Related papers: The expected duration of random sequential adsorpt…
Convenient variational formula for collective diffusion of many particles adsorbed at lattices of arbitrary geometry is formulated. The approach allows to find the expressions for the diffusion coefficient for any value of the system's…
We demonstrate that absorbing phase transitions in one dimension may be induced by the dynamics of a single site. As an example we consider a one-dimensional model of diffusing particles, where a single site at the boundary evolves…
We have performed extensive simulations of random sequential adsorption and diffusion of $k$-mers, up to $k=5$ in two dimensions with particular attention to the case $k=2$. We focus on the behavior of the coverage and of vacancy dynamics…
We suggest a rigorous definition of the pathwise flux across the boundary of a bounded open set for transient finite energy diffusion processes. The expectation of such a flux has the property of depending only on the current velocity $v$,…
Random sequential adsorption with diffusional relaxation, of two by two square objects on the two-dimensional square lattice is studied by Monte Carlo computer simulation. Asymptotically for large lattice sizes, diffusional relaxation…
A certain class of directed metric graphs is considered. Asymptotics for a number of possible endpoints of a random walk at large times is found.
We deal with a random graph model where at each step, a vertex is chosen uniformly at random, and it is either duplicated or its edges are deleted. Duplication has a given probability. We analyse the limit distribution of the degree of a…
We study the adsorption of homogeneous or heterogeneous polymers onto heterogeneous planar surfaces with exponentially decaying site-site correlations, using a variational reference system approach. As a main result, we derive simple…
In thermal equilibrium, a colloidal particle between two parallel plates immersed in a fluid which partially wets both the particle and the plates, is attracted by the walls. However, if the particle moves parallel to the plates, a…
We present the algorithm for generating strictly saturated random sequential adsorption packings built of rounded polygons. It can be used to study various properties of such packings built of a wide variety of different shapes and in…
Given a Poisson process on a bounded interval, its random geometric graph is the graph whose vertices are the points of the Poisson process and edges exist between two points if and only if their distance is less than a fixed given…
This paper concerns discrete-time occupancy processes on a finite graph. Our results can be formulated in two theorems, which are stated for vertex processes, but also applied to edge process (e.g., dynamic random graphs). The first theorem…
A telegraph process with an elastic barrier at the origin was studied in [5]; in particular the number of visits of the origin before the absorption is a geometric distributed random variable M. Some asymptotic results (large and moderate…
When the unconditioned process is a diffusion living on the half-line $x \in ]-\infty,a[$ in the presence of an absorbing boundary condition at position $x=a$, we construct various conditioned processes corresponding to finite or infinite…
The accumulation of small particles is analyzed in stationary flows through channels of variable width at small Reynolds number. The combined influence of pressure, viscous drag and thermal fluctuations is described by means of a…
Let A be the annulus in R^2 centered at the origin with inner and outer radii r(1-\epsilon) and r, respectively. Place points {x_i} in R^2 according to a Poisson process with intensity 1 and let G_A be the random graph with vertex set {x_i}…
We calculate the absorption spectra of a semiconductor microcavity into which a non-equilibrium exciton population has been pumped. We predict strong peaks in the spectrum corresponding to collective modes analogous to the Cooper modes in…
The conventional definition of extremality of a finite collection of sets is extended by replacing a fixed point (extremal point) in the intersection of the sets by a collection of sequences of points in the individual sets with the…
Analytical study of the distribution of phase of the transmission coefficient through 1D disordered absorbing system is presented. The phase is shown to obey approximately Gaussian distribution. An explicit expression for the variance is…
It is shown that a suspension of particles in a partially-filled, horizontal, rotating cylinder is linearly unstable towards axial segregation and an undulation of the free surface at large enough particle concentrations. Relying on the…