Related papers: On the dynamics of shallow ice sheets. Modelling a…
Linear and weakly nonlinear stability analyses of an externally shear-imposed, gravity-driven falling film over a uniformly heated wavy substrate are studied. The longwave asymptotic expansion technique is utilized to formulate a single…
Within the linearized three-dimensional theory of polymer gels, we consider a sequence of problems formulated on a family of cylindrical domains whose height tends to zero. We assume that the fluid pressure is controlled at the top and…
Sublimation of drifting snow, which is significant for the balances of mass and energy of the polar ice sheet, is a complex physical process with intercoupling between ice crystals, wind field, temperature, and moisture. Here a…
The shell map is a very simple representation of the structure of foams, combining the geometrical (random tiling) and dynamical (loss of information from an arbitrary cell out) aspects of disorder. The structure is built from the central…
The instability and nonlinear evolution of directional ocean waves is investigated numerically by means of simulations of the governing kinetic equation for narrow-band surface waves. Our simulation results reveal the onset of the…
We consider a layer of an inviscid fluid with free surface which is subject to vertical high-frequency vibrations. We derive three asymptotic systems of equations that describe slowly evolving (in comparison with the vibration frequency)…
Many microorganisms swim through gels, materials with nonzero zero-frequency elastic shear modulus, such as mucus. Biological gels are typically heterogeneous, containing both a structural scaffold (network) and a fluid solvent. We analyze…
We investigate the stability and nonlinear evolution of localized electron-scale current sheets using fully kinetic, electromagnetic particle-in-cell (PIC) simulations in two and three dimensions. By varying the current-sheet thickness, we…
We use a direct numerical integration of the Vlasov equation in spherical symmetry with a background gravitational potential to determine the evolution of a collection of particles in different models of a galactic halo. Such a collection…
In this paper we propose several models that describe the dynamics of liquid films which are covered by a high concentration layer of insoluble surfactant. First, we briefly review the 'classical' hydrodynamic form of the coupled evolution…
Morphological instability of the solid-liquid interface occuring in a crystal growing from an undercooled thin liquid being bounded on one side by a free surface and flowing down inclined plane is investigated by a linear stability analysis…
The rotating shallow water model is a simplification of oceanic and atmospheric general circulation models that are used in many applications such as surge prediction, tsunami tracking and ocean modelling. In this paper we introduce a class…
Ice sintering is a form of metamorphism that drives the microstructural evolution of an aggregate of grains through surface and volume diffusion. This leads to an increase in the grain-to-grain contact area ("neck") and density of the…
The approach of nonequilibrium evolution thermodynamics earlier offered is developed. It helps to describe the processes of defect formation within the adiabatic approximation. The basic equations system depends on the initial defects…
Two-dimensional free-surface potential flows of an ideal fluid over a strongly inhomogeneous bottom are investigated with the help of conformal mappings. Weakly-nonlinear and exact nonlinear equations of motion are derived by the…
We present a numerical study of a two dimensional granular medium consisting of hard inelastic disks. The evolution of the medium throughout a cooling process is monitored. Two different types of instabilities (shearing and clustering…
A dynamical model is proposed to describe the coupled decomposition and profile evolution of a free surface film of a binary mixture. An example is a thin film of a polymer blend on a solid substrate undergoing simultaneous phase separation…
This paper concerns a time-independent thermoelectric model with two different boundary conditions. The model is a nonlinear coupled system of the Maxwell equations and an elliptic equation. By analyzing carefully the nonlinear structure of…
We have calculated an evolution of protoplanetary disk from an extensive set of initial conditions using a time-dependent model capable of simultaneously keeping track of the global evolution of gas and water-ice. A number of…
We study spreading dynamics of nematic liquid crystal droplets within the framework of the long-wave approximation. A fourth order nonlinear parabolic partial differential equation governing the free surface evolution is derived. The…