Now showing items 1-6 of 6

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

      Burdzy, Krzysztof; Holyst, Robert; Ingerman, David (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. ...
    • Diffusion on curved, periodic surfaces 

      Burdzy, Krzysztof; Holyst, Robert; Plewezynski, D.; Aksimentiev, A. (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 ...
    • Efficient Markovian couplings: Examples and counterexamples 

      Burdzy, Krzysztof; Kendall, Wilfrid S. (Institute of Mathematical Statistics, 2000-05)
      In this paper we study the notion of an efficient coupling of Markov processes. Informally, an efficient coupling is one which couples at the maximum possible exponential rate, as given by the spectral gap. This notion ...
    • Mechanisms for facilitated target location and the optimal number of molecules in the diffusion search process 

      Burdzy, Krzysztof; Holyst, Robert (American Physical Society, 2001-06-26)
      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. (North-Holland (Elsevier), 2000-03-01)
      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 ...
    • A Skorobod-type lemma and a decomposition of reflected Brownian motion 

      Burdzy, Krzysztof; Toby, Ellen H. (Institute of Mathematical Statistics, 1995-04)
      We consider two-dimensional reflected Brownian motions in sharp thorns pointed downward with horizontal vectors of reflection. We present a decomposition of the process into a Brownian motion and a process which has bounded ...