Related papers: Dynamics of Interfaces in Superconductors
For the free boundary problem of the plasma-vacuum interface to three-dimensional ideal incompressible magnetohydrodynamics (MHD), the a priori estimates of smooth solutions are proved in Sobolev norms by adopting a geometrical point of…
Theory of the influence of the thermal fluctuations on the electric transport beyond linear response in superconductors is developed within the framework of the time dependent Ginzburg - Landau approach. The I - V curve is calculated using…
The effect of thermal fluctuations near a contact line of a liquid interface partially wetting an impenetrable substrate is studied analytically and numerically. Promoting both the interface profile and the contact line position to random…
We propose an efficient numerical method for the simulation of multi-phase flows with moving contact lines in three dimensions. The mathematical model consists of the incompressible Navier-Stokes equations for the two immiscible fluids with…
We derive the hydrodynamic limit of Glauber-Kawasaki dynamics. The Kawasaki part is simple and describes independent movement of the particles with hard core exclusive interactions. It is speeded up in a diffusive space-time scaling. The…
What is the interface temperature during phase transition (for instance, from liquid to vapor)? This question remains fundamentally unresolved. In the modeling of heat transfer problems with no phase change, the temperature and heat flux…
The evolution of the interface between two ideal dielectric liquids in a strong vertical electric field is studied. It is found that a particular flow regime, for which the velocity potential and the electric field potential are linearly…
The properties of interfaces in non-equilibrium situations are studied by constructing a density matrix with a space-dependent temperature. The temperature gradient gives rise to new terms in the equation for the order parameter. Surface…
Analyzing complex fluid flow problems that involve multiple coupled domains, each with their respective set of governing equations, is not a trivial undertaking. Even more complicated is the elaborate and tedious task of specifying the…
In this paper, we derive a thermodynamically consistent non-isothermal diffuse interface model for phase transition and interface evolution involving heat transfer. This model is constructed by integrating concepts from classical…
Elasticity theory provides an accurate description of the long-wavelength vibrational dynamics of homogeneous crystalline solids, and with supplemental boundary conditions on the displacement field can also be applied to abrupt…
We study the dynamical behavior of a one dimensional interface interacting with a sticky unpenetrable substrate or wall. The interface is subject to two effects going in opposite directions. Contact between the interface and the substrate…
We investigate the relaxation dynamics of heat transport in superconductors, shaped by the interplay of diffusion, nonlinearity, and magnetic fields. Focusing on regimes near the critical temperature Tc, we analyze two classes of relaxation…
We consider the free boundary problem for relativistic plasma--vacuum interfaces in two and three spatial dimensions. The plasma flow is governed by the equations of ideal relativistic magnetohydrodynamics, while the vacuum magnetic and…
Liquid-gas phase coexistence in a boundary-driven diffusive system is studied by analyzing fluctuating hydrodynamics of a density field defined on a one-dimensional lattice with a space interval $\Lambda$. When an interface width $\ell$ is…
An interface description and numerical simulations of model A kinetics are used for the first time to investigate the intra-surface kinetics of phase ordering on corrugated surfaces. Geometrical dynamical equations are derived for the…
We consider a coupled model for fluid flow and transport in a domain consisting of two bulk regions separated by a thin porous layer. The thickness of the layer is of order $\varepsilon$ and the microscopic structure of the layer is…
We present an approach to theoretical assessment of the mean specific interface area $(\delta{S}/\delta{V})$ for a well-stirred system of two immiscible liquids experiencing interfacial boiling. The assessment is based on the balance of…
The statistical mechanics of equilibrium interfaces has been well-established for over a half century. In the last decade, a wealth of observations have made increasingly clear that a new perspective is required to describe interfaces…
Neural field equations model population dynamics of large-scale networks of neurons. Wave propagation in neural fields is often studied by constructing traveling wave solutions in the wave coordinate frame. Nonequilibrium dynamics are more…