Related papers: Direct and inverse problems for the nonlinear time…
Bulk materials possessing a relative electric permittivity $\varepsilon$ close to zero exhibit giant Kerr nonlinearities. However, harnessing this response in guided-wave geometries is not straightforward, due to the extreme and…
We study the rate of convergence for (variational) eigenvalues of several non-linear problems involving oscillating weights and subject to different kinds of boundary conditions in bounded domains.
For semilinear wave equations on Lorentzian manifolds with quadratic derivative non-linear terms, we study the inverse problem of determining the background Lorentzian metric. Under some conditions on the nonlinear term, we show that from…
The anomalous Hall effect and magneto-optical Kerr effect have traditionally been associated with ferromagnets, but recent studies reveal their presence in noncollinear antiferromagnets due to nonzero Berry curvature despite negligible net…
In this paper we consider a special case of vacuum non-linear electrodynamics with a stress-energy tensor conformal to the Maxwell theory. Distinctive features of this model are: the absence of dimensional parameter for non-linearity…
We discuss the solution to Einstein's equations for a Lense-Thirring inspired metric describing a slowly rotating black hole coupled to nonlinear electrodynamics. We show that different schemes of rotation for the black hole exist; they…
Spatially dispersive (also known as non-local) electromagnetic media are considered where the parameters defining the permittivity relation vary periodically. Maxwell's equations give rise to a difference equation corresponding to the…
Nonlinear ultrasound imaging leverages harmonic wave generation to enhance contrast and spatial resolution beyond the capabilities of conventional linear techniques. This behavior is commonly modeled by the Westervelt equation, which…
For an initial-boundary value problem for a parabolic equation in the spatial variable $x=(x_1,.., x_n)$ and time $t$, we consider an inverse problem of determining a coefficient which is independent of one spatial component $x_n$ by extra…
We study Gaussian wave packet solutions for Maxwell's equations in an isotropic, inhomogeneous medium and derive a system of ordinary differential equations that captures the leading-order correction to geodesic motion. The dynamical…
Negative index materials are artificial structures whose refractive index has negative value over some frequency range. The study of these materials has attracted a lot of attention in the scientific community not only because of their many…
Time-reversal symmetry, together with space-inversion symmetry, is one of the defining properties of crystals, underlying phenomena such as magnetism, topology and non-trivial spin textures. Transition metal dichalcogenides (TMDs) provide…
Stationary axisymmetric binary systems of unequal co and counter-rotating extreme Kerr black holes apart by a conical singularity are studied. Both solutions are well identified as two $3$-parametric subfamilies of the Kinnersley-Chitre…
The topological nature of the band structure of a Weyl semimetal leads to a number of unique transport and optical properties. For example, the description of the propagation of an electromagnetic wave in a Weyl semimetal with broken…
This work is concerned with an inverse problem of identifying the current source distribution of the time-harmonic Maxwell's equations from multi-frequency measurements. Motivated by the Fourier method for the scalar Helmholtz equation and…
By modeling a linear, anisotropic and inhomogeneous magnetodielectric medium with two independent set of harmonic oscillators, electromagnetic field is quantized in such a medium. The electric and magnetic polarizations of the medium are…
We consider the time-harmonic acoustic wave scattering by a bounded {\it anisotropic inhomogeneity} embedded in an unbounded {\it anisotropic} homogeneous medium. The material parameters may have discontinuities across the interface between…
This paper addresses the inverse problem of simultaneously recovering multiple unknown parameters for semilinear wave equations from boundary measurements. We consider an initial-boundary value problem for a wave equation with a general…
The paper introduces a method to solve inverse problems for hyperbolic systems where the leading order terms are non-linear. We apply the method to the coupled Einstein-scalar field equations and study the question whether the structure of…
Pride (1994, Phys. Rev. B 50 15678-96) derived the governing model of electroseismic conversion, in which Maxwell's equations are coupled with Biot's equations through an electrokinetic mobility parameter. The inverse problem of…