Related papers: Gradual Diffusive Capture: Slow Death by Many Mosq…
Individual-based models of chemical or biological dynamics usually consider individual entities diffusing in space and performing a birth-death type dynamics. In this work we study the properties of a model in this class where the birth…
We consider the dynamics of diffusing particles in one space dimension with annihilation on collision and nucleation (creation of particles) with constant probability per unit time and length. The cases of nucleation of single particles and…
In the present note we analyze the one-dimensional multi-particle diffusion limited aggregation (MDLA) model: the initial number of particles at each positive integer site has Poisson distribution with mean $\mu$, independently of all other…
The mean square displacement per collision of a molecule immersed in a gas at equilibrium is given by its mean square displacement between two consecutive collisions (mean square free path) corrected by a prefactor in the form of a series.…
The risk of mosquito-borne disease outbreaks is tightly linked to the frequency at which mosquitoes feed on blood, also known as the biting rate. However, standard models of mosquito-borne disease transmission inherently assume that…
We study a discrete-time dynamical system of wild mosquito population with parameters: $\beta$ - the birth rate of adults; $\alpha$ - maximum emergence rate; $\mu>0$ - the death rate of adults; $\gamma$ - Allee effects. We prove that if…
Long DNA molecules can be mapped by cutting them with restriction enzymes inside a narrow channel. Once cut, the individual fragments thus produced move away from each other due to diffusion and entropic effects. We investigate how long it…
The survival probability of a particle diffusing in the two dimensional domain $x>0$ near a ``windy cliff'' at $x=0$ is investigated. The particle dies upon reaching the edge of the cliff. In addition to diffusion, the particle is…
The kinetics of the annihilation process, $A+A\to 0$, with ballistic particle motion is investigated when the distribution of particle velocities is {\it discrete}. This discreteness is the source of many intriguing phenomena. In the mean…
In this article we review the problem of reaction annihilation $A+A \rightarrow \emptyset$ on a real lattice in one dimension, where $A$ particles move ballistically in one direction with a discrete set of possible velocities. We first…
Using random walk simulations we explore diffusive transport through monodisperse sphere packings over a range of packing fractions, $\phi$, in the vicinity of the jamming transition at $\phi_{c}$. Various diffusion properties are computed…
We consider the single-file dynamics of $N$ identical random walkers moving with diffusivity $D$ in one dimension (walkers bounce off each other when attempting to overtake). Additionally, we require that the separation between neighboring…
Diffusive search for a static target is a common problem in statistical physics with numerous applications in chemistry and biology. We look at this problem from a different perspective and investigate the statistics of encounters between…
Particles moving along curved trajectories will diffuse if the curvature fluctuates sufficiently in either magnitude or orientation. We consider particles moving at a constant speed with either a fixed or with a Gaussian distributed…
Motivated by the diffusion-reaction kinetics on interstellar dust grains, we study a first-passage problem of mortal random walkers in a confined two-dimensional geometry. We provide an exact expression for the encounter probability of two…
This article studies the quasi-stationary behaviour of absorbed one-dimensional diffusion processes with killing on $[0,\infty)$. We obtain criteria for the exponential convergence to a unique quasi-stationary distribution in total…
We investigate the average time for the earliest particle to hit a spherical absorber when a homogeneous gas of freely diffusing particles with density $\rho$ and diffusivity $D$ is prepared in a deterministic state and is initially…
Collective diffusion coefficient in a one dimensional lattice gas adsorbate is calculated using variational approach. Particles interact via either a long-range, or a long range electron-gas-mediated (for a metallic substrate), or a…
The adsorption of particles diffusing in a half-space bounded by the substrate and irreversibly sticking to the substrate upon contacts is investigated. We show that when absorbing particles are planar disks diffusing in the…
We extend some results on the convergence of one-dimensional diffusions killed at the boundary, conditioned on extended survival, to the case of general killing on the interior. We show, under fairly general conditions, that a diffusion…