Seminars and Colloquia by Series

Gradient Corrections in Atomic Physics

Series
Math Physics Seminar
Time
Friday, October 27, 2017 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles Room 202
Speaker
Rafael BenguriaCatholic University of Chile
During the last few years there has been a systematic pursuit for sharp estimates of the energy components of atomic systems in terms of their single particle density. The common feature of these estimates is that they include corrections that depend on the gradient of the density. In this talk I will review these results. The most recent result is the sharp estimate of P.T. Nam on the kinetic energy. Towards the end of my talk I will present some recent results concerning geometric estimates for generalized Poincaré inequalities obtained in collaboration with C. Vallejos and H. Van Den Bosch. These geometric estimates are a useful tool to estimate the numerical value of the constant of Nam's gradient correction term.

Persistence of translation symmetry in the BCS model with radial pair interaction

Series
Math Physics Seminar
Time
Tuesday, March 28, 2017 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Alissa GeisingerUniversity of Tuebingen, Germany
We consider the two-dimensional BCS functional with a radial pair interaction. We show that the translational symmetry is not broken in a certain temperature interval below the critical temperature. For this purpose, we first introduce the full BCS functional and the translation invariant BCS functional. Our main result states that theminimizers of the full BCS functional coincide with the minimizers of the translation invariant BCS functional for temperatures in the aforementioned interval. In the case of vanishing angular momentum our results translate to the three dimensional case. Finally, we will explain the strategy and main ideas of the proof. This is joint work with Andreas Deuchert, Christian Hainzl and Michael Loss.

Gevrey smoothing of weak solutions of the homogeneous Boltzmann equation for Maxwellian molecules

Series
Math Physics Seminar
Time
Tuesday, March 14, 2017 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Tobias RiedKarlsruhe Institute of Technology
We study regularity properties of weak solutions of the homogeneous Boltzmann equation. While under the so called Grad cutoff assumption the homogeneous Boltzmann equation is known to propagate smoothness and singularities, it has long been suspected that the non-cutoff Boltzmann operator has similar coercivity properties as a fractional Laplace operator. This has led to the hope that the homogenous Boltzmann equation enjoys similar smoothing properties as the heat equation with a fractional Laplacian. We prove that any weak solution of the fully nonlinear non-cutoff homogenous Boltzmann equation (for Maxwellian molecules) with initial datum $f_0$ with finite mass, energy and entropy, that is, $f_0 \in L^1_2(\R^d) \cap L \log L(\R^d)$, immediately becomes Gevrey regular for strictly positive times, i.e. it gains infinitely many derivatives and even (partial) analyticity.This is achieved by an inductive procedure based on very precise estimates of nonlinear, nonlocal commutators of the Boltzmann operator with suitable test functions involving exponentially growing Fourier multipliers.(Joint work with Jean-Marie Barbaroux, Dirk Hundertmark, and Semjon Vugalter)

The one-dimensional discrete moment problem and the realisability problem in statistical mechanics

Series
Math Physics Seminar
Time
Monday, November 14, 2016 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Tobias KunaUnisrsity of Reading, UK
The discrete truncated moment problem considers the question whether given a discrete subsets $K \subset \mathbb{R}$ and a sequence of real numbers one can find a measure supported on $K$ whose (power) moments are exactly these numbers. The truncated moment is a challenging problem. We derive a minimal set of necessary and sufficient conditions. This simple problem is surprisingly hard and not treatable with known techniques. Applications to the truncated moment problem for point processes, the so-called relizability or representability problem are given. The relevance of this problem for statistical mechanics in particular the theory of classic liquids, is explained. This is a joint work with M. Infusino, J. Lebowitz and E. Speer.

On some models in classical statistical mechanics

Series
Math Physics Seminar
Time
Friday, April 15, 2016 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Alex GrigoThe University of Oklahoma
In this talk we will consider a few different mathematical models of gas-like systems of particles, which interact through binary collisions that conserve momentum and mass. The aim of the talk will be to present how one can employ ideas from dynamical systems theory to derive macroscopic properties of such models.

Self-Avoiding Modes of Motion in a Deterministic Lorentz Lattice Gas

Series
Math Physics Seminar
Time
Friday, October 16, 2015 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Ben WebbBrigham Young University
We consider the motion of a particle on the two-dimensional hexagonal lattice whose sites are occupied by flipping rotators, which scatter the particle according to a deterministic rule. We find that the particle's trajectory is a self-avoiding walk between returns to its initial position. We show that this behavior is a consequence of the deterministic scattering rule and the particular class of initial scatterer configurations we consider. Since self-avoiding walks are one of the main tools used to model the growth of crystals and polymers, the particle's motion in this class of systems is potentially important for the study of these processes.

Random reflections, symmetrizations, and foldings on the sphere

Series
Math Physics Seminar
Time
Tuesday, February 17, 2015 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Almut BurchardUniversity of Toronto
Two-point symmetrizations are simple rearrangementsthat have been used to prove isoperimetric inequalitieson the sphere. For each unit vector u, there is atwo-point symmetrization that pushes mass towardsu across the normal hyperplane.How can full rotational symmetry be recovered from partialinformation? It is known that the reflections at d hyperplanes in general position generate a dense subgroup of O(d);in particular, a continuous function that is symmetric under thesereflections must be radial. How many two-point symmetrizationsare needed to verify that a function which increases under thesesymmetrizations is radial? I will show that d+1 such symmetrizationssuffice, and will discuss the ergodicity of the randomwalk generated by the corresponding folding maps on the sphere.(Joint work with G. R. Chambers and Anne Dranovski).

Connes distance and aperiodic order

Series
Math Physics Seminar
Time
Friday, November 14, 2014 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Jean SavinienUniversity of Lorraine, Metz, France
We build a family of spectral triples for a discrete aperiodic tiling space, and derive the associated Connes distances. (These are non commutative geometry generalisations of Riemannian structures, and associated geodesic distances.) We show how their metric properties lead to a characterisation of high aperiodic order of the tiling. This is based on joint works with J. Kellendonk and D. Lenz.

Mixing rates of interacting particle systems

Series
Math Physics Seminar
Time
Thursday, November 6, 2014 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Yao LiCourrant Institute, NY
In this talk I will begin with our recent results on non-equilibrium steady states (NESS) of a microscopic heat conduction model, which is a stochastic particle system coupled to unequal heat baths. This stochastic model is derived from a mechanical chain model (Eckmann and Young 2006) by randomizing certain quantities while retaining the other features. We proved various results including the existence and uniqueness of NESS and the exponential rate of mixing. Then I will follow with an energy dependent Kac-type model that is obtained from an improved version of randomization of the “local" dynamics. We rigorously proved that this Kac-type model has a mixing rate $\sim t^{-2}$. In the end, I will show that slow (polynomial) mixing rates appear in a large class of statistical mechanics models.

Hopf fibrations for oceanic waves and turbulent pipe flows

Series
Math Physics Seminar
Time
Thursday, September 18, 2014 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Francesco FedeleSchool of Civil and Environmental Engineering, Georgia Tech
I propose a generalization of Hopf fibrations to quotient the streamwise translation symmetry of water waves and turbulent pipe flows viewed as dynamical systems. In particular, I exploit the geometric structure of the associated high dimensional state space, which is that of a principal fiber bundle. Symmetry reduction analysis of experimental data reveals that the speeds of large oceanic crests and turbulent bursts are associated with the dynamical and geometric phases of the corresponding orbits in the fiber bundle. In particular, in the symmetry-reduced frame I unveil a pattern-changing dynamics of the fluid structures, which explains the observed speed u ≈ Ud+Ug of intense extreme events in terms of the geometric phase velocity Ug and the dynamical phase velocity Ud associated with the orbits in the bundle. In particular, for oceanic waves Ug/Ud~-0.2 and for turbulent bursts Ug/Ud~0.43 at Reynolds number Re=3200.

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