Related papers: Regularity results for transmission problems with …
Architected 2D lattice materials are appealing for shape-shifting applications due to the tunable sign of Poisson's ratio. It is commonly believed that the positive and negative Poisson's ratios lead to anticlastic and synclastic curvatures…
We show that results about spaces or moduli spaces of positive scalar curvature metrics proved using index theory can typically be extended to non-negative scalar curvature metrics. We illustrate this by providing explicit generalizations…
Interfaces advancing through random media represent a number of different problems in physics, biology and other disciplines. Here, we study the pinning/depinning transition of the prototypical non-equilibrium interfacial model, i.e. the…
The transmission of polarized light through a two-dimensional randomly rough interface between two dielectric media has been much less studied, by any approach, than the reflection of light from such an interface. We have derived a reduced…
In 1,2 or 3 dimensions a scalar wave excited by a non-negative source in a viscoelastic medium with a non-negative relaxation spectrum or a Newtonian response or both combined inherits the sign of the source. The key assumption is a…
We consider a transmission problem where a structurally damped plate equation is coupled with a damped or undamped wave equation by transmission conditions. We show that exponential stability holds in the damped-damped situation and…
In this paper we address two boundary cases of the classical Kazdan-Warner problem. More precisely, we consider the problem of prescribing the Gaussian and boundary geodesic curvature on a disk of R^2, and the scalar and mean curvature on a…
The H^2-regularity of variational solutions to a two-dimensional transmission problem with geometric constraint is investigated, in particular when part of the interface becomes part of the outer boundary of the domain due to the saturation…
We study the transmission properties of a nonlinear periodic structure containing alternating slabs of a nonlinear right handed material and a linear left handed material. We find that the transmission associated with the zero averaged-…
We deal with decay and boundedness properties of radial functions belonging to Besov and Lizorkin-Triebel spaces. In detail we investigate the surprising interplay of regularity and decay. Our tools are atomic decompositions in combination…
We study the phenomenon of mass loss by a scalar charge -- a point particle which acts as a source for a (non-interacting) scalar field -- in (1+1)-dimensional and (2+1)-dimensional flat spacetime. We find that such particles are unstable…
We lay down a geometric-analytic framework to capture properties of energy dissipation within weak solutions to the incompressible Euler equations. For solutions with spatial Besov regularity, it is proved that the Duchon-Robert…
We examine a transmission problem driven by a degenerate quasilinear operator with a natural interface condition. Two aspects of the problem entail genuine difficulties in the analysis: the absence of representation formulas for the…
Negative and complex numbers are so familiar in modern mathematics, physics, and engineering that it is easy to forget how uncertain their status once was. They did not become established through a single route. This article follows four…
A particular mix of integral equations and discretization techniques is suggested for the solution of a planar Helmholtz transmission problem with relevance to the study of surface plasmon waves. The transmission problem describes the…
A negative symmetry is a nonlocal symmetry of special type. In this paper, we introduce a method for constructing negative symmetries from consistent triplets of differential and differential-difference equations. Moreover, we study the…
We propose a type of elastic metamaterial comprising fluid-solid composite inclusions which can possess negative shear modulus and negative mass density over a large frequency region. Such a solid metamaterial has a unique elastic property…
Viewed as approximations to quantum mechanics, classical evolutions can violate the positive-semidefiniteness of the density matrix. The nature of this violation suggests a classification of dynamical systems based on classical-quantum…
We shall study special regularity properties of solutions to some nonlinear dispersive models. The goal is to show how regularity on the initial data is transferred to the solutions. This will depend on the spaces where regularity is…
In this paper the characteristic matrix method is used to study the propagation of electromagnetic waves through one-dimensional lossy photonic crystals composed of negative and positive refractive index material layers with symmetric and…