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Infinite Dimensional and Stochastic Dynamical Systems(2)

已有 2622 次阅读 2015-4-22 09:34 |系统分类:科研笔记

(4) Theory and Applications of Stochastic PDEs

Stochastic Partial Differential Equations (SPDEs) are the mathematical tool of choice to model many physical, biological and economic systems subject to the influence of noise, be it intrinsic (modelling uncertainties, inherent features of the theory, ...) or extrinsic (environmental influences, random user input, ...). SPDEs also arise when considering deterministic models from random initial conditions, or as tractable approximations to complex deterministic systems. In many cases the presence of noise leads to new phenomena, both at the mathematical and the phenomenological level. The goal of this workshop is to bring in contact some of the world leaders in SPDE theory, especially those working on numerical approximations and applications, with applied mathematicians working on models that incorporate both spatial structure and randomness. We will focus in particular on numerical schemes, multiscale structures, finite dimensional approximations (for example finite element methods), asymptotic analysis, particle methods, etc. On a mathematical level, some of the topics of interest will be convergence rates, optimality criteria and limit theorems.


(5) Stochastic Modeling of the Oceans and Atmosphere

The oceans and the atmosphere define the environment in which we live, and its understanding is of tremendous economic and social importance. Mathematical models are a key component of our understanding of the oceans and the atmosphere, and thus the Earth’s climate system. Due to uncertainties in various processes or components in this coupled oceansatmosphere system, the mathematical models are subject to stochastic effects, such as uncertain parameters, random boundary or initial conditions, and missing or unresolved mechanisms. Therefore the coupled oceansatmosphere system is essentially a stochastic dynamical system, with multiple components, multiple timespace scales, and multiple interacting physicalchemicalbiological processes. Meanwhile, the field of stochastic dynamical systems has achieved significant progress in the past decade, benefiting from the fruitful crossfertilization of the dynamical systems and stochastic analysis communities. The further advances in the investigation of the coupled oceansatmosphere system, as a stochastic dynamical system, can greatly benefit from the participation of the stochastic dynamical systems community. The goal of this workshop is to bring together a group of experts from the oceansatmosphere community and the stochastic dynamical systems community, including some people who have been working in this interface, to summarize the past achievements and exchange ideas for future studies. It is expected that this workshop will play an important role in nurturing and guiding this exciting interdisciplinary field.


(6) Stochastic Modeling of Biological Processes

Stochasticity is unavoidable when considering biological systems and processes, both at the macro scale with populations surviving in rapidly and unpredictably changing environments, but also and especially at the molecular level, where entropic considerations can have significant implications. Not only must systems be robust but some systems actually rely upon Brownian motions in order to operate efficiently. The workshop will address topics from the spread of diseases, the dispersal of species in spatially random environments, neuronal acivity (singly and in networks), genetic evolution, cellular locomotion, wound healing, genetic regulatory systems, among other things.



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