相关论文: A free discontinuity model for smectic thin films

A metallic film of arbitrary thickness is considered. We show that the problem of description of surface plasma oscillations (surface plasmons) with reflection boundary conditions allows analytic solution. Besides, this problem allows…

The paper addresses the question if there exists a finite stopping time for an unforced motion of a yield stress fluid with free surface. A variation inequality formulation is deduced for the problem of yield stress fluid dynamics with a…

We consider the discrete atomistic setting introduced in \cite{PiVe1} to microscopically justify the continuum model related to the \emph{Winterbottom problem}, i.e., the problem of determining the equilibrium shape of crystalline film…

The van der Waals forces across a very thin liquid layer (nanofilm) in contact with a plane solid wall make the liquid nonhomogeneous. The dynamics of such flat liquid nanofilms is studied in isothermal case. The Navier-Stokes equations are…

We consider a thin film limit of a Landau-de Gennes Q-tensor model. In the limiting process we observe a continuous transition where the normal and tangential parts of the Q-tensor decouple and various intrinsic and extrinsic contributions…

In present work we calculated the three components of polarization in phenomenological theory framework by consideration of three Euler-Lagrange equations, which include mismatch effect and influence of misfit dislocations, surface…

Freezing in the vicinity of water-vapor interfaces is of considerable interest to a wide range of disciplines, most notably the atmospheric sciences. In this work, we use molecular dynamics and two advanced sampling techniques, forward flux…

We consider the simplest example of a time-dependent first order Hamilton-Jacobi equation, in one space dimension and with a bounded and Lipschitz continuous Hamiltonian which only depends on the spatial derivative. We show that if the…

Recent simulation studies of the surface tension, and other properties of thin free-standing films, have revealed unexpected finite size effects in which the variance of the properties vary monotonically with the in-plane width of the…

Smectic liquid crystals are materials formed by stacking deformable, fluid layers. Though smectics prefer to have flat, uniformly-spaced layers, boundary conditions can impose curvature on the layers. Since the layer spacing and curvature…

We study the annihilation of topological defect pairs in the quasi-twodimensional (2D) geometry of freely suspended smectic films. This elementary process is at the basis of all models describing the statistics of complex defect patterns.…

We establish the existence of spatially localised one-dimensional free surfaces of a ferrofluid near onset of the Rosensweig instability, assuming a general (nonlinear) magnetisation law. It is shown that the ferrohydrostatic equations can…

We prove optimal regularity and a detailed analysis of the free boundary of the solutions to the thin obstacle problem for nonparametric minimal surfaces with flat obstacles.

Nematic surfaces are thin liquid films endowed with in-plane orientational order. We study a variational model in which the nematic director is constrained to lie in the tangent space of an axisymmetric surface, and the associated surface…

Free interfaces of liquid crystals tend to minimise both capillarity and anchoring forces. Here we study nematic films in planar and radial geometries with antagonistic anchoring boundary conditions and one deformable interface. Assuming a…

We study the transition from flat to wrinkled region in uniaxially stretched thin elastic film. We set up a model variational problem, and study energy of its ground state. Using known scaling bounds for the minimal energy, the minimal…

Large-scale atomistic calculations, using empirical potentials for modeling semiconductors, have been performed on a stressed system with linear surface defects like steps. Although the elastic limits of systems with surface defects remain…

We analyze the solution of the Schr\"odinger equation arising in the treatment of a geometric model introduced to explain the origin of the observed shallow levels in semiconductors threaded by a dislocation density. We show (contrary to…

We study the regularity and well-posedness of physical solutions to the supercooled Stefan problem. Assuming only that the initial temperature is integrable, we prove that the free boundary, known to have jump discontinuities as a function…

We discuss instabilities of fluid films of nanoscale thickness, with a particular focus on films where the destabilising mechanism allows for linear instability, metastability, and absolute stability. Our study is motivated by nematic…