Mathematical Physics Seminar
April Schedule
Organizer- Joel L. Lebowitz
email: lebowitz@math.rutgers.edu
- Speaker- L. Gray, University of Minnesota
- Title-Phase Transitions in 1-Dimanesional Cellular Automata
Models of Traffic
- Time/place-Thursday, 4/3/03 11:30am in Hill 705
- Abstract-Traffic models provide a natural context for the phenomenon of phase
separation in 1-dimensional particle models with particle conservation,
since the formation of traffic jams can be thought of as a kind of
"coarsening" that leads to such a separation.
Some simple models will be discussed to illustrate some of the
features of particle dynamics that can produce this phenomenon.
Please note there will be a brown bag lunch between the 2
seminars this morning. Bring your sandwich.
Coffee and homemade cookies will be
available.
Speaker-D. Mukamel, The Weizmann Institute
Title-Phase Separation in One-Dimensional Driven Systems
Time/place-Thursday, 4/3/03 1:30pm in Hill 705
Abstract-Unlike systems in thermal equilibrium, certain one dimensional
driven diffusive models with local noisy dynamics exhibit
phenomena like phase transitions and phase separation.
A criterion for the existence of phase separation in such
systems will be described. It is based on a correspondence
between the dynamics of the driven model and that of a
related zero-range-process.
In models which have in the past been demonstrated to exhibit
phase separation, the phase separated state is of a peculiar
nature, with non-fluctuating density within the bulk of the
macroscopic domains. The criterion is used in order to introduce
a class of models which is shown to exhibit more ordinary
phase separated states with fluctuating bulk density.
Speaker- E. Lutz, Yale University
Title-Anomalous Levy diffusion: from the flight of an
albatross to optical lattices
Time/place-Thursday 4/10/03 11:30am in Hill 705
Abstract-We discuss the application of Levy stable distributions to the description
of physical systems with strong fluctuations. In particular, we derive a
master equation for quantum Levy processes using path integral methods. The
classical limit (fractional Klein-Kramers equation), Levy decoherence and
some related experiments are further addressed.
Please note there will be a brown bag lunch between the 2
seminars this morning. Bring your sandwich.
Coffee and homemade cookies will be
available.
Speaker-K. Gawedski, ENS-Lyon and IAS Princeton
Title-Fluctuation theorem for Lagrangian flow
Time/place-Thursday 4/10/03 1:30pm in Hill 705
Abstract-Large deviations function for stretching rates
in smooth random compressible velocities satisfies
a simple identity relating its values for opposite
rates. I shall discuss the example provided by
the Kraichnan ensemble of velocities and some open
problems.
Time/place-Thursday 4/17/03 NO SEMINAR
Speaker-M. Nicol, University of Surrey, England
Title-Statistical properties of endomorphisms
and compact group extensions
Time/place-Thursday 4/24/03 11:30am in Hill 705
Abstract-We consider the statistical properties of endomorphisms
under the assumption that the associated
Perron-Frobenius operator is quasicompact. In particular
we consider the central limit theorem, weak invariance principle and
law of the iterated logarithm
for sufficiently regular observations.
We also give sufficient conditions for quasicompactness of the
Perron-Frobenius operator to lift to the corresponding
equivariant operator on a compact group extension of the base.
This leads to statistical limit theorems
for equivariant observations on compact group extensions.
Examples considered include compact group extensions of
piecewise uniformly expanding maps (for example Lasota-Yorke maps),
and subshifts of finite type, as well as systems that are nonuniformly
expanding or nonuniformly hyperbolic.
Please note there will be a brown bag lunch between the 2
seminars this morning. Bring your sandwich.
Coffee and homemade cookies will be
available.
Speaker-S.Olla, Université de Paris-Dauphine
Title-Fluctuations in Systems with Conservation Laws
Time/place-Thursday 4/24/03 1:30pm in Hill 705
Abstract-In a molecular gas dynamics in equilibrium, the macroscopic evolution
of the fluctuations of the conserved quantities (density, momentum and
energy) is governed by the linearized Euler equations in a hyperbolic
scaling of space and time, while Navier-Stokes diffusion terms
appear in the diffusive scaling. Even for systems with stochastic dynamics
these are very challenging problems.
I will review some (few) recent results and (many) open problems in the
mathematically rigorous derivation of such limits.