Browsing EPrint Collection  Mathematics by Author "Holyst, Robert"
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2D Brownian motion in a system of reflecting barriers: effective diffusivity by a sampling method
Burdzy, Krzysztof; Holyst, Robert; Ingerman, David (Institute of Physics, 19940207)We study twodimensional 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. ... 
2D Brownian motion in a system of traps: Application of conformal transformations
Burdzy, Krzysztof; Holyst, Robert; Salisbury, Thomas S. (Institute of Physics, 1992)We study twodimensional 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 yaxis to the drift ... 
Configurational transition in a FlemingViottype model and probabilistic interpretation of Laplacian eigenfunctions
Burdzy, Krzysztof; Holyst, Robert; Ingerman, David; March, Peter (Institute of Physics, 19960607)We analyze and simulate a twodimensional Brownian multitype particle system with death and branching (birth) depending on the position of particles of different types. The system is confined in the twodimensional box, ... 
Diffusion on curved, periodic surfaces
Burdzy, Krzysztof; Holyst, Robert; Plewezynski, D.; Aksimentiev, A. (American Physical Society, 199907)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 ... 
A FlemingViat particle representation of Dirichlet Laplacian
Burdzy, Krzysztof; Holyst, Robert; March, Peter (SpringerVerlag GmbH, 200011)We consider a model with a large number N of particles which move according to independent Brownian motions. A particle which leaves a domain D is killed; at the same time, a different particle splits into two particles. ... 
Mechanisms for facilitated target location and the optimal number of molecules in the diffusion search process
Burdzy, Krzysztof; Holyst, Robert (American Physical Society, 20010626)We investigate the number N of molecules needed to perform independent diffusions in order to achieve bonding of a single molecule to a specific site in time t [subscript] 0. For a certain range of values of t [subscript] ... 
Reduction of dimensionality in a diffusion search process and kinetics of gene expression
Burdzy, Krzysztof; Holyst, Robert; Blazejezyk, M.; Goralski, G.; Bocquet, L. (NorthHolland (Elsevier), 20000301)In order to activate a gene in a DNA molecule a specific protein (transcription factor) has to bind to the promoter of the gene. We formulate and partially answer the following question: how much time does a transcription ...