## Search

Now showing items 1-7 of 7

#### 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 ...

#### A Fleming-Viat particle representation of Dirichlet Laplacian

(Springer-Verlag GmbH, 2000-11)

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. For large N, the particle distribution density converges to the normalized heat equation solution in D ...

#### 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 ...

#### 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 ...

#### 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 ...