October 20, 2018

Fields Institute Colloquium/Seminar in Applied Mathematics 2008-2009

Organizing Committee  
Jim Colliander (Toronto)  
Walter Craig (McMaster)  
Barbara Keyfitz (Fields)
Robert McCann (Toronto)
Adrian Nachman (Toronto)   
Mary Pugh (Toronto)  
Catherine Sulem (Toronto)


The Fields Institute Colloquium/Seminar in Applied Mathematics is a monthly colloquium series for mathematicians in the areas of applied mathematics and analysis. The series alternates between colloquium talks by internationally recognized experts in the field, and less formal, more specialized seminars.In recent years, the series has featured applications to diverse areas of science and technology; examples include super-conductivity, nonlinear wave propagation, optical fiber communications, and financial modeling. The intent of the series is to bring together the applied mathematics community on a regular basis, to present current results in the field, and to strengthen the potential for communication and collaboration between researchers with common interests. We meet for one session per month during the academic year. The organizers welcome suggestions for speakers and topics.

2008-09 talks held at the Fields Institute

Wednesday, May 13
2:10 p.m.
Giuseppe Savare (Universita di Pavia)
Viscous and rate-independent evolutions
Solutions of rate-independent evolution problems, as recently proposed by A. Mielke and his collaborators, can be obtained by solving a recursive minimization scheme which involves a functional governing the evolution perturbed by a suitable convex dissipation term. Rate-independence is guaranteed by the 1-homogeneity of the dissipation, which therefore has a linear growth. The same variational scheme, with quadratic (or at least superlinear) dissipation, plays a crucial role in the variational approach to
Gradient Flows and Doubly-nonlinear evolution equations.
It is therefore natural to investigate the relationships between these two theories, in particular when viscous approximations of rate- independent problems are considered: they are simply obtained by adding a (asymptotically small) quadratic perturbation to the dissipation term.
In this talk we address this kind of problems and we discuss some characterizations of the limit solutions obtained by general viscous approximations.
(Joint work in collaboration with A. Mielke and R. Rossi)

March 4, 2009
3:10 p.m.

Joint Fields/Physics Colloquium
Ehud Meron, Ben-Gurion University of the Negev
Periodic vs. scale-free patterns: reconciling the dichotomy of dryland vegetation
Field observations of vegetation patchiness in drylands reveal periodic patterns with characteristic length scales along with scale-free patterns characterized by broad patch-size distributions, often reported to obey power-laws. Despite the numerous theoretical and experimental studies that have been devoted to vegetation patchiness, this dichotomy of patterns is still poorly understood. Using a mathematical model that captures basic feedbacks between biomass and water and between above-ground and below-ground biomass, we elucidate mechanisms that control patch-size distributions in water-limited systems, and identify physical and ecological circumstances that lead to periodic patterns and to scale-free patterns.

March 5, 2009
4:10 p.m.
McLennan Physics 102
Joint Fields/Physics Colloquium
Ehud Meron, Ben-Gurion University of the Negev
The nonlinear physics of dryland landscapes

Jan. 14, 2009

Robert Krasny, University of Michigan
Lagrangian Simulations of Fluids and Plasmas
This talk describes recent Lagrangian simulations of incompressible fluids and collisionless plasmas. In both cases, the standard Eulerian formulation is replaced by a Lagrangian version given in terms of the flow map. This leads naturally to a particle discretization. The particles carry vorticity in the case of a fluid and electric charge in the case of a plasma. The induced velocity and electric field are expressed as singular integrals. The numerical method employs kernel regularization for stability, adaptive particle insertion for accuracy, and a multipole treecode for efficiency. Examples to be presented include electron beams in 1D plasmas, and vortex sheets and vortex rings in 2D and 3D fluids. The Lagrangian approach gives direct access to dynamics, revealing the onset of chaos in these flows.
December 10, 2008
3:10 p.m.
Neil Turok, Executive Director, Perimeter Institute for Theoretical Physics
What Banged?
Everything we now see in the Universe emerged from a big bang, 14 billion years ago. But what caused the bang? Was it the beginning of time, or a physical event in a pre-existing universe? The lecture will discuss two radically different theories, both extensions of Einstein's theory of general relativity, and how they may change our views of the evolution and the future of the universe, and of the nature of basic physical laws.
Nov 13, 2008
4:10 p.m.
McLennan Physics 102
Joint Fields/Physics Colloquium
Andrea Liu
, University of Pennsylvania
All around us things seem to get jammed. Before breakfast, coffee grounds and cereal jam as they refuse to flow into our filters and bowls. On the way to work, we are caught in traffic jams. In factories, powders jam as they clog in the conduits that were designed to have them flow smoothly from one side of the factory floor to the other. Our recourse in all these situations is to pound on our containers, dashboards and conduits until the jam miraculously disappears. We are usually so irritated by the jam that we do not notice that the approach to jamming and the jammed state, in all of these situations, have common properties and similar behaviors that are quite different from those in systems near the liquid-solid transition. I will discuss recent ideas and results that point towards some quantitative commonality between such jamming transitions and one of the oldest and most perplexing phenomena in condensed matter physics, namely the glass transition.
November 5, 2008
2:10 p.m.
Andrei Sobolevski, M. V. Lomonossov Moscow State University
Efficient Optimal Transport on the Circle

Consider the problem of optimally matching two measures on the circle, or equivalently two periodic measures on R, where the cost c(x, y) of
matching two points x, y satisfies the Monge condition: c(p, q) + c(r, s) < c(p, s) + c(r, q) whenever p < r and q < s. Motivated by the weak KAM theory, we introduce a notion of locally optimal transport plan and show that all locally optimal transport plans are conjugate to shifts. The theory is applied to a transportation problem arising in image processing: for two sets of point masses, both of which have the same total mass, find an optimal transport plan with respect to a given cost function that satisfies the Monge condition. For the case of N real-valued point masses we present an O(N log epsilon) algorithm that approximates the optimal cost within epsilon; when all masses are integer multiples of 1/M, the algorithm gives an exact solution in O(N log M) operations.
Julie Delon (Telecom Paris), Julien Salomon (U. Paris-Dauphine/CEREMADE), and Andrei Sobolevskii (U. Moscow)

October 22, 2008
2:10 p.m.
Jérémie Bec, CNRS Nice
Turbulent suspensions of heavy particles

Dust, droplets and other ?nite-size impurities with a large mass density suspended in incompressible turbulent flows are commonly encountered in many natural phenomena and industrial processes, such as the growth of raindrops in subtropical clouds, the formation of planetesimals in the early Solar system, and the combustion in Diesel engines. The most salient feature of such suspensions is the presence of strong inhomogeneities in the spatial distribution of particles, a phenomenon dubbed preferential concentration. We show that, depending on the spatial scale at which it is observed, the particle distribution can be of very different natures.

At dissipative scales, where the fluid flow is differentiable, the phase-space density of particles is supported on a dynamically evolving fractal set. This attractor is characterized by non-trivial multiscaling properties, which imply multiscaling of the coarse-grained spatial distribution of the mass
of particles. For larger length scales inside the inertial range of turbulence, the particle distribution is characterized by large voids where the mass is orders of magnitude below its average. Such regions are typically correlated with the vortical structures of the ?ow; this con?rms the classical phenomenological pictures that in turbulent ?ows, eddies act as small centrifuges and eject heavy particles leading to their concentration in the strain-dominated regions. The signature of this voids in the coarse-grained mass probability distribution is an algebraic behavior at small densities. We present a simple model for mass transport that reproduces the same distribution.

J. Bec, L. Biferale, M. Cencini, A. Lanotte, S. Musacchio & F. Toschi, Heavy particle concentration in turbulence at dissipative and inertial scales, Phys. Rev. Lett. 98, 084502, 2007, [arXiv:nlin/0608045] J. Bec & R. Chétrite, Toward a phenomenological approach to the clustering of heavy particles in turbulent flows, New J. Phys. 9, 77 (1-16), 2007, [arXiv:nlin/0701033] J. Bec, M. Cencini, R. Hillerbrand & K. Turitsyn, Stochastic suspensions of heavy particles, Physica D 237, 2037-2050, 2008, [arXiv:0710.2507]

Oct. 8, 2008
2:10 p.m
Michael Stiassnie, Technion
Recurrent solutions of Alber's equation for random water-wave fields
Oct. 8, 2008
3:10 p.m
Yuan Lou, The Ohio State University
The evolution of dispersal
We consider Lotka-Volterra reaction-diffusion-advection models for two competing species in a heterogeneous environment. The two species are assumed to be identical except their dispersal strategies: both species disperse by random movement and/or advection along environmental gradients, but one species has stronger biased movement than the other one. It is shown that two scenarios can occur: if only one species has a strong tendency to move upward the environmental gradients, the two species will coexist; if both species have such strong biased movements, the species with the stronger biased movement will go to extinct. The asymptotic behavior of the principal eigenvalue of an elliptic operator with large advection coefficient plays an important role in the analysis. This talk is based upon a series of joint works with Steve Cantrell, Xinfu Chen, Chris Cosner, and Richard Hambrock.

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