Modifications of statistics under dimer diffusion

TL;DR

This paper develops analytical formulas to describe the size distribution of systems after dimer diffusion, explosion, evaporation, and coalescence, providing a quick way to characterize systems where initial dimers vanish.

Contribution

It introduces a formal, analytic approach to model and compute size statistics following dimer-related processes, enhancing understanding of systems with initial dimers.

Findings

Derived explicit formulas for size distributions after dimer coalescence.

Provided a method for rapid calculation of system statistics post-dimer disappearance.

Validated formulas through theoretical analysis.

Abstract

The diffusion, "explosion" and "evaporation" of dimers and the subsequent coalescence are treated in a formal way by identifying and solving the differential equations deduced from the respective behaviors of dimers in the different cases. This study leads to analytic formulas allowing to calculate, in a simple and fast way, the size statistics obtained after the coalescence of the dimers or their constituents once the dimers have completely disappeared. These formulas are of capital interest to characterize systems in which the dimers initially present disappear. 4 Study assumptions. Six assumptions will be made for this study: 1. Initial probabilities are known.