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Analysis, Geometry, and Dynamical Systems Seminar   RSS

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11/11/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building
, Instituto Superior Técnico

Combining logic systems: Why, how, what for?

Motivated by applications in artificial intelligence and software engineering that require the joint use of different deduction formalisms, the interest in combination of logic systems has recently been growing, but the topic is also of interest on purely theoretical grounds. Several forms of combination have been studied, like product, fusion, temporalization, parameterization, synchronization and, more recently, fibring. In this guided tour of the issues raised by the combination of logics, we define fibring (the most general form of combination) in a very simple (yet useful) context, discuss some examples and establish some interesting transference results, namely preservation of strong completeness and nonpreservation of congruence. We end the tour with a brief reference to some open problems. The talk is based on a recent overview paper (together with C. Sernadas) available at http://www.cs.math.ist.utl.pt/ftp/pub/SernadasA/03-SS-fiblog22.pdf to appear in the CIM Bulletin.

04/11/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building
Paulo Pinto, Instituto Superior Técnico

Classification of Modular Invariants and Subfactors

21/10/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building
Nara Jung, Centro de Análise Matemática, Geometria e Sistemas Dinâmicos

Continuity properties of D2 u in BV2 with strict convergence

14/10/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building
, Université Paris 13

Homotopy equivalences between completed classifying spaces of finite groups

07/10/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building
, Instituto Superior Técnico

Dirac operator, instantons and holomorphic bundles

30/09/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building
, Universidade do Porto

Symmetry groupoids, synchrony, and coupled cell networks

23/09/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building
Joana Ventura, Instituto Superior Técnico

Homological algebra for the representation Green functor for Abelian groups

09/09/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building
, The University of Strathclyde in Glasgow

Multiplicity of periodic solutions in mean-field theories of magnetisation

29/07/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building
Leonardo Macarini, IMPA, Rio de Janeiro

Hofer-Zehnder sensitive capacity of cotangent bundles and symplectic submanifolds

We will consider a modified Hofer-Zehnder capacity sensitive to the homotopy class of the periodic orbits and show that if a symplectic manifold admits a free Hamiltonian circle action then it has bounded Hofer-Zehnder (sensitive) capacity. We give two applications of this result. Firstly, we prove that every closed symplectic submanifold has a neighborhood with finite Hofer-Zehnder capacity. Secondly, consider a closed manifold with an effective circle action whose fixed point set has trivial normal bundle. Then, its standard cotangent bundle has bounded Hofer-Zehnder capacity.

22/07/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building
, Wichita State University

Measures of maximal dimension for hyperbolic diffeomorphisms

15/07/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building
, Max-Planck-Institut für Physik komplexer Systeme, Dresden

Dimension estimates in nonconformal dynamical systems

14/07/2003, 11:00 — 12:00 — Room P3.10, Mathematics Building
Maria José Pacífico, Universidade Federal do Rio de Janeiro

Lorentz attractor versus singular hyperbolic attractor

08/07/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building
, Universitá degli Studi del Piemonte Orientale

Existence and nonexistence results for anisotropic quasilinear elliptic equations

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
, 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
, 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.

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