Related papers: Silence is bliss in a Platonic relationship
The fluctuations of scalar fields, that are invariant under rotations of the worldvolume, in Euclidian signature, can be described by a system of Langevin equations. These equations can be understood as defining a change of variables in the…
We construct and analyse the moduli space (collective coordinates) for a classical field theory in 1 + 1 dimensions that possesses complex stable multi-soliton solutions with real energies when PT-regularized. For the integrable…
Wave propagation and acoustic scattering problems require vast computational resources to be solved accurately at high frequencies. Asymptotic methods can make this cost potentially frequency independent by explicitly extracting the…
We propose a generalization of the two-dimensional eikonal-limit cloak derived from a conformal transformation to three dimensions. The proposed cloak is a spherical shell composed of only isotropic media; it operates in the transmission…
We consider multi-frequency inverse source problem for the discrete Helmholtz operator on the square lattice $\mathbb{Z}^d$, $d \ge 1$. We consider this problem for the cases with and without phase information. We prove uniqueness results…
We consider the many-body spectra of interacting bosonic quantum fields on a lattice in the semiclassical limit of large particle number $N$. We show that the many-body density of states can be expressed as a coherent sum over oscillating…
The surface plasmonic waves excited by a vertical or horizontal oriented Hertzian dipole above anisotropic and spatially dispersive two-dimensional surfaces of infinite extent embedded in planarly layered uniaxial media is investigated…
We report a rich spectrum of isolated solitons residing inside ({\it embedded } into) the continuous radiation spectrum in a simple model of three-wave spatial interaction in a second-harmonic-generating planar optical waveguide equipped…
We present a boundary integral formulation of electromagnetic scattering by homogeneous bodies that are characterized by linear constitutive equations in the frequency domain. By working with the Cartesian components of the electric, E and…
In this paper, we show for the first time the increasing stability of the inverse source problem for the n-dimensional Helmholtz equation at multiple wave numbers, which is different from the two-or three-dimensional Helmholtz equation. In…
Recent research in light scattering has prompted a re-evaluation of complex quantities, particularly in the context of complex frequency signals, which exhibit exponential growth or decay unlike traditional harmonic signals. We introduce a…
Halbach spheres provide a theoretically elegant means of generating highly homogeneous magnetic fields, but practical implementation is hindered by challenging fabrication and restricted interior access. This study examines discrete…
Cloaking using complementary media was suggested by Lai et al. in [8]. The study of this problem faces two difficulties. Firstly, this problem is unstable since the equations describing the phenomenon have sign changing coefficients, hence…
Solutions for the fields in a coated cylinder where the core radius is bigger than the shell radius are seemingly unphysical, but can be given a physical meaning if one transforms to an equivalent problem by unfolding the geometry. In…
Acoustic and magnetoacoustic waves are considered to be possible agents of chromospheric heating. We present a comparison of deposited acoustic energy flux with total integrated radiative losses in the middle chromosphere of the quiet Sun…
We present a new numerical scheme to solve the Helmholtz equation in a wave-guide. We consider a medium that is bounded in the $x_2$-direction, unbounded in the $x_1$-direction and $\varepsilon$-periodic for large $|x_1|$, allowing…
The phonon-bottleneck problem in the relaxation of two-level systems (spins) via direct phonon processes is considered numerically in the weak-excitation limit where the Schroedinger equation for the spin-phonon system simplifies. The…
A method for solving the half-space Sommerfeld problem is proposed, which allows us to obtain exact solutions in the form of Sommerfeld integrals, as well as their short-wave asymptotics. The first carried out by reducing the Sommerfeld…
We study scattering for the linear Helmholtz operator in two dimensions and develop a technique, which can be used to ascertain scattering of a given incident wave from very regular inhomogeneities. This technique is then applied to a…
We consider how transformation optics and invisibility cloaking can be used to construct models in subsets $\mathbb{R}^3$ with a varying metric, where the time-harmonic waves for a given angular wavenumber $k$, are equivalent to the waves…