Related papers: Orbital Beam Dynamics in Multipole Fields via Mult…
To manipulate orbital angular momentum (OAM) carried by light beams, there is a great interest in designing various optical elements from the deep-ultraviolet to the microwave. Normally, the OAM variation introduced by optical elements can…
In the context of data-driven control of nonlinear systems, many approaches lack of rigorous guarantees, call for nonconvex optimization, or require knowledge of a function basis containing the system dynamics. To tackle these drawbacks, we…
An operator theoretic approach to orthogonal rational functions on the unit circle with poles in its exterior is presented in this paper. This approach is based on the identification of a suitable matrix representation of the multiplication…
Spatial structure can arise in spatial point process models via a range of mechanisms, including neighbour-dependent directionally biased movement. This spatial structure is neglected by mean-field models, but can have important effects on…
Precision measurement of non-linear observables is an important goal in all facets of quantum optics. This allows measurement-based non-classical state preparation, which has been applied to great success in various physical systems, and…
In this paper, we develop a space-time upscaling framework that can be used for many challenging porous media applications without scale separation and high contrast. Our main focus is on nonlinear differential equations with multiscale…
In this work, a numerical modal decomposition approach is applied to model the optical field of laser light after propagating through a highly multi-mode fiber. The algorithm for the decomposition is based on the reconstruction of measured…
Mathematical models describing the cosmological evolution of classical and phantom scalar fields with self-action are formulated and analyzed. Systems of dynamical equations in the plane, describing homogeneous cosmological models, have…
In this paper, we propose compactly supported radial basis functions for solving some well- known classes of astrophysics problems categorized as non-linear singular initial ordinary dif- ferential equations on a semi-infinite domain. To…
Multipole expansion of an incident radiation field - that is, representation of the fields as sums of vector spherical wavefunctions - is essential for theoretical light scattering methods such as the T-matrix method and generalised…
Series expansions of isotropic Gaussian random fields on $\mathbb{S}^2$ with independent Gaussian coefficients and localized basis functions are constructed. Such representations with multilevel localised structure provide an alternative to…
In this series of eight papers we present the applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. In this part we consider variational wavelet approach for loops,…
The gravitational-radiation-induced inspiral of a binary system of compact objects is considered. A scheme is described to model the regime in which the gravitational interaction is too strong to use weak-field approximation methods, but…
Continuum kinetic simulations are increasingly capable of resolving high-dimensional phase space with advances in computing. These capabilities can be more fully explored by using linear kinetic theory to initialize the self-consistent…
We study orthogonal polynomials for a weight function defined over a domain of revolution, where the domain is formed from rotating a two-dimensional region and goes beyond the quadratic domains. Explicit constructions of orthogonal bases…
The main goal of the present paper is to study how polarization of photons affects their motion in a gravitational field created by a rotating massive compact object. We study propagation of the circularly polarized beams of light in a…
The modulational instability of broadband optical pulses in a four-state atomic system is investigated. In particular, starting from a recently derived generalized nonlinear Schr\"odinger equation, a wave-kinetic equation is derived. A…
A theoretical model is developed by exploiting the variational technique to investigate the evolution of an optical beam inside an optically pumped graded-index fiber amplifier. The variational analysis is a semi-analytical method that…
This work introduces the use of the Koopman operator theory to generate approximate analytical solutions for the zonal harmonics problem of a satellite orbiting a non-spherical celestial body. Particularly, the solution proposed directly…
We characterize the local properties of an optomechanical system comprising the movable mirror of a resonator and its intracavity field, mutually coupled via radiation-pressure. Our approach shows that both the state of the mirror and the…