Related papers: On the dynamics of shallow ice sheets. Modelling a…
The surface evolution model based on geometric partial differential equation is used to numerically study the kinetics of dewetting and dynamic morphologies for the localized pinhole defect in the surface of the ultrathin solid film with…
It is increasingly common for models of shallow-layer overland flows to include equations for the evolution of the underlying bed (morphodynamics) and the motion of an associated sedimentary phase. We investigate the linear stability…
The Whitham equation is a model for the evolution of small-amplitude, unidirectional waves of all wavelengths on shallow water. It has been shown to accurately model the evolution of waves in laboratory experiments. We compute…
Nonlinear evolution of one-dimensional planar perturbations in an optically thin radiatively cooling medium in the long-wavelength limit is studied numerically. The accepted cooling function generates in thermal equilibrium a bistable…
The formation of periodic wrinkles in soft layered materials due to mechanical instabilities is prevalent in nature and has been proposed for use in multiple applications. However, such phenomena have been explored predominantly in…
In this paper, we consider a non-linear fourth-order evolution equation of Cahn-Hilliard-type on evolving surfaces with prescribed velocity, where the non-linear terms are only assumed to have locally Lipschitz derivatives. High-order…
We consider a class of models for nonlinearly elastic surfaces in this work. We have in mind thin, highly deformable structures modeled directly as two-dimensional nonlinearly elastic continua, accounting for finite membrane and bending…
We study a spherical, self-gravitating fluid model, which finds applications in cosmic structure formation. We argue that since the system features nonlinearity and gravity-induced dispersion, the emergence of solitons becomes possible. We…
We explore the instabilities developed in a fluid in which viscosity depends on temperature. In particular, we consider a dependency that models a very viscous (and thus rather rigid) lithosphere over a convecting mantle. To this end, we…
We consider the modulational instability of nonlinearly interacting two-dimensional waves in deep water, which are described by a pair of two-dimensional coupled nonlinear Schroedinger equations. We derive a nonlinear dispersion relation.…
In this paper, we propose a variational formulation to study the singular evolution equations that govern the dynamics of surface modulations on crystals below the roughening temperature. The basic idea of the formulation is to expand the…
Ice sheet models are used to study the deglaciation of North America at the end of the last ice age (past 21,000 years), so that we might understand whether and how existing ice sheets may reduce or disappear under climate change. Though…
We investigate the evolution of interfaces among phases of the interstellar medium with different temperature. It is found that, for some initial conditions, the dynamical effects related to conductive fronts are very important even if…
Stability and convergence of full discretizations of various surface evolution equations are studied in this paper. The proposed discretization combines a higher-order evolving-surface finite element method (ESFEM) for space discretization…
The near membrane layer is defined as a region where the concentration of the substance transported across the membrane drops $k$ times. The time evolution of such a layer is studied experimentally by means of the laser interferometric…
A three-dimensional model of polydisperse reactive sedimentation is developed by means of a multilayer shallow water approach. The model consists of a variety of solid particles of different sizes and densities, and substrates diluted in…
A physical model and two-dimensional numerical method for computing the evolution and spectra of protostellar clouds are described. The physical model is based on a system of magneto-gasdynamical equations, including ohmic and ambipolar…
By performing two parallel numerical experiments -- solving the dynamical Hamiltonian equations and solving the Hasselmann kinetic equation -- we examined the applicability of the theory of weak turbulence to the description of the time…
Shallow free surface flows are often characterized by both subdomains that require high modeling complexity and subdomains that can be sufficiently accurately modeled with low modeling complexity. Moreover, these subdomains may change in…
During the wear process of surfaces in sliding friction, there is a running-in period during which the topography of surfaces changes with time before reaching the steady wear regime. In the steady wear regime, the statistical parameters…