TALK - Candidate for Probability Search
Stochastic Systems Seminar
Division of Applied Mathematics | |
TALK - Candidate for Probability Search
Area: Probability, stochastic processes, small noise perturbations, filtering... | |
Abstract: We discuss a circle of ideas relating to the effect of small noise upon conservative dynamical systems (mainly ODE's) with bifurcations. After quickly reviewing the classical reduction problem associated with a randomly-perturbed simple harmonic oscillator, we consider the effect of critical points upon such systems. In general, critical points lead to stochastic processes on "stratified spaces" such as graphs and whiskered spheres. We then discuss the nature and origin of the "glueing conditions" which govern these processes where the strata meet. We understand that these glueing conditions are tantamount to solvability criteria of a coupled collection of PDE's (which arise from a natural singular perturbations analysis). Time permitting, we finish by discussing some related open problems in this area.
TALK - Candidate for Probability Search
Area: Numerical methods for energy landscapes and their applications | |
Abstract: Many problems in physics, material sciences, chemistry and biology can be abstractly formulated as a system that navigates over a complex energy landscape of high or infinite dimensions. Well-known examples include pahse transitions of condensed matter, conformational changes of biopolymers, and chemical reactions. The state of these systems is confined for long periods of time in metastable regions in configuration space and only rarely switches from one region to another. The separation of time scale is a consequence of the disparity between the effective thermal energy and typical energy barrier in these systems, and their dynamics effectively reduce to a Markov chain on the metastable regions. The analysis and computation of the transition pathways and rates between the metastable states represent the major challenges, especially when the energy landscape exhibits multiscale features. I will present the numerical methods that have proven to be effective for some truly complex systems in material science and chemistry.
This is a joint work with Weinan E and Eric Vanden-Eijnden.
TALK - Candidate for Probability Search
Area: Communication networks, networking and traffic paradigms, ... | |
Abstract: Self-similar/heavy-tailed statistical phenomena are observed in a large number of natural and man-made systems ranging from earthquakes and genetics to telephone networks and operating systems. Effects of such phenomena on network performance have received considerable attention in past years but these studies have lacked mathematically sound results with clear engineering implications.
In this context, we develop a novel large deviations approach to establish the fundamental criticality of the exp{-sqrt[x]} distribution in the classical processor sharing model. This work is motivated by the recent application of processor sharing to modeling of TCP, a protocol that controls 90% of Internet traffic.
Scientific Computing Seminar
Princeton University, Department of Chemical Engineering and PACM **CANCELLED AND RESCHEDULED TO MARCH ... PLEASE NOTE |
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