Now showing items 1-6 of 6
Reduction of dimensionality in a diffusion search process and kinetics of gene expression
(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 factor, which activates a given gene, need in order to find this gene inside the nucleus of a cell? The ...
Efficient Markovian couplings: Examples and counterexamples
(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 is of interest not only for its own sake, but also of growing importance arising from the recent advent ...
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 ...
A Skorobod-type lemma and a decomposition of reflected Brownian motion
(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 variation away from the tip of the thorn. The construction is based on a new Skorohod-type lemma.
Mechanisms for facilitated target location and the optimal number of molecules in the diffusion search process
(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] 0, an increase from N to k · N molecules (k > 1) results in the decrease of search time from t [subscript] ...
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 ...