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Mass Transport Models on Networks

网络上的大众运输模型

基本信息

批准号：
155268393
负责人：
Professor Dr. Wolfhard Janke
金额：
--
依托单位：
Institut für Theoretische Physik
依托单位国家：
德国
项目类别：
Research Grants
财政年份：
2009
资助国家：
德国
起止时间：
2008-12-31 至 2013-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/155268393?language=en
关键词：
Mass Transport Models Networks

项目摘要

The study of mass transport processes in one-and two dimensional systems led to considerable progress in the understanding of statistical systems out-of-equilibrium, for which guiding principles and classification schemes are missing in general. Usually these studies focus on simple regular topologies. On the other hand, a variety of out-of-equilibrium processes is going on in natural systems, which are nowadays summarized under complex networks. The analysis of dynamical processes on complex networks is just in their infancy. An important class of processes is mass transport ( mass in a generic sense of flow of particles, energy, information or traffic) for which we shall implement the ubiquitous noise, inherent in any transport, via a stochastic description. We shall focus on generalizations of the zero-range process on non-trivial topologies, which may serve as building blocks for larger networks in the spirit of the renormalization group, but remain analytically tractable. For the field of network dynamics this should provide an analytic understanding as well as steps towards an embedding into a larger context and a classification of stationary states observed in network simulations. From the perspective of statistical physics out-of-equilibrium, our project aims at generalizations towards more realistic geometries, real processes such as protein traffic inside cells, and more realistic (e.g. open) boundary conditions, non-zero range processes with short- and long-range interactions and feedbacks, extensions of fluctuation theorems and analysis of transients in the approach of stationary states. The expertise of our two groups in mass transport and numerical simulations (W. Janke) and network dynamics and analytical calculations (H. Meyer-Ortmanns) will supplement each other and lead to a productive collaboration when it is combined.

对一维和二维系统中质量输运过程的研究使得对统计系统非平衡状态的理解取得了相当大的进展，这类系统通常缺乏指导原则和分类方案。这些研究通常集中在简单的规则拓扑上。另一方面，自然系统中也发生着各种不平衡过程，这些过程现在被归纳为复杂的网络。复杂网络上动态过程的分析才刚刚起步。一类重要的过程是质量传递（一般意义上的粒子、能量、信息或交通的流动），我们将通过随机描述实现任何传递中固有的无所不在的噪声。我们将关注非平凡拓扑上的零范围过程的推广，这些拓扑可以作为重正化群精神中更大网络的构建块，但在分析上仍然是可处理的。对于网络动力学领域，这应该提供一种分析性的理解，以及在更大的背景下嵌入的步骤，以及在网络模拟中观察到的固定状态的分类。从统计物理失衡的角度来看，我们的项目旨在推广到更现实的几何形状，真实的过程，如细胞内的蛋白质运输，更现实的（如开放）边界条件，具有短期和长期相互作用和反馈的非零范围过程，波动定理的扩展以及在稳态方法中的瞬态分析。我们两个小组在质量运输和数值模拟（W. Janke）和网络动力学和分析计算（H. Meyer-Ortmanns）方面的专业知识将相互补充，并在结合时产生富有成效的合作。