Related papers: Evolution of gas-filled pore in bounded particles
Formation, evolution, and vanishing of bubbles are common phenomena in our nature, which can be easily observed in boiling or falling waters, carbonated drinks, gas-forming electrochemical reactions, etc. However, the morphology and the…
The relativistic time evolution of multi-layer spherically symmetric shell systems---consisting of infinitely thin shells separated by vacuum regions---is examined. Whenever two shells collide the evolution is continued with the assumption…
We describe calculations of the properties of quantum fluids inside nanotubes of various sizes. Very small radius ($R$) pores confine the gases to a line, so that a one-dimensional (1D) approximation is applicable; the low temperature…
This paper investigates a diffusion process in a narrow tubular domain with reflecting boundary conditions, where the geometry serves as a singular perturbation of an underlying graph in $\mathbb{R}^2$ or $\mathbb{R}^3$. The construction…
When thin films are grown on a substrate by chemical vapor deposition, the evolution of the first deposited layers may be described, on mesoscopic scales, by dynamical models of the reaction-diffusion type. For monoatomic layers, such…
A model of the thin shell expanding into a uniform ambient medium is developed. Density perturbations are described using equations with linear and quadratic terms, and the linear and the nonlinear solutions are compared. We follow the time…
We present simulations of the dynamical evolution of young embedded star clusters. Our initial conditions are directly derived from X-ray, infrared, and radio observations of local systems, and our models evolve both gas and stars…
In this paper we consider the diffusion of nanoparticles taken up by a semi-permeable spherical cell placed in the path of a diffusive particle field generated by an external planar source. The cell interior and exterior are characterized…
By analytically solving some simple models of phase-ordering kinetics, we suggest a mechanism for the onset of non-equilibrium behaviour in colloid-polymer mixtures. These mixtures can function as models of atomic systems; their physics…
We analyse the evolution of cosmological perturbations which leads to the formation of large voids in the distribution of galaxies. We assume that perturbations are spherical and all components of the Universe - radiation, matter and dark…
We study the evolution of an initially random distribution of particles on a square lattice, under certain rules for `growing' and `culling' of particles. In one version we allow the particles to move laterally along the surface (mobile…
The linear hydrodynamic stability of a model for confined quasi-two-dimensional granular gases is analyzed. The system exhibits homogeneous hydrodynamics, i.e. there are macroscopic evolution equations for homogeneous states. The stability…
We study the diffusion-reaction-advection model for mobile chemical species together with the dissolution and precipitation of immobile species in a porous medium at the micro-scale. This leads to a system of semilinear parabolic partial…
We derive an upscaled model describing the aggregation and deposition of colloidal particles within a porous medium allowing for the possibility of local clogging of the pores. At the level of the pore scale, we extend an existing model for…
We study a quite general family of nonlinear evolution equations of diffusive type with nonlocal effects. More precisely, we study porous medium equations with a fractional Laplacian pressure, and the problem is posed on a bounded space…
We studied the evolution of the gas kinematics of galaxies by performing hydrodynamical simulations in a cosmological scenario. We paid special attention to the origin of the scatter of the Tully-Fisher relation and the features which could…
We investigate mathematical properties of the system of nonlinear partial differential equations that describe, under certain simplifying assumptions, evolutionary processes in water-saturated granular materials. The unconsolidated solid…
We investigate the motion of a particle around a low mass planet embedded in a non-turbulent gaseous disk. We take into account the effect of the gas structure that is modified by the gravitational interaction between the planet. We derive…
A diffused interface model describing the evolution of two conterminous incompressible fluids in a porous medium is discussed. The system consists of the Cahn-Hilliard equation with Flory-Huggins logarithmic potential, coupled via surface…
We study domain growth properties of two species of particles executing biased diffusion on a half-filled square lattice, consisting of just two lanes. Driven in opposite directions by an external ``electric'' field, the particles form…