Related papers: Local smoothing effects for the water-wave problem…
We present an exact three-dimensional wave solution to the shearing sheet equations of motion. The existence of this solution argues against transient amplification as a route to turbulence in unmagnetized disks. Moreover, because the…
We prove the local well-posedness of the 3D free-boundary incompressible ideal magnetohydrodynamics (MHD) equations with surface tension, which describe the motion of a perfect conducting fluid in an electromagnetic field. We adapt the…
We consider the capillary-gravity water wave equation in two dimensions. We assume that the fluid is inviscid, incompressible, irrotational and the air density is zero. We construct an energy functional and prove a local wellposedness…
This paper concerns the dynamics of two layers of compressible, barotropic, viscous fluid lying atop one another. The lower fluid is bounded below by a rigid bottom, and the upper fluid is bounded above by a trivial fluid of constant…
In this paper we discuss approximation of partially smooth functions. The problem arises naturally in the study of laminated currents.
The surface tension of interacting polymers in a good solvent is calculated theoretically and by computer simulations for a planar wall geometry and for the insertion of a single colloidal hard-sphere. This is achieved for the planar wall…
Near solid-liquid or liquid-liquid interfaces with dielectric contrast, charged particles interact with the induced polarization charge of the interface. These interactions contribute to an effective self-energy of the bulk ions and mediate…
We analyze the effect of a rough surface on shear thinning and shear thickening fluids, modeled by power law stress tensors. The roughness is modeled by a small wavelength and small amplitude oscillation, parametrized by eps. We study the…
The presence of ambient air in liquid-slamming events plays a crucial role in influencing the shape of the liquid surface prior to the impact, and the distribution of loads created upon impact. We study the effect of trapped air on impact…
We consider a one-dimensional elastic membrane, which is pushed by growing filaments. The filaments tend to grow by creating local protrusions in the membrane and this process has surface energy and bending energy costs. Although it is…
We study the surface tension of ionic solutions at air/water and oil/water interfaces. By using field-theoretical methods and including a finite proximal surface-region with ionic-specific interactions. The free energy is expanded to…
We consider the one-dimensional shallow water problem with capillary surfaces and moving contact {lines}. An energy-based model is derived from the two-dimensional water wave equations, where we explicitly discuss the case of a stationary…
Soft membranes are commonly employed in shape-morphing applications, where the material is programmed to achieve a target shape upon activation by an external trigger, and as coating layers that alter the surface characteristics of bulk…
We derive the incremental equations for a hyperelastic solid that incorporate surface tension effect by assuming that the surface energy is a general function of the surface deformation gradient. The incremental equations take the same…
We report on an experimental, theoretical and numerical study of slanted snaking of spatially localized parametrically excited waves on the surface of a water-surfactant mixture in a Hele-Shaw cell. We demonstrate experimentally the…
Some effects of surface tension on fully-nonlinear, long, surface water waves are studied by numerical means. The differences between various solitary waves and their interactions in subcritical and supercritical surface tension regimes are…
Effects of spatially varying interfacial parameters on the propagation of surface waves are studied. These variations can arise from inhomogeneities in coverage of surface active substances such as amphiphillic molecules at the fluid/gas…
We prove local smoothing estimates for the massless Dirac equation with a Coulomb potential in 2 and 3 space dimensions. Our strategy of proof is inspired by a paper of Burq et al. (2003) about Schroedinger and wave equations with…
Dielectric elastomers have recently been proposed for various biologically-relevant applications, in which they may operate in fluidic environments where surface tension effects may have a significant effect on their stability and…
We determine the surface tension of aqueous electrolyte solutions in contact with non-polar dielectric media using a thermomechanical approach, which involves deriving the stress tensor from the thermodynamic potential of an inhomogeneous…