道路布局在KPZ类。

IF 1.3 3区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL
Journal of Statistical Physics Pub Date : 2025-01-01 Epub Date: 2025-06-10 DOI:10.1007/s10955-025-03460-7
Márton Balázs, Sudeshna Bhattacharjee, Karambir Das, David Harper
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引用次数: 0

摘要

提出了一种基于最后通道渗流(last passage filtration, LPP)的道路布局和交通模型。一个简单的naïve论点表明,在观察我们周围的交通网络时,交通轨迹的合并是必须考虑的。这是第一通道渗透(FPP)模型的基本特征,在该模型中,附近的测地线自然地结合在一起,以寻找最容易通过景观的通道。道路设计者也在追求节约成本,因此FPP测地线是道路布局模型的直接候选。不幸的是,在FPP测地线上没有严格的详细知识。为了解决这个问题,我们使用指数LPP代替建立道路交通的随机模型并证明其某些特征。汽车从晶格的每一点出发,沿着半无限的测地线随机方向行驶。众所周知,指数LPP属于KPZ通用性类,人们普遍认为FPP具有非常相似的性质,因此我们的发现应该同样适用于基于FPP的建模。我们解决了该模型中几个与交通相关的量,并将我们的定理与现实生活中的道路网络进行了比较。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Road Layout in The KPZ Class.

We propose a road layout and traffic model, based on last passage percolation (LPP). An easy naïve argument shows that coalescence of traffic trajectories is essential to be considered when observing traffic networks around us. This is a fundamental feature in first passage percolation (FPP) models where nearby geodesics naturally coalesce in search of the easiest passage through the landscape. Road designers seek the same in pursuing cost savings, hence FPP geodesics are straightforward candidates to model road layouts. Unfortunately no detailed knowledge is rigorously available on FPP geodesics. To address this, we use exponential LPP instead to build a stochastic model of road traffic and prove certain characteristics thereof. Cars start from every point of the lattice and follow half-infinite geodesics in random directions. Exponential LPP is known to be in the KPZ universality class and it is widely expected that FPP shares very similar properties, hence our findings should equally apply to FPP-based modelling. We address several traffic-related quantities of this model and compare our theorems to real life road networks.

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来源期刊
Journal of Statistical Physics
Journal of Statistical Physics 物理-物理:数学物理
CiteScore
3.10
自引率
12.50%
发文量
152
审稿时长
3-6 weeks
期刊介绍: The Journal of Statistical Physics publishes original and invited review papers in all areas of statistical physics as well as in related fields concerned with collective phenomena in physical systems.
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