Related papers: Boundary interface conditions and solute trapping …

Convergence of the solutions of nonhomogeneous linear singularly perturbed systems to that of the corresponding reduced singular system on the half-line [0, $\infty $) is considered. To include the situation on a neighborhood of initial…

Understanding boundary layer flows in high Reynolds number (Re) turbulence is crucial for advancing fluid dynamics in a wide range of applications, from improving aerodynamic efficiency in aviation to optimizing energy systems in industrial…

From a simple model for the driven motion of a planar interface under the influence of a diffusion field we derive a damped nonlinear oscillator equation for the interface position. Inside an unstable regime, where the damping term is…

In the above paper the authors treat the boundary layer flow along a stationary, vertical, permeable, flat plate within a vertical free stream. Fluid is sucked or injected through the vertical plate. The fluid species concentration at the…

We discuss melting of alloys along grain boundaries as a free boundary problem for two moving solid-liquid interfaces. One of them is the melting front and the other is the solidification front. The presence of the triple junction plays an…

In this study, an alloy phase-field model is used to simulate solidification microstructures at different locations within a solidified molten pool. The temperature gradient $G$ and the solidification velocity $V$ are obtained from a…

We study the homogenization problem for a system of stochastic differential equation with local time terms that models a multivariate diffusion in presence of semipermeable hyperplane interfaces with oblique penetration. We show that this…

The interplay between the diffusion-controlled dynamics of a solidification front and the trajectory of a grain boundary groove at the solid-liquid interface is studied by means of thin-sample directional solidification experiments of a…

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…

Continuum solvent models have become a standard technique in the context of electronic structure calculations, yet, no implementations have been reported capable to perform molecular dynamics at solid-liquid interfaces. We propose here such…

We study the transition to turbulence in the asymptotic suction boundary layer (ASBL) by direct numerical simulation. Tracking the motion of trajectories intermediate between laminar and turbulent states we can identify the invariant object…

The numerical approximation of non-isothermal liquid-vapor flow within the compressible regime is a difficult task because complex physical effects at the phase interfaces can govern the global flow behavior. We present a sharp interface…

Interfacial boundary conditions determined from empirical or ad-hoc models remain the standard approach to model fluid flows over porous media, even in situations where the topology of the porous medium is known. We propose a non-empirical…

This paper proposes a diffuse-interface model for simulating gas-liquid-solid multiphase flows involving solid-liquid phase change, solute transport, and the Marangoni effect. In this model, a phase-field method is employed to capture the…

Travelling waves of densities of binary fluid mixtures are investigated near a critical point. The free energy is considered in a non-local form taking account of the density gradients. The equations of motions are applied to a universal…

We investigate symmetry breaking in a time-dependent billiard that undergoes a continuous phase transition when dissipation is introduced. The system presents unlimited velocity, and thus energy growth for the conservative dynamics. When…

We investigate the nature of vapor bubble nucleation near a nanoscale-curved convex liquid-solid interface using two models; an equilibrium Gibbs model for homogenous formation, and a nonequilibrium dynamic van der Waals/diffuse interface…

We calculate the exact stationary distribution of the one-dimensional zero-range process with open boundaries for arbitrary bulk and boundary hopping rates. When such a distribution exists, the steady state has no correlations between sites…

We study the motion of phase interfaces in a diffusive lattice equation with bistable nonlinearity and derive a free boundary problem with hysteresis to describe the macroscopic evolution in the parabolic scaling limit. The first part of…

Recently, Murthy et al. [2017] and Escande et al. [2020] adopted the Lattice Boltzmann Method (LBM) to model the linear elastodynamic behaviour of isotropic solids. The LBM is attractive as an elastodynamic solver because it can be…