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摘要翻译：
自由零程过程(FRZP)是描述粒子气体在网络相邻节点间跳跃动力学的一个简单随机过程。我们讨论了三种不同的复杂性增加的情况：(a)在过程中网络是固定的刚性几何上的FZRP；(b)在从给定的网络集合中选择的随机图上的FZRP；(c)在过程中拓扑以依赖于当前粒子分布的方式连续变化的动态网络上的FZRP。例(a)提供了凝结现象的一个非常简单的实现，凝结现象表现为粒子在最大程度的结点上出现凝结。情况(b)是非常有趣的，因为在典型的图系集上的平均作为系统的一种均匀化，从FZRP的观点来看，它使所有节点都是相同的。在情形(c)中，粒子的分布和网络的动力学是相互耦合的。这种耦合的强度取决于两个时间尺度的比值：拓扑结构的变化和FZRP的变化。我们将讨论这种相互作用的一个具体例子，并表明它导致了一个有趣的相图。
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英文标题：
《Free zero-range processes on networks》
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作者：
L. Bogacz, Z. Burda, W. Janke, and B. Waclaw
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最新提交年份：
2007
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分类信息：
一级分类：Physics 物理学
二级分类：Statistical Mechanics 统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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英文摘要：
A free zero-range process (FRZP) is a simple stochastic process describing the dynamics of a gas of particles hopping between neighboring nodes of a network. We discuss three different cases of increasing complexity: (a) FZRP on a rigid geometry where the network is fixed during the process, (b) FZRP on a random graph chosen from a given ensemble of networks, (c) FZRP on a dynamical network whose topology continuously changes during the process in a way which depends on the current distribution of particles. The case (a) provides a very simple realization of the phenomenon of condensation which manifests as the appearance of a condensate of particles on the node with maximal degree. The case (b) is very interesting since the averaging over typical ensembles of graphs acts as a kind of homogenization of the system which makes all nodes identical from the point of view of the FZRP. In the case (c), the distribution of particles and the dynamics of network are coupled to each other. The strength of this coupling depends on the ratio of two time scales: for changes of the topology and of the FZRP. We will discuss a specific example of that type of interaction and show that it leads to an interesting phase diagram.
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PDF链接：
https://arxiv.org/pdf/705.0549
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