Fundamental Function for the Lattice-based Random Walk Simulation in One Dimension

摘要

Recently, diffusion-influenced reactions attract increasing attention. It is well-known that diffusion-influenced reactions can be described by lattice-based random walk Monte Carlo simulations. Since the continuum limit of the random walk model is closely related to the diffusion process, we can straightforwardly simulate general diffusion-reaction systems with the lattice-based Monte Carlo simulation. Although the theories of the random walk on the lattice points have been regularly reported, the analytical results for diffusion-reaction systems on lattice points have been relatively rare.