01/07/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building
Hermano Frid, 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
Waldyr Oliva, CAMGSD and ISR - IST
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
David Kinderlehrer, Carnegie Mellon University
Remarks about diffusion mediated transportTypical 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 evolutionsWe 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 InvariantsThe 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
Renato Iturriaga, 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
Rui Loja Fernandes, Instituto Superior Técnico
Linearization of Poisson Brackets
29/04/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building
Luis Barreira, Instituto Superior Técnico
Poincaré recurrence, geodesic flows, hyperbolic geometryToday, 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
Tanya Schmah, 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
Jonathan Wattis, University of Nottingham
A Coarse-graining approximation for the Becker-Doring equations
25/03/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building
Waldyr Oliva, 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 motionWe 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 LayersWe consider a nonrelativistic quantum particle constrained to a curved hard-wall layer of constant width built over a noncompact surface embedded in . Under the assumption that the surface curvatures vanish at infinity, we find sufficient conditions which guarantee the existence of geometrically induced bound states.