Related papers: Statistical Models on Spherical Geometries
Materials with nanoscale phase separation are considered. These materials are formed by a mixture of several phases, so that inside one phase there exist nanosize inclusions of other phases, with random shapes and random spatial locations.…
Hard sphere systems are often used to model simple fluids. The configuration spaces of hard spheres in a three-dimensional torus modulo various symmetry groups are comparatively simple, and could provide valuable information about the…
We study the percolation properties of the growing clusters model. In this model, a number of seeds placed on random locations on a lattice are allowed to grow with a constant velocity to form clusters. When two or more clusters eventually…
We study the growth of slip line in a plastically deforming crystal by numerical simulation of a double-ended pile-up model with a dislocation source at one end, and an absorbing wall at the other end. In presence of defects, the pile-up…
From the spread of pollutants in the atmosphere to the transmission of nutrients across cell membranes, anomalous diffusion processes are ubiquitous in natural systems. The ability to understand and control the mechanisms guiding such…
We numerically study the jamming transition of frictionless polydisperse spheres in three dimensions. We use an efficient thermalisation algorithm for the equilibrium hard sphere fluid and generate amorphous jammed packings over a range of…
We consider binary liquid mixtures near their critical consolute points and exposed to geometrically flat but chemically structured substrates. The chemical contrast between the various substrate structures amounts to opposite local…
Percolation on complex networks is used both as a model for dynamics on networks, such as network robustness or epidemic spreading, and as a benchmark for our models of networks, where our ability to predict percolation measures our ability…
We have numerically studied the trapping problem in a two-dimensional lattice where particles are continuously generated. We have introduced interaction between particles and directionality of their movement. This model presents a critical…
In this paper we present simulations of a surface-adsorbed polymer subject to an elongation force. The polymer is modelled by a self-avoiding walk on a regular lattice. It is confined to a half-space by an adsorbing surface with attractions…
The aim of this paper is to investigate the distribution of a continuous homopolymer in the presence of an attractive finitely supported potential. The most intricate behavior can be observed if we simultaneously vary two parameters: the…
We study the random walk on dynamical percolation of $\mathbb{Z}^d$ (resp., the two-dimensional triangular lattice $\mathcal{T}$), where each edge (resp., each site) can be either open or closed, refreshing its status at rate $\mu\in…
In the present work, the cyclic polymer chains (rings) in structurally disordered environment (e.g. in the cross-linked polymer gel) are studied exploiting the model of closed self-avoiding walks (SAWs) trajectories on $d=3$-dimensional…
We study the phase behavior of a symmetric binary polymer blend which is confined into a thin film. The film surfaces interact with the monomers via short range potentials. We calculate the phase behavior within the self-consistent field…
A coarse-grained model for solutions of polymers in supercritical fluids is introduced and applied to the system of hexadecane and carbon dioxide as a representative example. Fitting parameters of the model to the gas-liquid critical point…
After a general introduction to the field, we describe some recent results concerning disorder effects on both `random walk models', where the random walk is a dynamical process generated by local transition rules, and on `polymer models',…
The spatial coverage produced by a single discrete-time random walk, with asymmetric jump probability $p\neq 1/2$ and non-uniform steps, moving on an infinite one-dimensional lattice is investigated. Analytical calculations are complemented…
It is known that many different types of finite random subgraph models undergo quantitatively similar phase transitions around their percolation thresholds, and the proofs of these results rely on isoperimetric properties of the underlying…
Solutions of hydrodynamical equations are presented for an equation of state allowing for a first-order phase transition. The numerical analysis is supplemented by analytical treatment provided the system is close to the critical point. The…
Activated Random Walk is a system of interacting particles which presents a phase transition and a conjectured phenomenon of self-organized criticality. In this note, we prove that, in dimension 1, in the supercritical case, when a segment…