# Stochastic simulations for aggregating systems with non-constant reaction rates

In this thesis, reactive multi-particle collision dynamics (RMPC) is used for the simulation of aggregation and aggregation-fragmentation systems. RMPC dynamics consists of collisions, reactions, and free streaming. Aggregation and fragmentation is modelled using a reactive mechanism. An infinite system of ODEs called the Smoluchowski differential equations has been used for comparison in the well mixed case. The exact solution for the infinite system is also compared with a finite system RK4 solution that is more appropriate for finite system RMPC simulations. The maximum cluster size is taken to be five, and the domain for stochastic simulations is cubic with periodic boundary conditions. Constant, additive, and multiplicative rates are discussed, and the affects of variations in aggregation and break-up rates are observed. Non-zero, monomer-only initial conditions are used, and the solution for aggregation is obtained with a monomer only initial-concentration equal to 1, as well as b, where b is a constant. The solution for aggregation and break-up is calculated using a monomer-only initial concentration equal to b. The RMPC simulations showed that the RMPC results had a good agreement with the finite-system RK4 solution specially for smaller particle sizes. There was stochastic noise in the RMPC results for all cases that became more pronounced with increase in break-up rate. The novelty of this work consists of RMPC simulation results for additive and multiplicative rates, which has not been simulated using RMPC before. For the system size considered in this work, stochastic effects can be further extended for larger cluster sizes, and to analyse different choices for aggregation and break-up rates.

## History

## Language

English## Degree

- Master of Science

## Program

- Applied Mathematics

## Granting Institution

Ryerson University## LAC Thesis Type

- Thesis