
Fields Institute Colloquium/Seminar in Applied Mathematics
20082009
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 superconductivity, 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.
200809
talks held at the Fields Institute

Wednesday,
May 13
2:10 p.m. 
Giuseppe
Savare (Universita di Pavia)
Viscous and rateindependent evolutions
Solutions of rateindependent 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. Rateindependence is guaranteed by the 1homogeneity
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 Doublynonlinear 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,
BenGurion University of the Negev
Periodic vs. scalefree patterns: reconciling the dichotomy
of dryland vegetation
Field observations of vegetation patchiness in drylands reveal
periodic patterns with characteristic length scales along
with scalefree patterns characterized by broad patchsize
distributions, often reported to obey powerlaws. 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
aboveground and belowground biomass, we elucidate mechanisms
that control patchsize distributions in waterlimited systems,
and identify physical and ecological circumstances that lead
to periodic patterns and to scalefree patterns.

March
5, 2009
4:10 p.m.
McLennan Physics 102 
Joint
Fields/Physics Colloquium
Ehud Meron, BenGurion University of the Negev
The
nonlinear physics of dryland landscapes 
Jan. 14, 2009
3:10pm

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 preexisting 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
Jamming
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 liquidsolid 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 realvalued 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. ParisDauphine/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 ?nitesize 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 phasespace density of particles is supported on a dynamically
evolving fractal set. This attractor is characterized by nontrivial
multiscaling properties, which imply multiscaling of the coarsegrained
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 straindominated regions. The signature
of this voids in the coarsegrained mass probability distribution
is an algebraic behavior at small densities. We present a
simple model for mass transport that reproduces the same distribution.
References:
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 (116), 2007,
[arXiv:nlin/0701033] J. Bec, M. Cencini, R. Hillerbrand &
K. Turitsyn, Stochastic suspensions of heavy particles, Physica
D 237, 20372050, 2008, [arXiv:0710.2507]



Oct.
8, 2008
2:10 p.m 
Michael
Stiassnie, Technion
Recurrent solutions of Alber's equation for random waterwave
fields 
Oct.
8, 2008
3:10 p.m 
Yuan
Lou, The Ohio State University
The evolution of dispersal
We consider LotkaVolterra reactiondiffusionadvection 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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