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Viscoelastic subdiffusion, transport and anomalous rate processes in multistablepotentials: in and out of thermal equilibrium, influence of time-periodic andstochastic fields

多稳态势中的粘弹性次扩散、输运和反常速率过程：热平衡内外，时间周期场和随机场的影响

基本信息

批准号：
193948139
负责人：
Privatdozent Dr. Igor Goychuk
金额：
--
依托单位：
Lehrstuhl für Kristallografie und Strukturphysik
依托单位国家：
德国
项目类别：
Research Grants
财政年份：
2011
资助国家：
德国
起止时间：
2010-12-31 至 2015-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/193948139?language=en
关键词：
Viscoelastic subdiffusion transport anomalous rate

项目摘要

This project is devoted to anomalously slow diffusion in complex viscoelastic media. Such subdiffusion is typified by long lived anti-correlations of a Brownian particle displacements rather than by diverging mean residence time in trapping domains. It can be described by Generalized Langevin Equation with a power law decaying memory friction and fractional Gaussian noise related by the fluctuation dissipation theorem. This project will take advantage of a complementary and more realistic approach where the memory kernel is approximated by a finite sum of exponentials exhibiting fractal scaling. This allows for a multi-dimensional Markovian embedding of a profoundly non-Markovian stochastic dynamics and for a beneficial use of well-established methodology developed for Markovian systems. This project is focusing on: (i) bistable subdiffusive dynamics mimicking conformational transitions in macromolecules due to intrinsic viscoelasticity, or due to viscoelasticity of the environment (e.g. enzymes or ionic channels in biological membranes), and (ii) viscoelastic transport in spatially periodic structures, especially driven out of the thermal equilibrium by time-periodic fields. A number of new anomalous nonequilibrium phenomena, such as e.g. subdiffusive rocking ratchets, will be investigated.

这个项目致力于研究复杂粘弹性介质中的异常缓慢扩散。这种次扩散的特点是布朗粒子位移的长寿命反关联，而不是捕获区平均停留时间的发散。它可以用广义朗之万方程来描述，该方程具有幂定律、衰减记忆摩擦和分数次高斯噪声，并与涨落耗散定理相关联。这个项目将利用一种补充的和更现实的方法，其中内存内核是由表现出分形比例的有限指数和来近似的。这允许多维马尔可夫嵌入深刻的非马尔科夫随机动力学，并允许有益地使用为马尔可夫系统开发的成熟的方法。这个项目的重点是：(I)双稳态亚扩散动力学，模拟由于本征粘弹性或由于环境(例如生物膜中的酶或离子通道)的粘弹性而导致的大分子的构象转变，以及(Ii)空间周期性结构中的粘弹性输运，特别是在时间周期场的驱动下脱离热平衡。我们将研究一些新的异常非平衡现象，例如亚扩散摇摆棘轮。