Related papers: Introduction to the Rotating Wave Approximation (R…
Electromagnetic waves, solving the full set of Maxwell equations in vacuum, are numerically computed. These waves occupy a fixed bounded region of the three dimensional space, topologically equivalent to a toroid. Thus, their fluid dynamics…
Rotation estimation plays a fundamental role in computer vision and robot tasks, and extremely robust rotation estimation is significantly useful for safety-critical applications. Typically, estimating a rotation is considered a non-linear…
Assuming that a formal approximation of multiple waves has been obtained by matched asymptotic methods, we derive a {\em Spatial Shadowing lemma} to construct exact solutions near the formal approximation. In Part I, we consider a general…
We discuss a general setup which allows the study of the perturbation theory of an arbitrary, locally harmonic 1D quantum mechanical potential as well as its multi-variable (many-body) generalization. The latter may form a prototype for…
The evolution of the quantum wave packet describing an atom trapped in the surface-tip junction of the scanning tunneling microscope is investigated by using the time-dependent Schroedinger equation, and by a quasi-classical Hamiltonian…
Gravitational waves deliver information in exquisite detail about astrophysical phenomena, among them the collision of two black holes, a system completely invisible to the eyes of electromagnetic telescopes. Models that predict…
Quasi-toroidal oscillations in slowly rotating stars are examined in the framework of general relativity. The oscillation frequency to first order of the rotation rate is not a single value even for uniform rotation unlike the Newtonian…
The axial mode oscillations are examined for relativistic rotating stars with uniform angular velocity. Using the slow rotation formalism and the Cowling approximation, we have derived the equations governing the r-mode oscillations up to…
Optical resonators are structures that utilize wave interference and feedback to confine light in all three dimensions. Depending on the feedback mechanism, resonators can support either standing- or traveling-wave modes. Over the years,…
Cavity polaritons, quasiparticles formed by coherent light-matter coupling, are at the heart of fundamental concepts of quantum optics. The quintessential signature of this coherent coupling is the Rabi oscillation, which results from the…
We present a systematic and robust approach to nonlinear gravitational perturbations of vacuum spacetimes. This approach provides a basis for a theory of nonlinear gravitational waves. In particular, we show that the system of perturbative…
The main purpose of this article is to establish the Runge-type approximation in $L^2(0,T;\widetilde{H}^s(\Omega))$ for solutions of linear nonlocal wave equations. To achieve this, we extend the theory of very weak solutions for classical…
An approach to special relativity is outlined which emphasizes the wave and field mechanisms which physically produce the relativistic effects, with the goal of making them seem more natural to students by connecting more explicitly with…
Scalar wave scattering by many small particles of arbitrary shapes with impedance boundary condition is studied. The problem is solved asymptotically and numerically under the assumptions a << d << lambda, where k = 2pi/lambda is the wave…
Other than scattering problems where perturbation theory is applicable, there are basically two ways to solve problems in physics. One is to reduce the problem to harmonic oscillators, and the other is to formulate the problem in terms of…
Semiconductor double quantum dot (DQD) qubits coupled via superconducting microwave resonators provide a powerful means of long-range manipulation of the qubits' spin and charge degrees of freedom. Quantum gates can be implemented by…
The ability to approach a physical phenomenon and grasp its major importance is a remarkable quality of understanding. This paper presents a rather elegant and novel way of looking at the resonance phenomenon, which among others shares a…
Many variants of the Wasserstein distance have been introduced to reduce its original computational burden. In particular the Sliced-Wasserstein distance (SW), which leverages one-dimensional projections for which a closed-form solution of…
It is the aim of the paper to present a new point of view on rotational elasticity in a nonlinear setting using orthogonal matrices. The proposed model, in the linear approximation, can be compared to the well known equilibrium equations of…
Gravitational waves from binary neutron stars in quasiequilibrium circular orbits are computed using an approximate method which we propose in this paper. In the first step of this method, we prepare general relativistic irrotational binary…