Related papers: Dual Time-Space Model of Wave Propagation
A model of the thin shell expanding into a uniform ambient medium is developed. Density perturbations are described using equations with linear and quadratic terms, and the linear and the nonlinear solutions are compared. We follow the time…
The position-representation wave function for multi-photon states and its equation of motion are introduced. A major strength of the theory is that it describes the complete evolution (including polarization and entanglement) of…
The instability and nonlinear evolution of directional ocean waves is investigated numerically by means of simulations of the governing kinetic equation for narrow-band surface waves. Our simulation results reveal the onset of the…
We present a theory of electron, electromagnetic, and elastic wave propagation in systems consisting of non-overlapping scatterers in a host medium. The theory provides a framework for a unified description of wave propagation in…
Fundamental concepts in the quasi-one-dimensional geometry of disordered wires and random waveguides in which ideas of scaling and the transmission matrix were first introduced are reviewed. We discuss the use of the transmission matrix to…
In this paper, we discuss the transport phenomena of electromagnetic waves in a two-dimensional random system which is composed of arrays of electrical dipoles, following the model presented earlier by Erdogan, et al. (J. Opt. Soc. Am. B…
We develop a unified formalism for describing the interaction of gravitational waves with matter that clearly separates the effects of general relativity from those due to interactions in the matter. Using it, we derive a general expression…
Multi-scale wave propagation problems are computationally costly to solve by traditional techniques because the smallest scales must be represented over a domain determined by the largest scales of the problem. We have developed and…
The time-space evolution of the field is described by the transport equation for the 2-dimensional wave energy spectrum density, S(x,t), spread in the space, x, and time, t. This equation has the forcing named the source function, F,…
Recent experiments have demonstrated that it is possible to alter the dispersion of a medium without significantly altering its absorption or refractive index and that this may be done while a wave propagates through the medium. This…
For odd anharmonic oscillators, it is well known that complex scaling can be used to determine resonance energy eigenvalues and the corresponding eigenvectors in complex rotated space. We briefly review and discuss various methods for the…
A formalism is introduced which may describe both standard linearized waves and gravitational waves in Isaacson's high-frequency limit. After emphasizing main differences between the two approximation techniques we generalize the Isaacson…
We consider principal properties of various wave regimes in two selected excitable systems with linear cross-diffusion in one spatial dimension observed at different parameter values. This includes fixed-shape propagating waves, envelope…
The recent increasing interest in the study of Lorentz-Finsler geometry has led to several applications to model real-world physical phenomena. Our purpose is to provide a simple, step-by-step review on how to build and implement such a…
In this work, we propose a model of Einstein--Gauss-Bonnet gravity coupled with two scalar fields. The two scalar fields are considered to be ``frozen'' or they become non-dynamical by employing appropriate constraints in terms of Lagrange…
Motivated by phenomenological questions in quantum gravity, we consider the propagation of a scalar field on a random lattice. We describe a procedure to calculate the dispersion relation for the field by taking a limit of a periodic…
Space-time modulation adds another powerful degree of freedom to the manipulation of classical wave systems. It opens the door for complex control of wave behavior beyond the reach of stationary systems, such as nonreciprocal wave transport…
The theory of traveling waves and spreading speeds is developed for time-space periodic monotone semiflows with monostable structure. By using traveling waves of the associated Poincar\'e maps in a strong sense, we establish the existence…
Shock wave theory was first studied for gas dynamics, for which shocks appear as compression waves. A shock wave is characterized as a sharp transition, even discontinuity in the flow. In fact, shocks appear in many different physical…
A spherical blast wave with relativistic velocity can be described by a similarity solution, that is used for theoretical models of gamma-ray bursts. We consider the linear stability of such a relativistic blast wave propagating into a…