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This paper is dedicated to the solidification of a water drop impacting a cold solid surface. In a first part, we establish a 1D solidification model, derived from the Stefan problem, that aims at predicting the freezing dynamic of a liquid…
This paper considers the problem of water wave scattering by a rectangular anisotropic elastic plate mounted on the ocean surface, with either free, clamped or simply-supported edges. The problem is obtained as an expansion over the dry…
We introduce a novel approach to simulate the interaction between fluids and thin elastic solids without any penetration. Our approach is centered around an optimization system augmented with barriers, which aims to find a configuration…
The equilibrium contact angle of a droplet resting on a solid substrate can reveal essential properties of the solid's surface. However, when the motion of a droplet on a surface shows significant hysteresis, it is generally accepted that…
Current-vortex sheet is one of the characteristic discontinuities in ideal compressible magnetohydrodynamics (MHD). The motion of current-vortex sheets is described by a free-interface problem of two-phase MHD flows with magnetic fields…
We explain the force balance in flowing marine ice sheets and the ice shelves they often feed. Treating ice as a viscous shear-thinning power law fluid, we develop an asymptotic (late-time) theory in two cases $-$ the presence or absence of…
We use a free energy lattice Boltzmann approach to investigate numerically the dynamics of drops moving across superhydrophobic surfaces. The surfaces comprise a regular array of posts small compared to the drop size. For drops suspended on…
We study the dewetting of a porous plate withdrawn from a bath of fluid. The microscopic contact angle is fixed to zero and the flow is assumed to be parallel to the plate (lubrication approximation). The ordinary differential equation…
We conjecture the existence of a relationship between frustration and the transition point at zero temperature of Ising spin glasses. The relation reveals that, in several Ising spin glass models, the concentration of ferromagnetic bonds is…
The surface tension of compliant materials such as gels provides resistance to deformation in addition to and sometimes surpassing that due to elasticity. This article studies how surface tension changes the contact mechanics of a small…
This article explores how a submerged elastic plate, clamped at one edge, interacts with water waves. Submerged elastic plates have been considered as potentially effective design elements in the development of wave energy harvesters but…
When a ball is dropped in fine, very loose sand, a splash and subsequently a jet are ob- served above the bed, followed by a granular eruption. To directly and quantitatively determine what happens inside the sand bed, high-speed X-ray…
The basal sliding of glaciers and ice sheets can constitute a large part of the total observed ice velocity, in particular in dynamically active areas. It is therefore important to accurately represent this process in numerical models. The…
Load-depth relation is the fundamental requisite in nanoindentation tests for thin layers, however, the effects of surface tension are seldom included. This paper concerns micro-/nano-sized indentation of a bonded elastic layer by a rigid…
The kinetics of interfaces in alloy solidification pose a classic free boundary problem. This paper introduces an approach that amalgamates the distinctive characteristics of sharp and diffuse interface models. The motion of the diffuse…
In this paper, we study the two phase flow problem with surface tension in the ideal incompressible magnetohydrodynamics. We first prove the local well-posedness of the two phase flow problem with surface tension, then demonstrate that as…
In this article, we study the free vibration and the mechanical buckling of plates using a three dimensional consistent approach based on the scaled boundary finite element method. The in-plane dimensions of the plate are modeled by…
We provide a complete description of the low temperature wetting transition for the two dimensional Solid-On-Solid model. More precisely we study the integer-valued field $(\phi(x))_{x\in \mathbb Z^2}$, associated associated to the energy…
The elastic deformation of a soft solid induced by capillary forces crucially relies on the excess stress inside the solid-liquid interface. While for a liquid-liquid interface this "surface stress" is strictly identical to the "surface…
We study the number and the length of systoles on complete finite area orientable hyperbolic surfaces. In particular, we prove upper bounds on the number of systoles that a surface can have (the so-called kissing number for hyperbolic…