Lennaert van Veen
PhD
Associate Professor
Graduate Program Director
MathematicsFaculty of Science
Using applied and computational dynamical systems theory to build a better understanding of physical and physiological processes
Languages
English, Dutch, French, German, Japanese, Spanish
lennaert.vanveen@ontariotechu.ca
905.721.8668 ext. 3642
Areas of expertise
- PhD - Applied Mathematics Utrecht University and the Royal Dutch Meteorological Institute, Netherlands 2002
- MSc - Theoretical Physics University of Amsterdam, Netherlands 1996
Equilibria and Periodic Orbits in 3D Navier-Stokes Flow on a Periodic Domain
Montréal, Québec December 4, 20152015 CMS Winter Meeting
Sub-Critical Transition Without Walls Workshop on Advancing Wall-Turbulence Model Development and Implementation
Durham, New Hampshire November 1, 2015University of New Hampshire Workshop
Simple Invariant Solutions in Homogeneous Isotropic Turbulence with Various External Forces
Paris, France July 15, 2015Sixth International Symposium on Bifurcations and Instabilities in Fluid Dynamics
Numerical Solution of the Kuramoto-Sivashinsky Initial-Boundary Value Problem
Waterloo, Ontario June 7, 2015Canadian Applied and Industrial Mathematics (CAIMS) 2015 Annual Meeting
Bifurcations and Self-Organisation in a Continuum Model of the Human Cortex
Cusco, Peru May 13, 2013Advanced Computational and Experimental Techniques in Nonlinear Dynamics Workshop
Pattern Formation in a Mean-Field Model of Electrocortical Activity
Paris, France July 13, 201323nd Annual Computational Neuroscience Meeting
Meta-Bifurcation Analysis of a Mean-Field Model of the Human Cortex
San Diego, California August 7, 2012Society for Applied and Industrial Mathematics (SIAM) Conference on the Life Sciences
Turing Instabilities in a Mean-Field Model of Electrocortical Activity
Atlanta, Georgia July 21, 201222nd Annual Computational Neuroscience Meeting
Dynamics of a Mean-Field Cortex Model
Seattle, Washington June 13, 2012SIAM Conference on Nonlinear Waves and Coherent Structures
Pattern Formation and Nonlinear Oscillations in a Neural Population Model
Chicago, Illinois March 31, 20122012 Annual Meeting of the Cognitive Neuroscience Society
PAMPAC, A Parallel Adaptive Method for Pseudo-Arclength Continuation
Published in ACM Transactions on Mathematical Software (TOMS) February 1, 2016D. A. Aruliah, Lennaert Van Veen & Alex Dubitski
Pseudo-arclength continuation is a well-established method for generating a numerical curve approximating the solution of an underdetermined system of nonlinear equations. It is an inherently sequential predictor-corrector method in which new approximate solutions are extrapolated from previously converged results and then iteratively refined. Convergence of the iterative corrections is guaranteed only for sufficiently small prediction steps. In high-dimensional systems, corrector steps are extremely costly to compute and the prediction step length must be adapted carefully to avoid failed steps or unnecessarily slow progress. We describe a parallel method for adapting the step length employing several predictor-corrector sequences of different step lengths computed concurrently.
View more - PAMPAC, A Parallel Adaptive Method for Pseudo-Arclength Continuation
Periodic Solutions to a Mean-Field Model for Electrocortical Activity
Published in The European Physical Journal Special Topics December 1, 2014L. van Veen & K. R. Green
We consider a continuum model of electrical signals in the human cortex, which takes the form of a system of semilinear, hyperbolic partial differential equations for the inhibitory and excitatory membrane potentials and the synaptic inputs. The coupling of these components is represented by sigmoidal and quadratic nonlinearities. We consider these equations on a square domain with periodic boundary conditions, in the vicinity of the primary transition from a stable equilibrium to time-periodic motion through an equivariant Hopf bifurcation. We compute part of a family of standing wave solutions, emanating from this point.
View more - Periodic Solutions to a Mean-Field Model for Electrocortical Activity
Open-Source Tools for Dynamical Analysis of Liley’s Mean-Field Cortex Model
Published in Journal of Computational Science May 1, 2014Kevin R.Green & Lennaert van Veen
Mean-field models of the mammalian cortex treat this part of the brain as a two-dimensional excitable medium. The electrical potentials, generated by the excitatory and inhibitory neuron populations, are described by nonlinear, coupled, partial differential equations that are known to generate complicated spatio-temporal behaviour. We focus on the model by Liley et al. (Network: Computation in Neural Systems 13 (2002) 67–113).
View more - Open-Source Tools for Dynamical Analysis of Liley’s Mean-Field Cortex Model
The Significance of Simple Invariant Solutions in Turbulent Flows
Published in Annual Review of Fluid Mechanics January 1, 2012Genta Kawahara, Markus Uhlmann and Lennaert van Veen
Recent remarkable progress in computing power and numerical analysis is enabling us to fill a gap in the dynamical systems approach to turbulence. A significant advance in this respect has been the numerical discovery of simple invariant sets, such as nonlinear equilibria and periodic solutions, in well-resolved Navier-Stokes flows. This review describes some fundamental and practical aspects of dynamical systems theory for the investigation of turbulence, focusing on recently found invariant solutions and their significance for the dynamical and statistical characterization of low-Reynolds-number turbulent flows.
View more - The Significance of Simple Invariant Solutions in Turbulent Flows
Homoclinic Tangle on the Edge of Shear Turbulence
Published in Physical Review Letters March 1, 2011Lennaert van Veen and Genta Kawahara
Experiments and simulations lend mounting evidence for the edge state hypothesis on subcritical transition to turbulence, which asserts that simple states of fluid motion mediate between laminar and turbulent shear flow as their stable manifolds separate the two in state space. In this Letter we describe flows homoclinic to a time-periodic edge state that display the essential properties of turbulent bursting. During a burst, vortical structures and the associated energy dissipation are highly localized near the wall, in contrast with the familiar regeneration cycle.
View more - Homoclinic Tangle on the Edge of Shear Turbulence
Metabifurcation Analysis of a Mean-Field Model of the Cortex
Published in Physica D: Nonlinear Phenomena May 15, 2011Federico Frascoli, Lennaert van Veen, Ingo Bojak & David T.J.Lileya
Mean-field models (MFMs) of cortical tissue incorporate salient, average features of neural masses in order to model activity at the population level, thereby linking microscopic physiology to macroscopic observations, e.g., with the electroencephalogram (EEG). One of the common aspects of MFM descriptions is the presence of a high-dimensional parameter space capturing neurobiological attributes deemed relevant to the brain dynamics of interest.
View more - Metabifurcation Analysis of a Mean-Field Model of the Cortex
On Matrix-Free Computation of 2D Unstable Manifolds
Published in SIAM Journal on Scientific Computing January 6, 2011Lennaert van Veen, Genta Kawahara, and Matsumura Atsushi
Recently, a flexible and stable algorithm was introduced for the computation of two-dimensional (2D) unstable manifolds of periodic solutions to systems of ordinary differential equations. The main idea of this approach is to represent orbits in this manifold as the solutions of an appropriate boundary value problem (BVP). The BVP is underdetermined, and a one-parameter family of solutions can be found by means of arclength continuation.
View more - On Matrix-Free Computation of 2D Unstable Manifolds
The Primary Flow Transition in the Baroclinic Annulus
Published in Modeling Atmospheric and Oceanic Flows: Insights from Laboratory Experiments and Numerical Simulations Chapter 2, Geophysical Monograph Series of the AGU November 14, 2014Gregory M. Lewis, Nicolas Périnet & Lennaert van Veen
This book provides a broad overview of recent progress in using laboratory experiments and numerical simulations to model atmospheric and oceanic fluid motions. This volume not only surveys novel research topics in laboratory experimentation, but also highlights recent developments in the corresponding computational simulations. As computing power grows exponentially and better numerical codes are developed, the interplay between numerical simulations and laboratory experiments is gaining paramount importance within the scientific community. The lessons learnt from the laboratory-model comparisons in this volume will act as a source of inspiration for the next generation of experiments and simulations.
View more - The Primary Flow Transition in the Baroclinic Annulus
Long-Term Invitation Fellowship
Japan Society for the Promotion of Science (JSPS) January 1, 2015Dr. van Veen was awarded a seven-month fellowship at the Faculty of Engineering Science at Osaka University in Japan.
Editor
Society of Applied and Industrial Mathematics (SIAM) Activity Group on Dynamical Systems January 1, 2012Dr. van Veen is Editor of SIAM's Dynamical Systems magazine. Previously, he served as secretary of SIAM's Activity Group, magazine editor-in-chief and portal editor-in-chief, each for two years.
Post-Doctoral Fellow
Australian Research Council Centre of Excellence September 1, 2005During his two-year fellowship, Dr. van Veen's research examined mathematics and statistics of complex systems.
Post-Doctoral Fellow
Japan Society for the Promotion of Science (JSPS) September 1, 2003During his two-year fellowship, Dr. van Veen explored research at the National Institute for Fusion Science in Toki, Gifu Prefecture, and the Department of Mechanical Engineering at Kyoto University.
Organization for Computational Neurosciences
Japan Society for the Promotion of Science (JSPS)
American Physical Society
Canadian Applied and Industrial Mathematics Society
Society for Industrial and Applied Mathematics
Shared Hierarchical Academic Research Computing Network (SHARCNet)
- Computational Science II (MATH 4020U)
This course provides a variety of results and algorithms from a theoretical point of view. Students study numerical differentiation and integration; interpolation and approximation of functions; quadrature methods; numerical solution of ordinary differential equations; the algebraic eigenvalue problem. Computer software such as Maple and MatLab will be used in assignments. - Partial Differential Equations (MATH 4050U)
This course considers advanced aspects of the theory, solution and physical interpretation of first and second order partial differential equations in up to four independent variables. This includes the classification of types of equations and the theory and examples of associated boundary-value problems. The concepts of maximum principles and Green’s functions are studied, as well as an introduction to nonlinear equations. A broad range of applications are considered. - High-Performance Computing (MCSC 6030G)
The goal of this course is to introduce students to the tools and methods of high-performance computing (HPC) using state-of-the-art technologies. The course includes an overview of high-performance scientific computing architectures (interconnection networks, processor arrays, multiprocessors, shared and distributed memory, etc.) and examples of applications that require HPC. The emphasis is on giving students practical skills needed to exploit distributed and parallel computing hardware for maximizing efficiency and performance. In a number of in-class projects, students implement numerical algorithms that can be scaled up for large systems of linear or nonlinear equations. Topics may include survey of computer architectures; efficiency guidelines for HPC; parallel algorithm design; programming tools; timing, profiling and benchmarking; and optimizations.
