2D Lattice Liquid Models

TL;DR

This paper introduces novel 2D lattice liquid models as primitive representations of soft-material membranes, exploring stochastic dynamics and anomalous diffusion phenomena through simulations on various lattice structures.

Contribution

It formulates and constructs two stochastic lattice liquid models, a vicious walk and a flow model, and analyzes their dynamics and diffusion behaviors.

Findings

Identified the frustration probability's approximate functional form.

Discovered anomalous diffusion in the flow model.

Analyzed relations to existing statistical models.

Abstract

A family of novel models of liquid on a 2D lattice (2D lattice liquid models) have been proposed as primitive models of soft-material membrane. As a first step, we have formulated them as single-component, single-layered, classical particle systems on a two-dimensional surface with no explicit viscosity. Among the family of the models, we have shown and constructed two stochastic models, a vicious walk model and a flow model, on an isotropic regular lattice and on the rectangular honeycomb lattice of various sizes. In both cases, the dynamics is governed by the nature of the frustration of the particle movements. By simulations, we have found the approximate functional form of the frustration probability, and peculiar anomalous diffusions in their time-averaged mean square displacements in the flow model. The relations to other existing statistical models and possible extensions of the models are also discussed.