发帖
雷达卡
摘要翻译：
研究了具有距离相关随机链路的小世界网络上的扩散驱动过程。随机折叠聚合物链上的传输、任务完成网络中的同步问题以及梯度驱动网络上的传输等因素推动了这类网络上扩散的研究。改变距离相关参数，在网络随机游动的背景下，我们得到了一个丰富的相图，具有不同的瞬态和重现相。我们在两种极限情况下进行了计算：在退火情况下，随机链节的重排速度较快；在淬火情况下，链节的重排速度较慢。在一大类相互作用系统中，在规则的晶格相互作用拓扑中加入任意小密度的、可能是长程的、淬灭的随机链路，将产生类似平均场（或退火）的行为。然而，在某些情况下，平均场标度分解，例如在扩散或“低维”小世界网络中的爱德华兹-威尔金森过程中。这种分解可以通过对随机链路进行微扰处理来理解，其中平均场（或退火）预测显示为朴素微扰展开的最低阶项。利用网络Laplacian的精确数值对角化，对渐近解析结果进行了数值验证。进一步，我们构造了一个有限规模的尺度框架来描述相关的可观测项，捕捉有限网络中的交叉行为。这一工作提供了一个详细的帐户自洽-微扰和重整化方法，简要介绍在两个较早的简短报告。
---
英文标题：
《Diffusion Processes on Small-World Networks with Distance-Dependent
Random-Links》
---
作者：
Balazs Kozma, Matthew B. Hastings, G. Korniss
---
最新提交年份：
2007
---
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
--
一级分类：Physics 物理学
二级分类：Disordered Systems and Neural Networks 无序系统与神经网络
分类描述：Glasses and spin glasses; properties of random, aperiodic and quasiperiodic systems; transport in disordered media; localization; phenomena mediated by defects and disorder; neural networks
眼镜和旋转眼镜；随机、非周期和准周期系统的性质；无序介质中的传输；本地化；由缺陷和无序介导的现象；神经网络
--
---
英文摘要：
We considered diffusion-driven processes on small-world networks with distance-dependent random links. The study of diffusion on such networks is motivated by transport on randomly folded polymer chains, synchronization problems in task-completion networks, and gradient driven transport on networks. Changing the parameters of the distance-dependence, we found a rich phase diagram, with different transient and recurrent phases in the context of random walks on networks. We performed the calculations in two limiting cases: in the annealed case, where the rearrangement of the random links is fast, and in the quenched case, where the link rearrangement is slow compared to the motion of the random walker or the surface. It has been well-established that in a large class of interacting systems, adding an arbitrarily small density of, possibly long-range, quenched random links to a regular lattice interaction topology, will give rise to mean-field (or annealed) like behavior. In some cases, however, mean-field scaling breaks down, such as in diffusion or in the Edwards-Wilkinson process in "low-dimensional" small-world networks. This break-down can be understood by treating the random links perturbatively, where the mean-field (or annealed) prediction appears as the lowest-order term of a naive perturbation expansion. The asymptotic analytic results are also confirmed numerically by employing exact numerical diagonalization of the network Laplacian. Further, we construct a finite-size scaling framework for the relevant observables, capturing the cross-over behaviors in finite networks. This work provides a detailed account of the self-consistent-perturbative and renormalization approaches briefly introduced in two earlier short reports.
---
PDF链接：
https://arxiv.org/pdf/704.2564
京公网安备 11010802022788号
