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We consider a discrete random walk on a diagonal lattice in two and three dimensions and obtain explicit solutions of absorption probabilities and probabilities of return in several domains. In three dimensions we consider both the cube and…
Using computer simulations in two dimensions we investigate the dynamics and structure of passive polymeric tracer with different topologies immersed in a low-density active particle bath. One of the key observations is that polymer exhibit…
We consider a discrete random walk (RW) in n dimensions . The RW is adapted with a geometric absorption process: at any discrete time there is a constant probability that absorption occurs in the current state. To model the RW with…
We consider the activated random walk (ARW) model on $\mathbb{Z}^d$, which undergoes a transition from an absorbing regime to a regime of sustained activity. In any dimension we prove that the system is in the active regime when the…
The distribution of monomers in a coating of grafted and adsorbing polymers is modelled using a grafted staircase polygon in the square lattice. The adsorbing staircase polygon consists of a bottom and a top lattice path (branches) and the…
The comprehensive computer simulation study of the phase diagram of the repulsive step potential system in three dimensions is represented. We show that the system with a simple purely repulsive isotropic potential demonstrates a number of…
We employ a three-dimensional molecular dynamics to simulate translocation of a polymer through a nanopore driven by an external force. The translocation is investigated for different three pore diameter and two different external forces.…
Many drug delivery systems suffer from undesirable interactions with the host immune system. It has been experimentally established that covalent attachment (irreversible adsorption) of suitable macromolecules to the surface of the drug…
We study a model of semi-flexible self-avoiding trails, where the lattice paths are constrained to visit each lattice edge at most once, with configurations weighted by the number of collisions, crossings and bends, on a Husimi lattice…
We study the adsorption-desorption of fluid molecules on a solid substrate by introducing a schematic model in which the adsorption/desorption transition probabilities are given by irreversible kinetic constraints with a tunable violation…
In view of recent intense experimental and theoretical interests in the biophysics of liquid-liquid phase separation (LLPS) of intrinsically disordered proteins (IDPs), heteropolymer models with chain molecules configured as self-avoiding…
We introduce a three-dimensional lattice gas model to study the glass transition. In this model the interactions come from the excluded volume and particles have five arms with an asymmetrical shape, which results in geometric frustration…
Magnetic polymers are examples of composite soft materials in which the competition between the large configurational entropy of the soft substrate (polymer) and the magnetic interaction may give rise to rich equilibrium phase diagrams as…
A modified lattice gas model is proposed to study pedestrian evacuation from a single room. The payoff matrix in this model represents the complicated interactions between selfish individuals, and the mean force imposed on an individual is…
We study a discrete-space model of active matter with excluded volume. Particles are restricted to the sites of a triangular lattice, and can assume one of three orientations. Varying the density and noise intensity, Monte Carlo simulations…
We study the effective radius of weakly self-avoiding star polymers in one, two, and three dimensions. Our model includes $N$ Brownian motions up to time $T$, started at the origin and subject to exponential penalization based on the amount…
We prove that a class of random walks on $\Z^2$ with long-range self-repulsive interactions have a diffusive-ballistic phase transition.
In these lecture notes, which are based on the mini-course given at 2013 Prague School on Mathematical Statistical Physics, we discuss ballistic phase of quenched and annealed stretched polymers in random environment on ${\mathbb Z}^d$ with…
Experiments of periodically sheared colloidal suspensions or soft amorphous solids display a transition from reversible to irreversible particle motion that, when analysed stroboscopically in time, is interpreted as an absorbing phase…
We consider a model consisting of a self-avoiding polygon occupying a variable density of the sites of a square lattice. A fixed energy is associated with each $90^\circ$-bend of the polygon. We use a grand canonical ensemble, introducing…