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#### 2-D Brownian motion in a system of traps: Application of conformal transformations

(Institute of Physics, 1992)

We study two-dimensional Brownian motion in a periodic system of traps using conformal transformations. The system is periodic in the x and y directions. We calculate the ratio of the drift along the y-axis to the drift along the x-axis. The drift of the Brownian particle is induced by conditioning and by the asymmetry of
the ...

#### Diffusion on curved, periodic surfaces

(American Physical Society, 1999-07)

We present a simulation algorithm for a diffusion on a curved surface given by the equation [omega](r)50. The algorithm is tested against analytical results known for diffusion on a cylinder and a sphere, and applied to the diffusion on the P, D, and G periodic nodal surfaces. It should find application in an interpretation ...

#### 2-D Brownian motion in a system of reflecting barriers: effective diffusivity by a sampling method

(Institute of Physics, 1994-02-07)

We study two-dimensional Brownian motion in an ordered periodic system of linear reflecting barriers using the sampling method and conformal transformations. We calculate the effective diffusivity for the Brownian particle. When the periods are fixed but the length of the barrier goes to zero, the effective diffusivity in ...

#### Configurational transition in a Fleming-Viot-type model and probabilistic interpretation of Laplacian eigenfunctions

(Institute of Physics, 1996-06-07)

We analyze and simulate a two-dimensional Brownian multi-type particle system with death and branching (birth) depending on the position of particles of different types. The system is confined in the two-dimensional box, whose boundaries act as the sink of Brownian particles. The branching rate matches the death rate so that ...