Related papers: Scarf for Lifshitz
When a spatially localized stress is applied to a growing one-dimensional interface, the interface deforms. This deformation is described by the effective surface tension representing the stiffness of the interface. We present that the…
Infrared divergences obscure important analytic properties of scattering amplitudes, indicating gaps in our understanding of unitarity, causality, and crossing symmetry in theories with long-range forces. Using the exactly solvable model of…
The porous medium type reaction-diffusion equation and the Hele-Shaw problem are two free boundary problems linked through the incompressible (Hele-Shaw) limit. We investigate and compare the sharp power concavities of the pressures on…
This paper is concerned with the problem of scattering of time-harmonic electromagnetic waves from an impenetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is established, employing the integral…
The notion of tissue surface tension has provided a physical understanding of morphogenetic phenomena such as tissue spreading or cell sorting. The measurement of tissue surface tension so far relied on strong approximations on the…
We investigate the sharp material interface limit of the Darcy-Boussinesq model for convection in layered porous media with diffused material interfaces, which allow a gradual transition of material parameters between different layers. We…
(Electric) polarization tensors describe part of the leading order term of asymptotic voltage perturbations caused by low volume fraction inhomogeneities of the electrical properties of a medium. They depend on the geometry of the support…
We study the action on currents and differential forms on compact Riemannian manifolds under $C^0$-limits of diffeomorphisms. Using tools from geometric analysis, measure theory, and homotopy theory, we establish several convergence…
We present a diffuse-interface model for the solid-state dewetting problem with anisotropic surface energies in ${\mathbb R}^d$ for $d\in\{2,3\}$. The introduced model consists of the anisotropic Cahn--Hilliard equation, with either a…
The surface of metal, glass and plastic objects is often characterized by microscopic scratches caused by manufacturing and/or wear. A closer look onto such scratches reveals iridescent colors with a complex dependency on viewing and…
In this work, we consider a torque caused by the well known quantum mechanical Casimir effect arising from quantized field fluctuations between plates with inhomogeneous, sharply discontinuous, dielectric properties. While the Casimir…
Quantum vacuum energy has been known to have observable consequences since 1948 when Casimir calculated the force of attraction between parallel uncharged plates, a phenomenon confirmed experimentally with ever increasing precision. Casimir…
In this paper we study the homogenization of the Dirichlet problem for the Stokes equations in a perforated domain with multiple microstructures. First, under the assumption that the interface between subdomains is a union of Lipschitz…
The paper addresses the problem of a a semi-infinite plane crack along the interface between two 3D isotropic half-spaces. Two methods of solution have been considered in the past: Lazarus and Leblond (1998) applied the "special" method by…
We consider the transport of conserved charges in spatially inhomogeneous quantum systems with a discrete lattice symmetry. We analyse the retarded two point functions involving the charge and the associated currents at long wavelengths,…
The Casimir-Lifshitz interaction between metamaterials is studied using a model that takes into account the structural heterogeneity of the dielectric and magnetic properties of the bodies. A recently developed perturbation theory for the…
Surface plasmon polaritons propagating along curved metal-dielectric interfaces experience geometry-induced modifications absent on flat surfaces. In this work, we derive a covariant, effective two-dimensional wave equation for the…
The paper concerns the sharp boundary regularity estimates in homogenization of Dirichlet problem for Stokes systems. We obtain the Lipschitz estimates for velocity term and $L^\infty$ estimate for pressure term, under some reasonable…
In a dislocation problem, a paradoxical discordance is known to occur between an original smooth curve and an infinitesimally discretized curve. To solve this paradox, we have investigated a non-hypersingular expression for the integral…
We compare theoretical expectations for the Casimir force with the results of precise measurements. The force is calculated at finite temperature for multilayered covering of the bodies using the Lifshitz theory. We argue that the…