arXiv subjects
Publications and source records attributed to Dietmar Wendt.
The discrete class algorithm presented in this paper is an efficient simulation tool for stochastic processes governed by a reasonably small set of transition rates. The algorithm is presented, its performance compared to prevailing methods and applications to epitaxial growth and neuronal models are sketched. Source code is available from the author's WWW-site.
We describe a new algorithm for simulating complex Markoff-processes. We have used a reaction-cell method in order to simulate arbitrary reactions. It can be used for any kind of RDS on arbitrary topologies, including fractal dimensions or configurations not being related to any spatial geometry. The events within a single cell are managed by an event handler which has been implemented independently of the system studied. The method is exact on the Markoff level including the correct treatment of finite numbers of molecules. To demonstrate its properties, we apply it on a very simple reaction-diffusion-systems (RDS). The chemical equations A+A -> inert and A+B -> inert in 1 to 4 dimensions serve as models for systems whose dynamics on an intermediate time scale are governed by fluctuations. We compare our results to the analytic approach by the scaling ansatz. The simulations confirm the exponents of the A+B system within statistical errors, including the logarithmic corrections in the dimension d=2. The method is capable to simulate the crossover from the reaction to diffusion limited regime, which is defined by a crossover time depending on the system size.