Related papers: A free discontinuity model for smectic thin films
Surface incompressibility, also called inextensibility, imposes a zero-surface-divergence constraint on the velocity of a closed deformable material surface. The well-posedness of the mechanical problem under such constraint depends on an…
A comprehensive review of current analytical models, experimental techniques, and influencing factors is carried out to highlight the current challenges in this area. The study of fluid-solid boundary conditions has been ongoing for more…
In this paper we look for minimizers of the energy functional for isotropic compressible elasticity taking into consideration the effect of a gravitational field induced by the body itself. We consider the displacement problem in which the…
We develop an analytical tool which is adept for detecting shapes of oscillatory functions, is useful in decomposing homogenization problems into limit-problems for kinetic equations, and provides an efficient framework for the validation…
We consider a one-phase nonlocal free boundary problem obtained by the superposition of a fractional Dirichlet energy plus a nonlocal perimeter functional. We prove that the minimizers are H\"older continuous and the free boundary has…
Probing the fluid dynamics of thin films is an excellent tool to study the solid/liquid boundary condition. There is no need for external stimulation or pumping of the liquid due to the fact that the dewetting process, an internal…
We explain theoretically peculiarities of the smectic A -- hexatic B equilibrium phase coexistence in a finite temperature range recently observed experimentally in free standing smectic films [I.A.Zaluzhnyy et al., Physical Review E,…
The classical problem of foam film rupture dynamics has been investigated when surfaces exhibit very high rigidity due to the presence of specific surfactants. Two new features are reported. First a strong deviation to the well-known…
We study the deformation and dewetting of liquid films under impinging gas jets using experimental, analytical and numerical techniques. We first derive a reduced-order model (a thin-film equation) based on the long-wave assumption and on…
Thin metal films are subject to the pressure caused by the zero point oscillations of the electromagnetic field, which depends upon the film optical properties and, in case of deposition onto a substrate, upon the substrate reflectivity. It…
Subsurface flows are commonly modeled by advection-diffusion equations. Insufficient measurements or uncertain material procurement may be accounted for by random coefficients. To represent, for example, transitions in heterogeneous media,…
The axisymmetric flow of a thin liquid film is considered for the problem of a vertically rotating disk that is partially immersed in a liquid bath. A model for the fully three-dimensional free-boundary problem of the rotating disk, that…
In this paper, we discuss a particular model arising from sinking of a rigid solid into a thin film of fluid, i.e. a fluid contained between two solid surfaces and part of the fluid surface is in contact with the air. The fluid is governed…
In this paper we review simulation and experimental studies of thermal capillary wave fluctuations as an ideal means for probing the underlying disjoining pressure and surface tensions, and more generally, fine details of the Interfacial…
The influence of surface defects on the critical properties of magnetic films is studied for Ising models with nearest-neighbour ferromagnetic couplings. The defects include one or two adjacent lines of additional atoms and a step on the…
A new approach to the treatment of magnetic fluctuations in thin films of type I superconductors is introduced. Results for the dependence of free energy, specific heat and order parameter profile on the film thickness near the equilibrium…
We consider a toy model of rate independent droplet motion on a surface with contact angle hysteresis based on the one-phase Bernoulli free boundary problem. We introduce a notion of solutions based on an obstacle problem. These solutions…
We propose a microscopic model to describe the scattering of light by atoms in optical lattices. The model is shown to efficiently capture Bragg scattering, spontaneous emission and photonic band gaps. A connection to the transfer matrix…
We study numerically the effect of thermal fluctuations and of variable fluid-substrate interactions on the spontaneous dewetting of thin liquid films. To this aim, we use a recently developed lattice Boltzmann method for thin liquid film…
We construct a mathematical model for a diffusiophoretic motion of a deformable droplet, which is floating on a liquid surface and is driven by the surface tension gradient originating from the surface concentration field of the chemicals…