Related papers: Helmholtz's theorem for two retarded fields and it…
For Maxwell's equations with nonlinear polarization we prove the existence of time-periodic breather solutions travelling along slab or cylindrical waveguides. The solutions are TE-modes which are localized in space directions orthogonal to…
This paper introduces a time-domain combined field integral equation for electromagnetic scattering by a perfect electric conductor. The new equation is obtained by leveraging the quasi-Helmholtz projectors, which separate both the unknown…
A relativistic equation is deduced for the bound state of two particles, by assuming a proper boundary condition for the propagation of the negative-energy states. It reduces to the (one-body)Dirac equation in the infinite limit of one of…
Single- and multi-valued solutions of homogeneous Maxwell equations in vacuum are considered, with ''sources'' formed by the (point- or string-like) singularities of the field strengths and, generally, irreducible to any delta-functions'…
The Friedrichs extension of minimal linear relation being bounded below and associated with the discrete symplectic system with a special linear dependence on the spectral parameter is characterized by using recessive solutions. This…
I construct combined electric and magnetic field variables which independently represent energy flows in the forward and backward directions respectively, and use these to re-formulate Maxwell's equations. The emphasis is on detailed…
We consider the convected Helmholtz equation modeling linear acoustic propagation at a fixed frequency in a subsonic flow around a scattering object. The flow is supposed to be uniform in the exterior domain far from the object, and…
The presence of the term $\left(\case{v}{c}\right)$ that characterizes the electrodynamic retarded potentials, also known as Li\'enard-Wiechert potentials, is thought to be reminiscent of a Doppler effect. Here, we show that these…
In the formulation of the problem of scattering of monochromatic waves and the numerical simulation of the solution to the Helmholtz equation, there is a computational inconvenience: the calculation is performed on a finite grid of…
In this paper Maxwell equations are used to analyze the propagation of oscillating electric and magnetic fields from a moving electric dipole source. The results show that both the magnetic field and electric fields generated propagate…
In this paper, we consider an electrodynamics of higher derivatives coupled to a Lorentz-violating background tensor. Specifically, we are interested in a dimension-five term of the CPT-odd sector of the nonminimal Standard-Model Extension.…
Solution of Helmholtz equation with impedance boundary condition on finite interval is equivalently reformulated as steady state of initial boundary value problem for first order hyperbolic system of partial differential equations.…
A major challenge of many diffraction calculations, using some form of the Rayleigh-Sommerfeld formulas, is the integration of a highly oscillatory integrand. Here we derive a potentially useful alternative form of solution to the Helmholtz…
We give simple proofs of the Davenport--Heilbronn theorems, which provide the main terms in the asymptotics for the number of cubic fields having bounded discriminant and for the number of 3-torsion elements in the class groups of quadratic…
We show that the "defective" terms in the expression that Dondera [Phys. Rev. D 98, 096008 (2018)] obtained for the momentum of the retarded field of an accelerating point charge are mathematically well justified. The repair should not be…
This article establishes a first-principles statistical field theory of fully developed isotropic turbulence. Applying an exact Helmholtz decomposition to the local angular momentum field ($\Lvec = \rvec \times \uvec$) reveals a segregation…
Here we are investigating the one dimensional inverse source problem for Helmholtz equation where the source function is compactly supported in our domain. We show that increasing stability possible using multi-frequency wave at the two end…
We consider a model system of two coupled Hopfield neurons, which is described by delay differential equations taking into account the finite signal propagation and processing times. When the delay exceeds a critical value, a limit cycle…
Maxwell's equations describe the evolution of electromagnetic fields, together with constraints on the divergence of the magnetic and electric flux densities. These constraints correspond to fundamental physical laws: the nonexistence of…
An uniqueness theorem for the inverse problem in the case of a second-order equation defined on the interval [0,1] when the boundary forms contain combinations of the values of functions at the points 0 and 1 is proved. The auxiliary…