Related papers: Statistical Models on Spherical Geometries
We study the one dimensional three species monomer-monomer reaction model in the reaction controlled limit using mean-field theory and dynamic Monte Carlo simulations. The phase diagram consists of a reactive steady state bordered by three…
Using extensive Monte Carlo simulations, we investigate the surface adsorption of self-avoiding trails on the triangular lattice with two- and three-body on-site monomer-monomer interactions. In the parameter space of two-body, three-body,…
An infinite hierarchy of layering transitions exists for model polymers in solution under poor solvent or low temperatures and near an attractive surface. A flat histogram stochastic growth algorithm known as FlatPERM has been used on a…
How many times a diffusing molecule can permeate across a membrane or be adsorbed on a substrate? We employ the encounter-based approach to find the statistics of adsorption or permeation events for molecular diffusion in a general…
A brief review of our recent studies aiming at a better understanding of the scaling behaviour of polymers in disordered environments is given. The main emphasis is on a simple generic model where the polymers are represented by…
The process of adsorption on a planar repulsive, "marginal" and attractive wall of long-flexible polymer chains with excluded volume interactions is investigated. The performed scaling analysis is based on formal analogy between the polymer…
A monitored quantum system undergoing a cyclic evolution of the parameters governing its Hamiltonian accumulates a geometric phase that depends on the quantum trajectory followed by the system on its evolution. The phase value will be…
A solid-on-solid growth model for dimer adsorption and desorption is introduced and studied numerically. The special property of the model is that dimers can only desorb at the edges of terraces. It is shown that the model exhibits a…
We discuss the generalization of a classical problem involving an $N$-step ideal polymer adsorption at a sticky boundary (potential well of depth $U$). It is known that as $N$ approaches infinity, the path undergoes a 2nd-order localization…
Models of random walks are considered in which walkers are born at one location and die at all other locations with uniform death rate. Steady-state distributions of random walkers exhibit dimensionally dependent critical behavior as a…
The fluctuations of two-dimensional extended objects membranes is a rich and exciting field with many solid results and a wide range of open issues. We review the distinct universality classes of membranes, determined by the local order,…
We consider two intimately related statistical mechanical problems on $\mathbb{Z}^3$: (i) the tricritical behaviour of a model of classical unbounded $n$-component continuous spins with a triple-well single-spin potential (the $|\varphi|^6$…
We consider exploration algorithms of the random sequential adsorption type both for homogeneous random graphs and random geometric graphs based on spatial Poisson processes. At each step, a vertex of the graph becomes active and its…
The hydrodynamic flow field generated by self-propelled active particles and swimming microorganisms is strongly altered by the presence of nearby boundaries in a viscous flow. Using a simple model three-linked sphere swimmer, we show that…
The problem of surface effects at a fluid/force field boundary is investigated. A classical simple fluid with a locally introduced field simulating a solid is considered. For the case of a hard-core field, rigid, exponential, realistic, and…
Modeling of polymer chains has received a lot of attention in mathematics. In fact, probabilistic models that naturally arise in statistical mechanics have been widely studied by mathematicians for the very challenging and novel problems…
We analyze the critical connectivity of systems of penetrable $d$-dimensional spheres having size distributions in terms of weighed random geometrical graphs, in which vertex coordinates correspond to random positions of the sphere centers…
Discontinuous percolation transitions and the associated tricritical points are manifest in a wide range of both equilibrium and non-equilibrium cooperative phenomena. To demonstrate this, we present and relate the continuous and first…
Polymer adsorption on fractally rough walls of varying dimensionality is studied by renormalization group methods on hierarchical lattices. Exact results are obtained for deterministic walls. The adsorption transition is found continuous…
The percolation threshold for flow or conduction through voids surrounding randomly placed spheres is rigorously calculated. With large scale Monte Carlo simulations, we give a rigorous continuum treatment to the geometry of the…