
hr
pDate: strong8 February 2010/strongbrTime: strong11.30-12.30h/strongbrRoom: strongL120/strongbrbrSpeaker: strongSasa Dujko, Institute of Physics, University of Belgrade, Serbia/strong (visiting Ute)brTitle: emNon-equilibrium transport of electrons and positrons in neutral gases/embrbrstrongAbstract:/strong
Advancements in modern day technology associated with non-equilibrium
low-temperature magnetized plasma discharges to particle detectors, and
from positron traps to medical diagnostics techniques such as Positron
Emission Tomography demand the most accurate modeling of the underlying
charged particle transport processes involved. In order to meet this
demand, the groups at the James Cook University in Townsville
(Australia) and Institute of Physics in Belgrade (Serbia) have
undertaken a program to understand the kinetic behavior of charged
particle swarms under the combined action of electric and magnetic
fields in neutral gases. The scope of this program has covered a variety
of hydrodynamic and non-hydrodynamic studies of electron and positron
transport processes in varying configurations of electric and magnetic
fields when non-conservative collisions are operative. Two complementary
techniques are developed and employed: a multi-term solution of
Boltzmann’s equation and Monte Carlo simulation technique, both adapted
to consider the time-dependent hydrodynamic and steady state
non-hydrodynamic conditions. New and significant numerical results are
presented to highlight the rich and diverse range of kinetic phenomena
observed in varying configuration of electric and magnetic fields. In
this talk we will discuss the origin and mechanisms for such phenomena,
their sometimes paradoxical manifestations and possible physical
implications which arise from their explicit use in realistic
applications./p
hr
pDate: strong9 February 2010/strongbrTime: strong10.30-11.30h/strongbrRoom: strongL120/strongbrbrSpeaker: strongFrancesco Calogero, University of Rome La Sapienza /strong(visiting Jason)brTitle: emIsochronous dynamical systems, the arrow of time and the definition of deterministic chaos/embrbrstrongAbstract:/strong Please see a href=http://homepages.cwi.nl/%7Erademach/Calogero.pdfhere/a./p
hr
pDate: strong30 March 2010/strongbrTime: strong10.30-11.30h/strongbrRoom: strongL120/strongbrbrSpeaker: strongJoris Bierkens /strong(visiting Barry)brTitle: emLong Term Dynamics of Stochastic (Delay) Equations/embrbrstrongAbstract:/strong
Control systems are often influenced by a delay. For example, you can
think of what happens when you try to have a comfortable shower but
instead end up adjusting the tap without obtaining the desired water
temperature. Apart from delay, noise and uncertainty are often
significant factors in control systems.brIn this talk a general
framework is presented on how to model systems with delay and noise as a
stochastic delay differential equation. It turns out that such
equations may be interpreted as stochastic evolution equations in an
infinite dimensional space.brI will discuss some results on the long
term behaviour of such evolution equations, namely whether there exists a
unique invariant measure, and whether the system is stable.brMy aim is to present some general ideas, rather than specialist results./p
hr
pDate: strong13 April 2010/strongbrTime: strong10.30-11.30h/strongbrRoom: strongL120/strongbrbrSpeaker: strongAli Abbas, University of Metz/strong (visiting Willem)brTitle: emA Fourth Order Hermitian Box Scheme with Fast Solver for the Poisson Problem in Two and Three Dimensions/embrbrstrongAbstract:/strong
A new fourth order box-scheme for the Poisson problem in a square and a
cube grid is introduced. The design is based on a hermitian box
approach, combinining the approximation of the gradient by the fourth
order hermitian derivative , with a conservative discrete formulation on
boxes of length 2h. The goal is twofold. First to show that fourth
order accuracy is achiveable both for the primary unknown and the
gradient. Second, to describe a fast direct algorithm, based on the
capacitance matrix method, using the FFT. Several numerical results are
given assessing the O(N^2 ln(N)) computing complexity in a square and
O(N^3 ln(N)) in a cube./p
hr
pDate: strongCANCELLED! 20 April 2010/strongbrTime: strong10.30-11.30h/strongbrRoom: strongL120/strongbrbrSpeaker: strongGeorge Naidis/strong (visiting Ute)brTitle: emSimulation of streamer dynamics in atmospheric-pressure He-Ar plasma jets/em/p
hr
pDate: strong4 May 2010/strongbrTime: strong10.30-11.30h/strongbrRoom: strongL120/strongbrbrSpeaker: strongJoost Batenburg, newly at CWI!/strongbrTitle: emTomography: state-of-the-art and future challenges/embrbrstrongAbstract:/strong
Tomography is a powerful technique for three-dimensional imaging that
deals with image reconstruction from a series of projection images,
acquired along a range of viewing directions. In recent years,
significant progress has been made in reconstructing images from limited
projection data (i.e., few projections, truncated projections, limited
angular range), by incorporating various forms of prior knowledge. In
this talk I will introduce the basic concepts of tomography and
tomographic reconstruction and present some recent theoretical and
practical results. Subsequently, I will provide an overview of future
research plans on parameter estimation problems for tomography, and the
possibilities for solving them: either by elegant mathematical
manipulation or by large-scale scientific computing, exploiting the
power of modern parallel hardware such as GPUs./p
hr
pDate: strong11 May 2010/strongbrTime: strong10.30-11.30h/strongbrRoom: strongL120/strongbrbrSpeaker: strongRob Stevenson, UvA/strongbrTitle: emAdaptive wavelet methods for solving operator equations: An overview and recent results/embrbrstrongAbstract:/strong
We discuss the state of the art in the field of adaptive wavelet
methods for solving operator equations that were introduced by Cohen,
Dahmen and DeVore in 2000 and 2002. With an operator equation, we mean
an equation of the form $Bu=f$, where $B$ is a (linear) boundedly
invertible mapping between ${\mathcal X}$ and ${\mathcal Y}'$ with
${\mathcal X}$ and ${\mathcal Y}$ being some Hilbert spaces. By
equipping ${\mathcal X}$ and ${\mathcal Y}$ with Riesz bases, an
equivalent formulation of the problem is given by a bi- infinite matrix
vector equation ${\bf B}{\bf u}={\bf f}$. Examples include well-posed
boundary value problems, integral equations or parabolic initial
boundary value problems. Constructing these Riesz bases as wavelet
bases, for a large class of problems the matrix $ {\bf B}$ can be well
approximated by sparse matrices. This allowed the design of adaptive
schemes for solving the bi-infinite matrix vector equation that
converge with the best possible rate in linear complexity. In
particular, we will discuss the application of these schemes when
tensor product wavelet bases are applied. In that case, the schemes
have the unique feature that this best possible rate does not
deteriorate as function of the space dimension. One promising
application that we will discuss is that to the simultaneous
space-time variational formulation of parabolic evolution equations,
where, due to the tensor product structure, the additional time
dimension does not increase the order of complexity to solve the
system./p
hr
pDate: strong18 May 2010/strongbrTime: strong10.30-11.30h/strongbrRoom: strongL120/strongbrbrSpeaker: strongGeorge Naidis/strong (visiting Ute)brTitle: emSimulation of streamer dynamics in atmospheric-pressure He-Ar plasma jets/em/p
hr
pDate: strong25 May 2010/strongbrTime: strong10.30-11.30h/strongbrRoom: strongL120/strongbrbrSpeaker: strongBen Leimkuhler, University Edinburgh/strong (visiting Jason)brTitle: emControlling molecular dynamics: gentle stochastic methods and thermostatting efficiency/embrbrstrongAbstract:/strong
Molecular dynamics simulations rely on controls which constrain the
ensemble to reflect environmental factors (e.g. fixed temperature and
pressure conditions). A popular and reliable technique for controlling
temperature is the Langevin dynamics method which replaces an extended
system by a finite one in which stochastic and dissipative perturbations
balance out, elegantly reproducing the conditions of thermodynamic
equilibrium. The use of these perturbations unfortunately precludes the
use of Langevin dynamics for the computation of dynamical properties
(e.g. temporal autocorrelations) which reflect the averaged evolution
under microcanonical (constant energy) flow; such temporal
autocorrelations are at the very heart of many simulation challenges,
e.g. the computation of protein conformational relaxation.brIn order
to overcome this defect of Langevin dynamics, several novel techniques
have recently been proposed [1,2]. These methods purport to exert a
smaller influence on the dynamics, while also providing ergodic sampling
through the use of stochastic terms. Until now the foundation for these
claims has not been available. In this talk I will explain how we have
recently analyzed the convergence to equilibrium for each of these
methods, in particular for the method of [2] by making certain strong
quasi-equilibrium assumptions. We are able to verify these assumptions
for a Lennard-Jonese liquid and we then show good agreement between
averages and relaxation rates computed using an ensemble of molecular
dynamics simulations and the solutions of a simple planar nonlinear
differential equation system. Our observations suggest that the novel
methods [1,2] are more efficient (in a sense to be explained in the
talk) than Langevin dynamics by a factor of order sqrt(n), where n is
the number of degrees of freedom.brbrThis talk describes joint work with Emad Noorizadeh (Edinburgh University) and Oliver Penrose (Heriot Watt University)brbr[1]
G. Busey, D. Donadio, and M. Parinello, Canonical sampling through
velocity rescaling, J. Chem Phys 126, 014101 (2007)
doi:10.1063/1.2408420br[2] B. Leimkuhler, E. Noorizadeh and F. Theil, A
gentle stochastic thermostat for molecular dynamics, J. Stat. Phys.
135, 261-277 (2009) doi: 10.1007/s10955-009-9734-0/p
hr
pDate: strong8 June 2010/strong/p
pTime: strong11.30-12.30h /strong(NB: this is 1 hour later than usual)/p
pRoom: strongL015/strong/p
pSpeaker: strongDomenico Lahaye, TU Delft /strong/p
pTitleem: Two and a Half Years of Computational Electromagnetism in Delft: An Overview/em/p
pstrongAbstract/strong:
How has expertise acquired during four years at the CWI evolved? In
this talk we give an overview of our recent research activities in the
computation of quasi-stationary electromagnetic fields. We will cover
both the aspects of modeling (direct problem) and of optimization
(inverse problem). In engineering practice, the ability to properly
access electromagnetically induced effects due to time-varying sources
is of prime importance. We will give an example of the computation of
induced voltages in protective equipment of modern power grids and of
the computation of induced currents in the next generation wind
turbines. Introducing state-of-the-art modeling tools allowed us to
(apart from making several friends) embark on different projects in
which optimization plays a role. The non-destructive testing of oil
pipelines for corrosion spots serve as an example here. The projects
mentioned are carried outr in close collaboration with the Departement
of Electrical Power Engineering of the TU Delft and with TNO./p
hr
pDate: strong15 June 2010/strong/p
pTime: strong10.30-11.30h/strongbrRoom: strongL120/strongbrbrSpeaker: strongFleur Zeldenrust, UvA/strongbrTitle: emEvery neuron its own code: information transfer in thalamocortical relay cells/embrbrstrongAbstract:/strong
Two points of view play an important role in studying the brain: the
question of how different components influence the electrical behaviour
of brain cells (neurons) and the question of what information they
process. Combining these views results in the question of how the signal
processing properties of a neuron are influenced by the basic
components of the neuron and how it is embedded in a network. This
question will be discussed using the example of thalamocortical relay
neurons (tc relay neurons). The thalamus is a part of the brain that
controls several information flows to and from the cortex. The basal
ganglia provide the thalamus with inhibitory input. The thalamocortical
relay neurons of the thalamus have two response modes: so-called spikes
and bursts. The question what these spikes and bursts code for and how
the basal ganglia can influence this coding still remains open. The
coding of tc relay neurons is assessed both in experiments and in
computational models. We are using reverse correlation techniques
(Spike-Triggered Average (STA) and Spike-Triggered Covariance (STC)) to
investigate the information processing of tc relay neurons and to
compare our models with experiments. We inject a Gaussian noise current
into the tc relay neuron to mimic thalamocortical communication next to a
DC current to put the neuron in different firing regimes (bursting or
spiking). We investigated to what features in the input spikes and
bursts respond in the different regimes. We found that the responses of
these neurons are highly reproducible, which means that they indeed code
for specific features./p
hr
pDate: strong25 June 2010 /strong (NB: this is a Friday)brTime: strong13.30-15.45h/strongbrRoom: strongL120/strongbrbrSpeakers: strongTakanori Hino, National Maritime Research Institute, Tokyo/strong and strongJeroen Wackers, Ecole Centrale de Nantes/strong (both visiting Barry)brbr 13.30-14.30h: strongTakanori Hino/strongbr strongTitle:/strong Development and Applications of Marine CFD at NMRIbr strongAbstract:/strong
NMRI, the National Maritime Research Institute, Japan, is developing
CFD software for marine applications. Its products, which include two
RANS solvers and a grid generator, are widely used in industry.br
After introducing the outline of the CFD software, the numerical
algorithm of a particular RANS solver, which employs an unstructured
grid method, is presented. The solver is based on a finite-volume method
and can compute turbulent free-surface flows around an advancing ship.
Spatial as well as temporal discretizations, turbulence and free-surface
modeling are discussed. Results for industrial applications are
presented, which show the capability of the method.brbr 14.45-15.45h: strongJeroen Wackers/strongbr strongTitle:/strong Towards adaptive goal-oriented computing in marine flow simulationbrstrongAbstract:/strong
The Numerical Modelling group of the Fluid Dynamics Laboratory at Ecole
Centrale de Nantes works on the development of advanced numerical
methods in fluid dynamics that can be applied directly in the industrial
practice. The ISIS-CFD flow solver, developed by the group, is
commercialised; its main field of application is marine and offshore
hydrodynamics.brAdaptive grid refinement has been a major area of
development for ISIS-CFD in the past three years. The main interest of
this development is the creation of a method that is robust and
dependable for a wide area of different, realistic flow aplications. The
grid refinement method is operational since the end of last year.brIn
the first part of my talk, I will present the refinement method and its
various applications. In particular, I will focus on the use of tensor
refinement criteria as the most general way to specify any kind of
anisotropic grid refinement, which will be illustrated with two very
different refinement criteria.brTo finish, I will discuss some ideas
concerning a recently started development, the use of adjoint-based
goal-oriented refinement criteria, and the particular challenges related
to their use for water flow simulation./p
hr
pDate: strong6 July 2010/strongbrTime: strong10.30-11.30h/strongbrRoom: strongL120/strongbrbrSpeaker: strong Ron White, James Cook University, Australia/strong (visiting Ute)brTitle: em Kinetic theory of positron transport in gaseous and soft-condensed systems/embrbrstrongAbstract:/strong
A quantitative understanding of positron transport processes in gases
and soft-condensed matter under highly non-equilibrium conditions is of
interest from both fundamental and applied viewpoints, including medical
diagnostics and therapeutic techniques, e.g., positron emission
tomography (PET) and positherapy respectively, and radiation safety. In
this presentation we will discuss how the kinetic theoretical techniques
developed over many years specifically for electron and ion swarms in
gases are presently being adapted to study positron transport in both
gaseous and soft-condensed systems, including bio-materials. We will
focus on the progress towards a rigorous model of positron transport in
soft-condensed matter and amorphous systems, as part of the positron
physics program in Australia to model the PET process. The governing
kinetic equation along with its numerical and analytical solution will
be presented./p
hr
pDate: strong9 July 2010/strong (Note the date!)brTime: strong10.30-11.30h/strongbrRoom: strongL120/strongbrbrSpeaker: strong Saleh Tanveer, Ohio State, USA/strong (visiting Ute)brTitle: em tba/embrbrstrongAbstract:/strong tba/p
hr
pDate: strong17 August 2010/strongbrTime: strong10.30-11.30h/strongbrRoom: strongL120/strongbrbrSpeaker: strong Frank Giraldo, Naval Postgraduate School /strong (visiting Jason)brTitle: emIn Search of Efficient High-Order Time-Integrators for Compressible Navier-Stokes/embrbrstrongAbstract:/strong
Much work has been invested in the construction of high-order methods
for approximating spatial derivatives of nonlinear partial differential
equations such as Navier-Stokes. However, often times, the
time-integrators used are only 2nd order at best when used implicitly
and 4th order when used explicitly. Explicit methods are wonderful (easy
to implement and available to higher order) but for many applications
(such as compressible Navier-Stokes) the speed of the acoustic waves
severely limits the maximum time-step allowed to maintain stability.brbr
Therefore, we seek to construct high-order methods (in both space and
time) that are efficient (in terms of lowering the wallclock time of the
model). To this end, we are exploring IMEX (multi-step and multi-stage
methods) and fully-implicit methods (Newton-Krylov); as is the case for
all implicit methods, scalability on distributed-memory computers is an
issue (due to the large number of off-processor communications). We seek
to ameliorate this deficiency through the implementation of
specially-designed preconditioners./p
hr
pDate: strong24 August 2010/strongbrTime: strong10.30-11.30h/strongbrRoom: strongL120/strongbrbrSpeaker: strongSergiy Zhuk, INRIA Paris-Rocquencourt/strong (visiting Jason)brTitle: emData assimilation with minimax state estimation approach: theory and examples/embrbrstrongAbstract:/strong
The talk describes the general Minimax State Estimation (MSE) framework
for models described by non-linear evolution equations. It presents
geometrical ideas underlying the MSE with focus on the notions of a
reachability set and it's Tchebysheff center. The analytical description
of the reachability set will be stated in terms of dynamic programming
method. A synthetic numerical example illustrating application of MSE
for Euler equation will be presented./p
hr
p
a name=fall2010/a/p
h3Fall 2010/h3
hr
pDate: strong7 September 2010/strongbrTime: strong10.30-11.30h/strongbrRoom: strongL120/strongbrbrSpeaker: strongChristoph Köhn/strong (aio applicant visiting Ute)brTitle: emN = 4 supergravity of a T - compacti?ed sixdimensional theory/embrbrstrongAbstract:/strong
Supergravitational theories can be considered as low energy limit of
string theories which are supposed to be good candidates in order to
unify quantum theory and Einstein’s general relativity. Unfortunately
string theories and - in the same way - supergravitational theories
live in more than four space- time dimensions so that one has to reduce
the whole theory from D gt; 4 dimensions down to D = 4 dimensions. In
this talk the bosonic part of a sixdimensional supergravity shall be
reduced to four dimensions on a two- dimensional torus T^2. The
resulting action can be compared with a general action which describes
every N = 4 supergravity so that all components, which form the general
action, can be determined with the help of all terms appearing in the
reduced action. For this purpose one has to treat the mass- less and
massive case separatly. At ?rst one can determine some components of
the general theory in the massless case. Indeed, this task seems to
become very di?cult because there are two-form ?elds in the reduced
theory which do not appear in the general action (the same problem
appears for electric and magnetic vectors). In order to solve this
problem one has to dualize these ?elds: Two-form ?elds are dual to
scalars and magnetic vectors are dual to electric vectors. After having
performed these dualizations it is possible to determine all terms
which construct the massless theory and to rewrite the reduced theory
in the general form of the N = 4 supergravity in four dimen- sions.
These terms have to be valid for the massive theory,too, because this
theory has to go over to the massless theory in the limit of vanishing
masses. But there are additional parameters which do not appear in the
massless case. Using the formerly determined terms it is possible to
determine these missing parameters. This ?nally leads to the conclusion
that actually the action which has been deduced by dimensional
reduction can be rewritten in the general way every N = 4 supergravity
can be formed in four dimensions./p
hr
pDate: strong19 October 2010/strongbrTime: strong11.30-12.30h/strongbrRoom: strongL120/strongbrbrSpeaker: strongProf. Bram van Leer, University of Michigan /strong (visiting Barry)brTitle: emHistory of CFD, Part II/embrbrstrongAbstract:/strong Click a href=http://homepages.cwi.nl/%7Erademach/mac-sem-CFDII.htmlhere/a - it's worth it!/p
hr
pDate: strong16 November 2010/strongbrTime: strong13.30-14.30h/strong (NB: not the usual time!)brRoom: strongL120/strongbrbr Speaker: strong Freddy Bouchet, ENS Lyon/strong brTitle: emNon-equilibrium statistical mechanics of two dimensional turbulence and geophysical flows/embr brstrongAbstract: /strongThe
equilibrium statistical mechanics of two dimensional and geostrophic
turbulence, predicts the outcome for the large scales of the flow,
resulting from the turbulent mixing. I will focus on physical ideas in
order to emphasize how concepts from statistical ideas: phase
transition, phase diagrams, and phase coexistence, have been
successfully applied to geophysical fluid dynamics. For instance this
theory allowed us to model the detailed properties of the Great Red Spot
and other localized structures of Jupiter's troposphere.brbr A
first aim of the talk is to discuss the range of applicability of this
theory to ocean dynamics. This range is probably limited due the
inertial assumption underlying this equilibrium approach. Still we will
show that the theory is able to reproduce in much details localized
structures like westward mid-basin jets (Gulf Stream, Kuroshio) and
ocean vortices (rings). We also uncover the relations between strong
eastward mid-basin inertial jets, like the Kuroshio extension and the
Gulf Stream, and statistical equilibria.brbr An important (and
justified) criticism of the equilibrium theory is its inability to take
into account the forcing and dissipation, which play an essential role.
The second aim of this talk is to present new results for a
non-equilibrium theory of the mixing of the potential vorticity that
takes these into account. We first describe new sets of invariant
measures. We show that we can predict from those non-equilibrium phase
transitions, where the flow switches randomly between two different
large scale patterns. The main interest of the theory is to predict the
range of parameters of this bistability phenomena and to predict the
mean streamfunction for each of these two states. We discuss future
geophysical applications of these new theoretical results./p
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pDate: strong23 November 2010/strongbr Time: strong11.30-12.30h/strongbrRoom: strongL120/strongbrbrSpeaker: strong Roel Luppes, IWI, RU Groningen/strong (visting Yunus)brTitle: emThe simulation of sloshing liquid and water waves/embrbrstrongAbstract:/strongThe
CFD simulation tool ComFLOW has been developed for the simulation of
sloshing liquids and two-phase flow in e.g. offshore applications.
During the talk, several applications will be presented.br ComFLOW
solves the Navier-Stokes equations in both water and air, with 2nd order
accuracy in both space and time. The water surface is advected by means
of a modified Volume-of-Fluid (VOF) method, with improved accuracy
through a height-function approach, ensuring a sharp interface without
smearing. During the talk, several numerical techniques will be
discussed, such as a gravity-consistent density averaging method and
absorbing boundary conditions.br The numerical treatment of the
average density around the interface requires special attention. Naive
geometrical averaging results in spurious velocities and instabilities.
With the so-called 'gravity-consistent' density averaging method, severe
instabilities near the free surface can be avoided. The momentum
equation for a fluid at rest provides a condition for the discrete
average of the density.br An Absorbing Boundary Condition (ABC) has
been developed for wave simulations around offshore structures in open
domains. The ABC is based on a rational function approximation of the
linear dispersion relation for waves, combined with the traditional
Sommerfeld outflow condition. By employing ABC's, outflow boundaries can
be located relatively close to the object, without influencing outgoing
waves or generating numerical reflections, which reduces the number of
grid-points considerably./p
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pDate: strong7 December 2010/strongbrTime: strong10.30-11.30h/strongbrRoom: strongL120/strongbrbrSpeaker: strong Oskar Prill, Stuttgart/strong (visting Jens)brTitle: em Metastability of localized structures in nonlinear periodic media/embrbrstrongAbstract:/strong
Based on a model equation of nonlinear optics, we study the question as
to whether localized structures in nonlinear periodic media with and
without defects can exist for all times. Specifically, we consider a
nonlinear Klein-Gordon equation with a perturbed Lam\'e potential in
one space dimension. We show that, generically, the solutions to the
linearized problem decay with a rate of t^(-1/3) w.r.t. the L^{\infty}
norm. In weighted L^2 norms, we even get a time decay of t^(-3/2). br
We then apply these results to the nonlinear problem. The asymptotic
stability of the vacuum solution can be proved regardless whether the
discrete spectrum of the Hill operator associated to our problem is
empty or contains exactly one eigenvalue. However, as for the rates the
solutions in a small neighborhood of the origin vanish with, we have to
discriminate between the two cases: While the solutions to the
nonlinear problem decay with the linear rate in the eigenvalue-free
situation, there is an anomalously slow decay in the presence of an
eigenvalue. The latter phenomenon is referred to as metastability of
the corresponding solutions./p
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pDate: strong14 December 2010/strongbrTime: strong10.30-11.30h/strongbrRoom: strongL120/strongbrbrSpeaker: strong Carlos Escudero Liebana, Madrid/strong (visting Jens)brTitle: em Some remarks on the analysis of a model of epitaxial growth /embrbrstrongAbstract:/strong
Epitaxial growth is characterized by the deposition of new material on
existing layers of the same material under high vacuum conditions. This
technique is used in the semiconductor industry for the growth of thin
films. In case of molecular beam epitaxy the deposition takes place at a
very slow rate and almost atom by atom. The goal in most situations of
thin film growth is growing an ordered crystal structure with a flat
surface. But in epitaxial growth it is quite usual finding a mounded
structure generated along the surface evolution. Attempting to perform
ab initio quantum mechanical calculations in this system is
computationally too demanding, what opens the way to the introduction of
simplified models. These have been usually developed within the realm
of non-equilibrium statistical mechanics, and can be of a discrete
probabilistic nature or have the form of a differential equation.
Discrete models usually represent adatoms (the atoms deposited on the
surfaces) as occupying lattice sites. They are placed randomly at one
such site and then they are allowed to move according to some rules
which characterize the different models. A different modeling
possibility is using partial differential equations. In this talk we
will focus on rigorous and numerical analysis of a partial differential
equation which has been introduced in the context of epitaxial growth. /p
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p
a name=spring2011/a/p
h3Spring 2011 MAC colloquia/h3
hr
pDate: strong1.3./strongbrTime: strong11.30-12.30h/strongbrRoom: strongL120 /strongbrbrJan Verwer planned to give this colloquium.
Sadly, Jan passed away on Feb 16th. The planned talked was titled em Composition methods, Maxwell's equations and source functions./em/p
pnbsp;/p
pDate:nbsp;strong31.5./strongbrTime:nbsp;strong11.30-12.30h/strongbrRoom:nbsp;strongL016nbsp;/strongbrbrSpeaker:nbsp;strongBlair Perot (University of Massachusetts,nbsp;strongTheoretical and Computational Fluid Dynamics/strong),nbsp;/strongbrTitle:nbsp;emThe relationship between Keller Box schemes and other mimetic methods/embrbrstrongAbstract:/strong/p
pThe Keller Box scheme is a face-based method for solving partial differential equations that has numerous attractive mathematical and physical properties. It is shown that one way of explaining these attractive properties is to note that the scheme discretizes partial derivatives exactly and only makes approximations in the algebraic constitutive relations appearing in the PDE. However, the resulting exact Discrete Calculus associated with the Keller-Box scheme is shown to be fundamentally different from all other mimetic (physics capturing) numerical methods known to the speaker. The analysis of the Keller Box scheme suggests that a unique exact discrete calculus does not exist. nbsp;It also suggests that existing analysis techniques based on concepts in algebraic topology (in particular – the discrete de Rham complex) are unnecessarily narrowly focused because they do not represent the Keller Box scheme. Some performance tests of the Keller Box scheme solving the unsteady advection-diffusion equation are presented./p
pnbsp;/p
pDate: strong7.6./strongbrTime: strong11.30-12.30h/strongbrRoom: strongL120 /strongbrbrSpeaker: strongEgbert Westerhof (FOM Rijnhuizen), /strongbrTitle: emNumerical modeling of fusion plasmas/embrstrongbr/strong/p
pDate:nbsp;strong4.10./strongbrTime:nbsp;strong11.30-12.30h/strongbrRoom:nbsp;strongL120nbsp;/strongbrbrSpeaker:nbsp;strongLuc Florak (Eindhoven),nbsp;/strongbrTitle:nbsp;em Neuro amp; Cardio Imaging from a Mathematical Perspective /embrbrstrongAbstract:/strong/p
pThe Imaging Science amp; Technology Eindhoven (IST/e) is a cross-divisional collaboration involving several image related research groups at Eindhoven University of Technology in The Netherlands. It is built on four pillars: image acquisition, biomedical image analysis, mathematical image analysis, and visualization, and covers two main themes: cardio imaging and neuro- imaging. The aim of IST/e is to bridge the gap between methodological sciences, notably mathematics, physics, and computer science, on the one hand, and biomedical and clinical sciences on the other hand. IST/e has collaborations with various clinics and with industry. I will present mathematical models with the help of which we address challenges from both themes./p
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h3Fall 2011 MAC colloquia/h3
hr
pnbsp;/p
pDate: strong8.11./strongbrTime: strong11.30-12.30h/strongbrRoom: strongL120 /strongbrbrSpeaker: strongGabriel Wittum (Frankfurt), /strongbrTitle: emTaylor-like Analysis of Variance-Expansion methods for
high dimensional PDEs arising in ﬁnance/embrbrstrongAbstract:/strong
The solution of many problems in computational ﬁnance can be found by solving
high dimensional partial differential equation. Path-dependent options, or options
depending on many underlyings, are only two examples of these problems. Due to
the high dimensionality, Monte Carlo methods are widely used for the solution of
this kind of problems despite their poor convergence behaviour. br
Several methods for the solution of PDEs arising in the mentioned context have
been developed, e.g. sparse grids, Fourier methods, or seperated representation
methods. br
It is widely recognized that high-dimensional problems often posess an underly-
ing structure commonly called effective dimension [1], which explains the good
performance of Quasi-Monte Carlo methods for problems in ﬁnance. Analysis of
variance (ANOVA) decompositions can exploit the low superposition dimension
of the problems, and the corresponding expansion can often be truncated up to
second order terms. Reisinger and Wittum [2] however, developed an asymptotic
expansion of the problem in its eigenvalues. br
We show that the asymptotic expansion developed by Reisinger and Wittum is a
special, Taylor-like ordering of the ANOVA decomposition’s terms which shows
remarkably exact results while using fewer terms than the standard ANOVA de-
composition. We expand the methodology to a Taylor-expansion of second order
and show the accuracy of the expansion through several examples, i.e. geomet-
ric and arithmetric basket options on a hypothetical ﬁve-dimensional basket and a
basket on the german main equity index (DAX). Furthermore we derive a priori es-
timations of the individual contributions in the case of the geometric basket. Since
this is not possible in the case of the arithmetric basket because of its more com-
plex structure, we investigate the inﬂuence of the individual valuation parameters
(i.e. correlations, volatilities, strike price and basket weights) on the contribution
of the individual ANOVA terms. brbr
strongReferences/strongbr
[1] X. Wang and K.T. Fang. The effective dimension and quasi-monte carlo inte-
gration. Journal of Complexity, 19(2):101–124, 2003. br
[2] C. Reisinger and G. Wittum. Efﬁcient hierarchical approximation of high-
dimensional option pricing problems. SIAM Journal on Scientiﬁc Computing,
29(1):440, 2008.
/p
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pDate: strong6.12./strongbrTime: strong11.30-12.30h/strongbrRoom: strongL120 /strongbrbrSpeaker: strong Harald van Brummelen (TU/e), /strongbrTitle: emgoal-adaptive methods for multiscale flow problems/embrbrstrongAbstract:/strong
Adaptive finite-element methods based on goal-oriented a-posteriori error estimates provide a very powerful
paradigm for approximating goal functionals (observables) of flow problems that exhibit multiple scales, e.g.,
transitional molecular/continuum flows and coupled problems such as fluid-structure interaction. Based on the
solution of a suitable dual problem, the contribution of local errors in the solution to the error in the goal functional
is estimated, and only the regions that yield a dominant contribution are refined. In such a manner, a computational
model is generated, that provides an optimal approximation to the goal functional.br
In this presentation, I will discuss the basics of goal-oriented error estimation and goal-adaptive refinement. Next,
I will present applications of the methodology to a prototype Boltzmann equation and to fluid-structure interaction.
Numerical results are presented for both these applications.br
Further reading:br
[1] E.H. van Brummelen, K.G. van der Zee, V.V. Garg, and S. Prudhomme, 'Flux evaluation in primal and dual
boundary-coupled problems', Tech. Report 11-22, Institute for Computational Engineering and Sciences, 2011.br
[2] K.G. van der Zee, E.H. van Brummelen, I. Akkerman, and R. de Borst, 'Goal-oriented error estimation and adaptivity
for fluid-structure interaction using exact linearized adjoints', Comput. Methods Appl. Mech. Engrg. 200 (2011), 2738–2757.br
[3] P.W. Fick, E.H. van Brummelen, and K.G. van der Zee, 'On the adjoint-consistent formulation of interface conditions
in goal-oriented error estimation and adaptivity for fluid-structure interaction', Comput. Methods Appl. Mech. Engrg. 199
(2010), 3369–3385.br
[4] W. Hoitinga and E.H. van Brummelen, 'A discontinuous-Galerkin finite-element method for a 1D prototype of the Boltzmann
equation', J. Comput. Phys. 230 (2011), 6115–6135.br
[5] W. Hoitinga, 'Goal-adaptive discretization of a one-dimensional Boltzmann equation', Ph.D. thesis, Delft University
of Technology, 2011.
/p
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h3Spring 2011 MAC seminars/h3
hr
pDate: strong29.3/strongbrTime: strong10.30-11.30h/strongbrRoom: strongL120 /strongbrbrSpeaker: strongReinout Quispel (LaTrobe U.) (visiting Jason), /strongbrTitle: emEnergy-Preserving Numerical Integration Methods/embrbrstrongAbstract:/strong
/p
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pDate: strong17.5./strongbrTime: strong10.30-11.30h/strongbrRoom: strongL120 /strongbrbrSpeaker: strongMaciej Krupa, Nijmegen (visiting Jens)/strongbrTitle: emClustered oscillations in a model of gamma rhythm/embrbrstrongAbstract:/strong
We consider a model of gamma oscillations known as PING (Pyramidal INterneuron Gamma). A PING model consists of two coupled populations of cells, excitatory (pyramidal) cells and inhibitory cells (interneurons). We review the earlier work of Börgers and Kopell who demonstrated the existence oscillatory solutions with both populations firing synchronously (and with frequency in gamma range). Subsequently we present our results on the existence of clustered solutions; we show that the excitatory cells may fire in clusters if they have a long refractory period, i.e. if they do not respond to input in the early stage of their cycle. We consider two nbsp;models of excitatory cells, a Miles-Traub cell with adaptation, and a phase model with a custom designed coupling function, created in order to explain the mechanism of the clustered firing. Finally, we discuss the effects of shunting vs hyperpolarizing inhibition./p
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a name=fall2011/a/p
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h3Fall 2011 MAC seminars/h3
pDate: strong16.8./strongbrTime: strong11.30-12.30h/strongbrRoom: strongL120 /strongbrbrSpeaker: strong Tristan van Leeuwen, Vancouver (visiting Joost)/strongbrTitle: emWave-equation traveltime tomography for seismic inversion /embrbrstrongAbstract:/strong
The inference of subsurface medium parameters from seismic data can be posed as a PDE-constrained data-fitting procedure. This approach is successful in reconstructing medium perturbations that are in the order of the dominant wavelength present in the data. In practice, the data lack low frequency content and this means that one needs a good initial guess of the slowly varying component of the medium. For a wrong starting model an iterative least-squares reconstruction procedure is likely to end up in a local minimum. We propose to use a different measure of the misfit that makes the optimization problem more tractable in terms of the slowly varying velocity structures. This technique may be seen as a generalization of traveltime tomography. As opposed to more conventional tomographic techniques however, the input data - the travetlmes- are not directly observed. The newly-proposed misfit detects the traveltime difference automatically in a way that allows us to derive Frechet derivatives w.r.t to the medium parameters. We discuss the theoretical underpinnings of the method and give some numerical examples./p
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pDate: strong22. Nov. 2011/strongbrTime: strong11.30-12.30h/strongbrRoom: strongL120 /strongbrbrSpeaker: strongHannes Uecker, Oldenburg (visiting Jens)/strongbrTitle: emApproximating the dynamics of active cells
in a diffusive medium by ODEs - Homogenization with Localization/embrbrstrongAbstract:/strong
Bacteria may change their behavior depending on
the population density. Here we study a dynamical model in which
cells of radius $R$ within a diffusive medium communicate with each
other via diffusion of a signalling substance produced by the cells.
The model consists of an initial boundary value
problem for a parabolic PDE describing the exterior concentration
$u$ of the signalling substance, coupled with
$N$ ODEs for the masses $a_i$ of the substance within each cell.
We show that for small $R$ the model can be approximated by
a hierarchy of models, namely first a system of $N$ coupled
delay ODEs, and in a second step by $N$ coupled ODEs.
We give some illustrations of the dynamics of
the approximate model. Joint work with J. Müller./p