| Abstract: |
| We will discuss the modeling and simulation stochastic reaction-drift-diffusion models, formulating a particle-based model appropriate for studying spatial transport and chemical reactions at the single-cell scale. The model accounts for molecular diffusion, drift due to one and two-body potentials, and chemical reactions between molecules, and is formulated to ensure the preservation of key equilibrium properties such as detailed balance of reversible reactions. We develop continuous-time Markov chain-based numerical methods for efficiently simulating the dynamics of the particle model, demonstrating new methods that can resolve interaction potentials on general unstructured meshes, provide second-order convergence in the mesh spacing, and preserve detailed balance of both reaction and drift-diffusion fluxes. |
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