Finite-Size-Scaling Studies of Reaction-Diffusion Systems Part II: Open Boundary Conditions

TL;DR

This paper analytically solves the coagulation-decoagulation model on a finite one-dimensional lattice with open boundaries, deriving exact concentration expressions and analyzing their finite-size scaling behavior, highlighting differences from periodic boundaries.

Contribution

It provides an exact analytical solution for the model with open boundaries and characterizes its finite-size scaling, which was not previously known.

Findings

Exact solution for concentration derived

Finite-size scaling function found to be boundary-condition dependent

Scaling function independent of initial conditions

Abstract

We consider the coagulation-decoagulation model on an one-dimensional lattice of length $L$ with open boundary conditions. Based on the empty interval approach the time evolution is described by a system of $\frac{L(L+1)}{2}$ differential equations which is solved analytically. An exact expression for the concentration is derived and its finite-size scaling behaviour is investigated. The scaling function is found to be independent of initial conditions. The scaling function and the correction function for open boundary conditions are different from those for periodic boundary conditions.