Front formation in a ballistic annihilation model
Jaros{\l}aw Piasecki, Pierre-Antoine Rey, Michel Droz
TL;DR
This paper investigates a one-dimensional ballistic annihilation model with initially separated species, deriving exact properties of the annihilation front and demonstrating its Brownian wandering behavior around the mean.
Contribution
It provides an exact analysis of the front dynamics in a ballistic annihilation model with separated initial conditions, revealing its stochastic wandering nature.
Findings
Exact derivation of the annihilation front properties
Demonstration of Brownian wandering of the front
Insights into the dynamics of spatially separated annihilation processes
Abstract
We study a simple one-dimensional model of ballisticaly-controlled annihilation in which the two annihilating species are initially spatially separated. The time dependent properties of the annihilation front are exactly derived. It is shown that the front wanders in a brownian fashion around its average value.
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