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Coherent Synchrotron Radiation can severely limit the performance of accelerators designed for high brightness and short bunch length. Examples include light sources based on ERLs or FELs, and bunch compressors for linear colliders. In…
The two-fermion relativistic wave equations of Constraint Theory are reduced, after expressing the components of the $4\times 4$ matrix wave function in terms of one of the $2\times 2$ components, to a single equation of the…
In this paper, for compressible Euler equations in multiple space dimensions, we prove the break-down of classical solutions with a large class of initial data by tracking the propagation of radially symmetric expanding wave including…
Solution of the nonlinear Klein-Gordon equation perturbed by small external force is investigated. The perturbation is represented by finite collections of harmonics. The frequencies of the perturbation vary slowly and pass through the…
We show that dispersive shock waves resulting from the nonlinearity overbalancing a weak leading-order dispersion can emit resonant radiation owing to higher-order dispersive contributions. We analyze such phenomenon for the defocusing…
We present a calculation of the conservative two-body Hamiltonian of a compact binary system including a spinning black hole. We include up-to third order corrections in Newton's constant $G$, all orders in velocity, and linear and…
We propose a new method for calculating reflection and transmission coefficients for an arbitrarily polarized electromagnetic plane wave incident on a one-dimensional dielectric medium of finite thickness and with dielectric permittivity…
The complex Helmholtz equation $(\Delta + k^2)u=f$ (where $k\in{\mathbb R},u(\cdot),f(\cdot)\in{\mathbb C}$) is a mainstay of computational wave simulation. Despite its apparent simplicity, efficient numerical methods are challenging to…
The investigation into the scattering of plane waves by a periodic array of parallel cylinders utilizes the method of cylindrical wave decomposition, thereby reducing the problem complexity to a series of linear algebraic equations. This…
Assume that $(X, d, \mu)$ is a space of homogeneous type in the sense of Coifman and Weiss. In this article, motivated by the breakthrough work of P. Auscher and T. Hyt\"onen on orthonormal bases of regular wavelets on spaces of homogeneous…
The low-energy dynamics of any system admitting a continuum of static configurations is approximated by slow motion in moduli (configuration) space. Here, following Ferrell and Eardley, this moduli space approximation is utilized to study…
This paper develops an efficient numerical method for the inverse scattering problem of a time-harmonic plane wave incident on a perfectly reflecting random periodic structure. The method is based on a novel combination of the Monte Carlo…
In this article, we solve the Duffin--Kemmer--Petiau (DKP) equation in the presence of hyperbolic tangent potential for spin-one particles. By partitioning the spin-one spinor, we show that the DKP equation is equivalent to the…
This chapter presents a selection of theoretical and numerical tools suitable for the study of wave propagation in time-dependent media. The focus is on one-dimensional spring-mass chains whose properties are modulated in space and time in…
The superradiant emission properties from an atomic ensemble with cascade level configuration is numerically simulated. The correlated spontaneous emissions (signal then idler fields) are purely stochastic processes which are initiated by…
The impedance matrix method is applied to study the scattering of flexural waves propagating in an infinite thin plate containing an $N$-beam resonator. The resonator consists of a circular hole containing a smaller plate connected to the…
The investigation of dynamics of intense solitary wave groups of collinear surface waves is performed by means of numerical simulations of the Euler equations and laboratory experiments. The processes of solitary wave generation, reflection…
We study {\it analytically} the characteristic resonance spectrum of charged massive scalar fields linearly coupled to a spherically symmetric charged reflecting shell. In particular, we use analytical techniques in order to solve the…
A quasi-Keplerian parameterisation for the solutions of second post-Newtonian (PN) accurate equations of motion for spinning compact binaries is obtained including leading order spin-spin and next-to-leading order spin-orbit interactions.…
After cosmic inflation, coherent oscillations of the inflaton field about a monomial potential $V(\phi)\sim \phi^k$ result in an expansion phase characterized by a stiff equation-of-state $w\simeq(k-2)/(k+2)$. Sourced by the oscillating…