In this thesis, I propose a general stochastic simulation algorithm for particle based lattice model using the concepts of Gillespie's stochastic simulation algorithm, which was originally designed for well-stirred systems. I describe the details about this method and analyze its complexity compared with the StochSim algorithm, another simulation algorithm originally proposed to simulate stochastic lattice model. I compare the performance of both algorithms with application to two different examples: the May-Leonard model and Ziff-Gulari-Barshad model. Comparison between the simulation results from both algorithms has validate our claim that our new proposed algorithm is comparable to the StochSim in simulation accuracy. I also compare the efficiency of both algorithms using the CPU cost of each code and conclude that the new algorithm is as efficient as the StochSim in most test cases, while performing even better for certain specific cases. / Computer simulation has been developed for almost one century. Stochastic lattice model, which follows the physics concept of lattice, is defined as a kind of system in which individual entities live on grids and demonstrate certain random behaviors according to certain specific rules. It is mainly studied using computer simulations. The most widely used simulation method to for stochastic lattice systems is the StochSim algorithm, which just randomly pick an entity and then determine its behavior based on a set of specific random rules. Our goal is to develop new simulation methods so that it is more convenient to simulate and analyze stochastic lattice system. In this thesis I propose another type of simulation methods for the stochastic lattice model using totally different concepts and procedures. I developed a simulation package and applied it to two different examples using both methods, and then conducted a series of numerical experiment to compare their performance. I conclude that they are roughly equivalent and our new method performs better than the old one in certain special cases.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/96455 |
| Date | January 2019 |
| Creators | Liu, Weigang |
| Contributors | Computer Science, Cao, Yang, Onufriev, Alexey V., Cheng, Shengfeng |
| Publisher | Virginia Tech |
| Source Sets | Virginia Tech Theses and Dissertation |
| Language | en_US |
| Detected Language | English |
| Type | Thesis |
| Format | ETD, application/pdf |
| Rights | Creative Commons Attribution 4.0 International, http://creativecommons.org/licenses/by/4.0/ |
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