Related papers: Linear morphological stability analysis of the sol…
Freezing of polymer solutions has been extensively investigated from many aspects, especially the complex pattern formation. The cell/dendrite micro-structures are believed to be in the type of diffusion-induced M-S instability. However,…
Liquid structure at solid-liquid interfaces is critical for many natural and engineered processes ranging from biological signal transduction to electrochemical energy conversion. Advanced experimental and computational methods have…
This paper studies the dynamics of an incompressible fluid driven by gravity and capillarity forces in a porous medium. The main interest is the stabilization of the fluid in Rayleigh-Taylor unstable situations where the fluid lays on top…
Starting from a phase-field description of the isothermal solidification of a dilute binary alloy, we establish a model where capillary waves of the solidification front interact with the diffusive concentration field of the solute. The…
We give a general phenomenological description of the steady state 1D front propagation problem in two cases: the solidification of a pure material and the isothermal solidification of two component dilute alloys. The solidification of a…
Simple observations of evaporating solutions reveal a complex hierarchy of spatio-temporal instabilities. We analyze one such instability suggested by the qualitative observations of Du and Stone and find that it is driven by a novel…
The linear stability of stratified two-phase flows in rectangular ducts is studied numerically. The linear stability analysis takes into account all possible infinitesimal three-dimensional disturbances and is carried out by solution of the…
We study numerically the nonlinear dynamics of a shear banding interface in two dimensional planar shear flow, within the non-local Johnson Segalman model. Consistent with a recent linear stability analysis, we find that an initially flat…
We first establish existence for all positive time near equilibrium for the moving interface problem between the Navier-Stokes equations for the evolving fluid phase (moved by the fluid velocity) and an elastic body modelled by the linear…
The linear stability of rapid granular flow on a slope under gravity against the longitudinal perturbation is analyzed using hydrodynamic equations. It is demonstrated that the steady flow uniform along the flow direction becomes unstable…
During the laser powder bed fusion (L-PBF) process, the built part undergoes multiple rapid heating-cooling cycles, leading to complex microstructures with nonuniform properties. In the present work, a computational framework, which weakly…
We prove local well-posedness for the Muskat problem on the half-plane, which models motion of an interface between two fluids of distinct densities (e.g., oil and water) in a porous medium (e.g., an aquifer) that sits atop an impermeable…
Accurate and computationally accessible models of liquid film flows allow for optimizing coating processes such as hot-dip galvanization and vertical slot-die coating. This paper extends the classic three-dimensional integral boundary layer…
In this paper we analyze a fully discrete numerical scheme for solving a parabolic PDE on a moving surface. The method is based on a diffuse interface approach that involves a level set description of the moving surface. Under suitable…
This paper is devoted to the nonlinear analysis of a kinetic model introduced by Saintillan and Shelley to describe suspensions of active rodlike particles in viscous flows. We investigate the stability of the constant state $\Psi(t,x,p) =…
We have developed a Green-Kubo relation that enables accurate calculations of friction at solid-liquid interfaces directly from equilibrium molecular dynamics (MD) simulations and that provides a pathway to bypass the time-scale limitations…
This work outlines a new multi-physics-compatible immersed rigid body method for Eulerian finite-volume simulations. To achieve this, rigid bodies are represented as a diffuse scalar field and an interface seeding method is employed to…
We consider the motion of two inviscid, compressible, and electrically conducting fluids separated by an interface across which there is no fluid flow in the presence of surface tension. The magnetic field is supposed to be nowhere…
The stability of steady, dynamic, anti-plane slipping at a planar interface between two dissimilar anisotropic linear elastic solids is studied. The solids are assumed to possess a plane of symmetry normal to the slip direction, so that…
By a refinement of the technique used by Johnson and Zumbrun to show stability under localized perturbations, we show that spectral stability implies nonlinear modulational stability of periodic traveling-wave solutions of reaction…