Master thesis presentation Ilias-Marios Sarris, MPCAS

Abstract:

This thesis conducts a comprehensive investigation of well-mixed and diffusion-driven annihilation processes in single-species systems using a stochastic lattice model. The study aims to validate the proposed model and examine the system’s behavior in various scenarios. Initially, a simple one-dimensional diffusion process without reactions is employed to test the model, with the results demonstrating close agreement with analytical predictions and numerical solutions, thereby establishing the model’s credibility.

The well-mixed annihilation process, involving the annihilation of k=2,3,4 particles, is examined, and the results are observed to closely adhere to the mean-field behavior as described by the theory. The characteristic exponent of the density for different k values and the annihilation rate are inferred from simulation data using linear regression on logarithmically transformed data points, further corroborating the model’s capacity to simulate the well-mixed annihilation process.

Regarding the diffusion-driven annihilation process, the asymptotic behavior of the particle density is found to be consistent with the literature, with m(t) \sqrt{8πDt} approaching 1 for late times, irrespective of the diffusion coefficient or reaction rates. This finding suggests that the single-species two-particle annihilation-diffusion process is predominantly governed by diffusion during latent times.

In addition, the study explores the influence of periodic boundary conditions on the system’s kinetics by introducing correlations between particles. The investigation focuses on the case where k=4 to determine whether the system remains reaction-driven at late times, as suggested by mean-field descriptions. The findings provide valuable insights into the complex interplay between diffusion and reaction in single-species annihilation diffusion systems.

Supervisor: Johannes Hofmann
Examiner: Bernhard Mehlig
Opponent: Alfred Weddig Karlsson