Analysis, Geometry, and Dynamical Systems Seminar   RSS

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01/07/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building
, Instituto de Matemática Pura e Aplicada, Rio de Janeiro e Centro de Matemática e Aplicações Fundamentais

Soluções espacialmente periódicas para as equações de Euler em dinâmica dos gases relativística

26/06/2003, 16:30 — 17:30 — Room P3.10, Mathematics Building

Non-holonomic Systems and the Geometry of Constraints

26/06/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building
Jair Koiller, Fundação Getúlio Vargas, Rio de Janeiro

Flagelar Locomotion Via Geometric Mechanics

26/06/2003, 14:30 — 15:30 — Room P3.10, Mathematics Building
Matthew Perlmutter, CAMGSD - IST

Gauged Poisson Structures

26/06/2003, 11:00 — 12:00 — Room P3.10, Mathematics Building
Giorgio Fusco, Università degli Studi dell'Aquila

Three Time Scales in the Steepest Descent Dynamics of a Regularized Nonconvex Functional of the Gradient

26/06/2003, 10:00 — 11:00 — Room P3.10, Mathematics Building
Piero Negrini, Universitá di Roma I - La Sapienza

Integrability, Nonintegrability and Chaos in a System Related to the Riemann Ellipsoid Problem

23/06/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building
, Carnegie Mellon University

Remarks about diffusion mediated transport

Typical flow regimes in aerodynamics and fluid dynamics involve large Reynolds numbers. There are important issues regarding, for example, the relationship between kinetic and potential energy or turbulent behaviour. Here we shall discuss diffusion mediated transport, a property of systems with quite small Reynolds numbers, about 0.05. This is the environment of the living cell.

Diffusion mediated transport is implicated in the operation of many molecular level systems. These include some liquid crystal and lipid bilayer systems, and, especially, the motor proteins responsible for eukaryotic cellular traffic. All of these systems are extremely complex and involve subtle interactions on varying scales. Earlier, we were interested in the design of material microstructure, typically in order to optimize the performance of devices that do work by changing their microstructure. In such gadgets, like shape memory or magnetostrictive, energy transduction is very close to equilibrium in order to minimize the energy budget - think about remote controls. The chemical mechanical transduction in motor proteins is, by contrast, quite distant from equilibrium. These systems function in a dynamically metastable range.

We give a general dissipation principle and illustrate how it may be used to describe transport, for example in flashing rachet and conventional kinesin type motors. We introduce new methods based on the Monge-Kantorovich problem and Wasserstein metric to explore this. The equations we obtain are analogous to the ones already formulated by Astumian, and Oster, Ermentrout, and Peskin, and by Adjari and Prost and their collaborators. What is necessary for transport? What is the role of diffusion? What is the role of other elements of the system and how can dissipation be exploited to understand this? How successful are we? The opportunity to discover the interplay between chemistry and mechanics and to elaborate the implications of metastability could not offer a more exciting venue.

We are reporting here on joint work with Michel Chipot, Jean Dolbeault, Stuart Hastings, and Michal Kowalczyk.

17/06/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building
Cristodor Ionescu, Institute of Mathematics, Romanian Academy, Bucharest

Some remarks on evolutions

We present some result concerning evolutions of Noetherian local rings of characteristic zero using Andre-Quillen homology of commutative rings.

12/06/2003, 11:00 — 12:00 — Room P3.10, Mathematics Building
Christopher Earles, Rice University, Houston

Residue Theorems and Lie Algebroid Invariants

The recent work of Harvey and Lawson has resulted in a family of residue theorems relating the singular sets (viewed as rectifiable currents) of a vector bundle map to the Chern-Weil characteristic forms of the bundles. Many of the classical singularity theorems (e.g., the Argument Principle, the Poincare-Hopf Index Theorem, and the Riemann-Roch Theorem) are special cases of these more general formulae.

In this talk, I will review briefly the techniques used by Harvey and Lawson and give an account of current work to extend these to the study of Lie algebroids.

03/06/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building
, CIMAT, Guanajuato

Convergence of viscosity solutions of random Hamilton Jacobi equations

27/05/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building
Miguel Rodríguez Olmos, Instituto Superior Técnico

The topology of symplectic quotients for cotangent bundles

20/05/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building
Claudia Valls, Università di Roma

Weak KAM Theory for multidimensional maps

13/05/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building
Gianluigi Del Magno, Centro de Análise Matemática, Geometria e Sistemas Dinâmicos

Ergodic semifocusing billiards

06/05/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building
, Instituto Superior Técnico

Linearization of Poisson Brackets

29/04/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building
, Instituto Superior Técnico

Poincaré recurrence, geodesic flows, hyperbolic geometry

Today, we are arguably in possession of a satisfactory approach to a quantitative description of recurrence. As one knows well: Poincaré only established that orbits return infinitely often, not how often or when they return.

This will be a colloquium type exposition of recent results that shed new light on the subject, also discussing joint work with Benoît Saussol, Christian Wolf, and Gianluigi Del Magno. The talk will include the view of the (maybe classical) hyperbolic geometer and briefly some consequences for number theory. No prerequisites from dynamical systems or ergodic theory will be necessary.

08/04/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building
, University of Warwick

The local geometry of symmetric Hamiltonian systems on cotangent bundles

01/04/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building
, University of Nottingham

A Coarse-graining approximation for the Becker-Doring equations

25/03/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building
, Centro de Análise Matemática, Geometria e Sistemas Dinâmicos e Instituto de Sistemas e Robótica

On the dimension and smoothness of attractors

18/03/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building
Alexei Davydov, Vladimir State University, Russia

Optimal strategies of time averaged optimization of cyclic motion

We consider dynamic inequalities with locally bounded derivatives on the circle and optimize the time averaged profit along admissible motions which are defined for all nonegative time. We describe the nature of optimal strategies, generic swichings between them when the problem depends additionally from a one dimensional parameter, and also the respective singularities of the averaged profit like a function of the parameter.

11/03/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building
David Krejcirik, Centro de Análise Matemática, Geometria e Sistemas Dinâmicos

Bound States in Curved Quantum Layers

We consider a nonrelativistic quantum particle constrained to a curved hard-wall layer of constant width built over a noncompact surface embedded in R3 . Under the assumption that the surface curvatures vanish at infinity, we find sufficient conditions which guarantee the existence of geometrically induced bound states.

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