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Professor of Applied Mathematics

Faculty of Science, Ontario Tech University

Also Director of the Modelling and Computational Science program.

• Dynamical Systems
• Scientific Computing

Professor of Applied Mathematics

Department of Mathematics, Concordia University

Postdoctoral researcher and lecturer at La Trobe University

AMS COE on Mathematics and Statistics of Complex Systems

Postdoctoral researcher

National Institute for Fusion Science and Kyoto University

PhD

Utrecht University

Applied Mathematics

MSc

University of Amsterdam

Theoretical Physics

Transfer Matrix Analysis of Random Tiling Models using the Bethe Ansatz

MSc. thesis at the University of Amsterdam

My Master's thesis on the statistical properties of random tilings of the plane using transfer matrices.

Time scale interaction in low-order climate models

PhD thesis at Utrecht University

Although nominally about climate modelling, this thesis is mostly about the bifurcation analysis of systems with multiple time scales.

The interplay of dynamics and statistics in physical and biological models

This program comprises three interrelated projects in the intersection of nonlinear dynamics and statistics: fluid turbulence, moving interfaces and the motility of bacteria. In each of these phenomena, intricate nonlinear dynamics give rise to robust properties of quantities averaged over time, space or realizations. In fluid turbulence, the continuous formation and breakdown of coherent structures conspire to produce, on average, the famous Kolmogorov power law for the distribution of energy over spatial scales. In the study of moving interfaces, in particular model in the famous model by Kuramoto and Sivashinsky, it is an open question what statistical behaviour the transient dynamics result in. Over thirty five years ago, Yakhot conjectured that the statistical properties of the model should be the same as those of the Kardar-Parisi-Zhang universality class. The premise is that the fast motion on small scales effectively acts as stochastic forcing on the slow motion on large scales. There is, however, no conclusive evidence to support or reject the conjecture. We will use cutting-edge, GPU based algorithms of computational dynamical systems theory to shed new light on these classical problems. The mathematical description of bacterial motility is much younger than that of fluid turbulence and interface formation. Since experiments have revealed details of the motion of individual cells, the most common approach to simulating collective motion is agent based. If the simulation is long enough, and contains enough agents, it can exhibit the formation of clusters of cells that move in unison. However, even with the aid of GPU computing, we can only simulate microscopically small clusters. Our question is whether we can formulate a continuum model of cluster formation. Since coarse-grained, continuous simulations are more tractable, they will allow us to address open questions about the macroscopic properties of collective motion, such as captured by distributions of cluster sizes.

• RGPIN-2019-05443