Simulating nondiffusive dynamics in reaction-diffusion systems
Publicerad
Författare
Typ
Examensarbete för masterexamen
Master's Thesis
Master's Thesis
Modellbyggare
Tidskriftstitel
ISSN
Volymtitel
Utgivare
Sammanfattning
Reaction-diffusion systems are a class of mathematical models with broad applications
across physics, chemistry and biology. While very versatile, a limitation of
these systems is that they assume diffusion as the only means of motion. To allow
for broader application, especially in the realm of condensed matter physics, there
is a need to take into account other transport processes. This thesis aims to implement
an existing Monte Carlo algorithm for efficient simulation of single-species
reaction-diffusion systems on a lattice, and subsequently extend it to also handle
nondiffusive dynamics. The considered nondiffusive model is a simple toy model of
correlated motion that preserves center of mass, and the nondiffusive nature of this
kinetic model is both justified theoretically and demonstrated by simulation. It is
then used in conjunction with single-species annihilation with the goal of finding
how the particle density scales over time with such dynamics.
The implementation of the base algorithm shows behavior consistent with theory
and previous computational results. In order to show the nondiffusivity of the correlated
motion model, the time evolution of the mean squared displacement is examined
and it is found to be subdiffusive and slightly slower than expected. Whether
this slower evolution is due to limitations in the theory or the computational model
is unknown. When simulating two-particle single species annihilation, the particle
density is observed to quickly reach the same steady state of 2/11 inverse length
units independent of parameter settings, and no apparent power laws are found in
the approach to this steady state. What these results suggest is that there exist
certain invariant configurations of the lattice in which no more reactions can occur.
This leaves open the opportunity for more reasearch into the equilibrium states of
various system geometries and types of reaction.
Beskrivning
Ämne/nyckelord
diffusion, reaction, annihilation, correlated motion, Monte Carlo, meansquared displacement, steady state