Two-dimensional lattice liquid models

Abstract

A family of models of liquid on a two-dimensional 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 some honeycomb lattices 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.

The Concept of Cooperative Dynamics in Simulations of Soft Matter

“…After introducing constraints (stiff bonds) into this model the structure and dynamics of macromolecular systems were studied [51][52][53][54][55]. Two models of soft-material membrane were developed directly from the DLL model which appeared to be appropriate for studies of subdiffusive behavior [56,57].…”

2D Lattice Liquid Models

“…10 might be because of this strong restriction of the fluctuations. We then expect that softening the projection in the addition may change the intermediate plateau part of the MSDs, and this point is to be explored more elsewhere [11].…”

“…To invoke the expression, the models must be first written in the form of algebras. We have put aside this procedure, and therefore, to be given elsewhere [11].…”

“…Note the concept of the temperature can naturally be installed by letting x, p be a function of T , for example, by x ≡ e −ε/T /deg and p ≡ 1 − x • deg. Thermodynamic behaviour will depend on the manifes-tation of the functional forms of x and p. Some of the above proposals will be studied elsewhere [11] Another very interesting yet possibly very hard model to solve is the fluid model with memory effect. As we mentioned in the manuscript, the "potential" probabilities can potentially carry the information from the past so that the past partially control the forthcoming event through the probabilities.…”