Related papers: Permittivity optimization for Maxwell's eigenvalue…
We analyze the formal equivalence between the electromagnetic energy conservation law derived from Maxwell's equations in an optical microcavity and the conservation of a probability fluid associated with the de Broglie-Bohm theory for an…
In this paper we compare the candidates to be spectral minimal partitions for two criteria: the maximum and the average of the first eigenvalue on each subdomains of the partition. We analyze in detail the square, the disk and the…
Maxwells equations are fundamental to our understanding of electromagnetic fields, but their solution can be computationally demanding, even for high-performance computing clusters. Quantum computers offer a promising alternative for…
We study the free boundary problem for a plasma-vacuum interface in ideal incompressible magnetohydrodynamics. Unlike the classical statement when the vacuum magnetic field obeys the div-curl system of pre-Maxwell dynamics, to better…
The paper is devoted to a systematic study and characterizations of notions of local maximal monotonicity and their strong counterparts for set-valued operators that appear in variational analysis, optimization, and their applications. We…
We prove variants of known singularity theorems ensuring the existence of a region of finite lifetime that are particularly well applicable if the solution admits a conformal extension, a property satisfied e.g. by maximal Cauchy…
In this paper, we study a maximization and a minimization problem associated with a Poisson boundary value problem. Optimal solutions in a set of rearrangements of a given function define stationary and stable flows of an ideal fluid in two…
We consider the Maxwell's equations with perfect electric conductor boundary conditions in three-dimensional unbounded domains which are the union of a bounded resonator and one or several semi-infinite waveguides. We are interested in the…
We derive a Maximum Principle for optimal control problems with constraints given by the coupling of a system of ODEs and a PDE of Vlasov-type. Such problems arise naturally as ${\Gamma}$-limits of optimal control problems subject to ODE…
We consider the Steklov eigenvalues of the Laplace operator as limiting Neumann eigenvalues in a problem of boundary mass concentration. We discuss the asymptotic behavior of the Neumann eigenvalues in a ball and we deduce that the Steklov…
We investigate Maxwell-scalar models on radially symmetric spacetimes in which the gauge and scalar fields are coupled via the electric permittivity. We find the conditions that allow for the presence of minimum energy configurations. In…
A problem of the skin effect in the Maxwell plasma is solved analytically by the method of expansion in eigenfunctions based on the Vlasov-Maxwell kinetic equation with a self-consistent electric field. Specular electron reflection from the…
We consider the free boundary problem for the plasma-vacuum interface in ideal compressible magnetohydrodynamics (MHD). In the plasma region, the flow is governed by the usual compressible MHD equations, while in the vacuum region we…
Optimized, necessary and sufficient conditions for the identification of the Schmidt number will be derived in terms of general Hermitian operators. These conditions apply to arbitrary mixed quantum states. The optimization procedure…
This paper is devoted to providing quantitative bounds on the location of eigenvalues, both discrete and embedded, of non self-adjoint Lam\'e operators of elasticity $-\Delta^\ast + V$ in terms of suitable norms of the potential $V$. In…
In this paper, we derive sufficient and necessary maximum principles for a stochastic optimal control problem where the system state is given by a controlled stochastic differential equation with default. We prove existence of a unique…
Invariant conditions for conformable fractional problems of the calculus of variations under the presence of external forces in the dynamics are studied. Depending on the type of transformations considered, different necessary conditions of…
Optimization problems with both control variables and environmental variables arise in many fields. This paper introduces a framework of personalized optimization to han- dle such problems. Unlike traditional robust optimization,…
We establish new analytic and numerical results on a general class of rational operator Nevanlinna functions that arise e.g. in modelling photonic crystals. The capability of these dielectric nano-structured materials to control the flow of…
We consider the Einstein-Maxwell system as a Cauchy initial value problem taking the electric and magnetic fields as independent variables. Maxwell's equations in curved spacetimes are derived in detail using a 3+1 formalism and their…