Mitran T L, Melchert O, Hartmann A K
Institut für Physik, Universität Oldenburg, Carl-von-Ossietzky Strasse, 26111 Oldenburg, Germany and Faculty of Physics, University of Bucharest, 077125 Magurele-Ilfov, P. O. Box MG-11, Romania.
Institut für Physik, Universität Oldenburg, Carl-von-Ossietzky Strasse, 26111 Oldenburg, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Dec;88(6):062101. doi: 10.1103/PhysRevE.88.062101. Epub 2013 Dec 2.
The main characteristics of biased greedy random walks (BGRWs) on two-dimensional lattices with real-valued quenched disorder on the lattice edges are studied. Here the disorder allows for negative edge weights. In previous studies, considering the negative-weight percolation (NWP) problem, this was shown to change the universality class of the existing, static percolation transition. In the presented study, four different types of BGRWs and an algorithm based on the ant colony optimization heuristic were considered. Regarding the BGRWs, the precise configurations of the lattice walks constructed during the numerical simulations were influenced by two parameters: a disorder parameter ρ that controls the amount of negative edge weights on the lattice and a bias strength B that governs the drift of the walkers along a certain lattice direction. The random walks are "greedy" in the sense that the local optimal choice of the walker is to preferentially traverse edges with a negative weight (associated with a net gain of "energy" for the walker). Here, the pivotal observable is the probability that, after termination, a lattice walk exhibits a total negative weight, which is here considered as percolating. The behavior of this observable as function of ρ for different bias strengths B is put under scrutiny. Upon tuning ρ, the probability to find such a feasible lattice walk increases from zero to 1. This is the key feature of the percolation transition in the NWP model. Here, we address the question how well the transition point ρ(c), resulting from numerically exact and "static" simulations in terms of the NWP model, can be resolved using simple dynamic algorithms that have only local information available, one of the basic questions in the physics of glassy systems.
研究了在二维晶格上具有实值淬火无序的晶格边缘上的有偏贪婪随机游走（BGRW）的主要特征。这里的无序允许负边权重。在先前的研究中，考虑到负权重渗流（NWP）问题，已表明这会改变现有静态渗流转变的普适类。在本研究中，考虑了四种不同类型的BGRW以及一种基于蚁群优化启发式的算法。关于BGRW，数值模拟期间构建的晶格游走的精确构型受两个参数影响：一个无序参数ρ，它控制晶格上负边权重的数量；一个偏置强度B，它控制游走者沿某个晶格方向的漂移。随机游走是“贪婪的”，因为游走者的局部最优选择是优先遍历具有负权重的边（这与游走者的“能量”净增益相关）。这里，关键的可观测量是晶格游走终止后呈现总负权重的概率，这里将其视为渗流。研究了该可观测量在不同偏置强度B下作为ρ的函数的行为。通过调整ρ，找到这样一个可行晶格游走的概率从零增加到1。这是NWP模型中渗流转变的关键特征。在这里，我们解决这样一个问题：使用仅具有局部信息的简单动态算法，能多好地解析由NWP模型的数值精确和“静态”模拟得出的转变点ρ(c)，这是玻璃态系统物理学中的基本问题之一。
