Mass Transport Models on Networks

对一维和二维系统中的质量传输过程的研究导致了对非平衡统计系统的理解取得了长足的进步，对非平衡统计系统的指导原则和分类方案通常是缺失的。通常这些研究集中在简单的正则拓扑上。另一方面，自然系统中正在发生着各种不平衡的过程，这些过程现在被总结为复杂网络。对复杂网络动态过程的分析还处于初级阶段。一类重要的过程是质量传输(粒子、能量、信息或交通的一般意义上的质量)，我们将通过随机描述来实现任何传输中固有的无处不在的噪声。我们将集中讨论零程过程在非平凡拓扑上的推广，在重整化群的精神下，零程过程可以作为更大网络的构建块，但在分析上仍然是容易处理的。对于网络动力学领域，这应该提供一种分析性的理解，以及朝着嵌入到更大的背景中以及在网络模拟中观察到的静止状态的分类的步骤。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结构，真实的过程，如细胞内的蛋白质交通，以及更现实的(例如，开放)边界条件，具有短期和远程相互作用和反馈的非零程过程，涨落定理的扩展，以及用定态方法分析瞬变。我们两个团队在质量传输和数值模拟(W.Janke)以及网络动力学和分析计算(H.Meyer-Ortmanns)方面的专业知识将相辅相成，当它们结合在一起时，将导致富有成效的合作。

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.