Related papers: Restoring geometrical optics near caustics using s…
We develop generalized polynomial chaos (gPC) based stochastic Galerkin (SG) methods for a class of highly oscillatory transport equations that arise in semiclassical modeling of non-adiabatic quantum dynamics. These models contain…
We present a geometric optics theory for the transport of quantum particles (or classical waves) in a chiral and dissipative periodic crystal subject to slowly varying perturbations in space and time. Taking account of some properties of…
We consider the possible effects of gravitational lensing by globular clusters on gravitational waves from asymmetric neutron stars in our galaxy. In the lensing of gravitational waves, the long wavelength, compared with the usual case of…
A mixed mimetic spectral element method is applied to solve the rotating shallow water equations. The mixed method uses the recently developed spectral element histopolation functions, which exactly satisfy the fundamental theorem of…
Typical applications of gravitational lensing use the properties of electromagnetic or gravitational waves to infer the geometry through which those waves propagate. Nevertheless, the optical fields themselves - as opposed to their…
In this paper we discuss propagation of the weak high-frequency gravitational waves in a curved spacetime background. We develop a so-called spinoptics approximation which takes into account interaction of the spin of the field with the…
Metasurfaces -- ultrathin structures composed of subwavelength optical elements -- have revolutionized light manipulation by enabling precise control over electromagnetic waves' amplitude, phase, polarization, and spectral properties.…
We apply topological methods to obtain global continuation results for harmonic solutions of some periodically perturbed ordinary differential equations on a $k$-dimensional differentiable manifold $M \subseteq \mathbb{R}^m$. We assume that…
We provide a geometric optics description in spaces of low regularity, $L^2$ and $H^1$, of the transport of oscillations in solutions to linear and some semilinear second-order hyperbolic boundary problems along rays that graze the boundary…
Coupled wave equations are popular tool for investigating longitudinal dynamical effects in semiconductor lasers, for example, sensitivity to delayed optical feedback. We study a model that consists of a hyperbolic linear system of partial…
In atomic, molecular, and nuclear physics, the method of complex coordinate rotation is a widely used theoretical tool for studying resonant states. Here, we propose a novel implementation of this method based on the gradient optimization…
A homogeneous Riemannian space $(M= G/H,g)$ is called a geodesic orbit space (shortly, GO-space) if any geodesic is an orbit of one-parameter subgroup of the isometry group $G$. We study the structure of compact GO-spaces and give some…
This paper proposes a deep recurrent Rotation Averaging Graph Optimizer (RAGO) for Multiple Rotation Averaging (MRA). Conventional optimization-based methods usually fail to produce accurate results due to corrupted and noisy relative…
We present a study of geometric phases in classical wave and polarisation optics using the basic mathematical framework of quantum mechanics. Important physical situations taken from scalar wave optics, pure polarisation optics, and the…
We initiate the study of gravitational-wave lensing in the wave-optics regime within modified gravity. We consider a phenomenological setup in which the gravitational-wave amplitude obeys a curvature-coupled propagation equation. This…
We consider a region $M$ in $\mathbb{R}^n$ with boundary $\partial M$ and a metric $g$ on $M$ conformal to the Euclidean metric. We analyze the inverse problem, originally formulated by Dix, of reconstructing $g$ from boundary measurements…
In this paper, global optimization (GO) Lipschitz problems are considered where the multi-dimensional multiextremal objective function is determined over a hyperinterval. An efficient one-dimensional GO method using local tuning on the…
Symmetry-driven phenomena arising in nonlocal metasurfaces supporting quasi-bound states in the continuum (q-BICs) have been opening new avenues to tailor enhanced light-matter interactions via perturbative design principles. Geometric…
Geometric optics is analysed using the techniques of Presymplectic Geometry. We obtain the symplectic structure of the space of light rays in a medium of a non constant refractive index by reduction from a presymplectic structure, and using…
The geometric phase is a universal concept in modern physics and has enabled the development of metasurfaces for versatile wavefront shaping. However, its realization in metasurfaces has been restricted to circularly polarized light,…