相关论文: Scaling Limits for Beam Wave Propagation in Atmosp…

Small amplitude inhomogeneous plane waves are studied as they propagate on the free surface of a predeformed semi-infinite body made of Bell constrained material. The predeformation corresponds to a finite static pure homogeneous strain.…

We study the asymptotic behavior of solutions for the semilinear damped wave equation with variable coefficients. We prove that if the damping is effective, and the nonlinearity and other lower order terms can be regarded as perturbations,…

Diffraction is one of the universal phenomena of physics, and a way to overcome it has always represented a challenge for physicists. In order to control diffraction, the study of structured waves has become decisive. Here, we present a…

We consider Gaussian random waves on hyperbolic spaces and establish variance asymptotics and central limit theorems for a large class of their integral functionals, both in the high-frequency and large domain limits. Our strategy of proof…

We consider the exit problem for small white noise perturbation of a smooth dynamical system on the plane in the neighborhood of a hyperbolic critical point. We show that if the distribution of the initial condition has a scaling limit then…

An integro-differential equation describing the angular distribution of beams is analyzed for a medium with random inhomogeneities. Beams are trapped because inhomogeneities give rise to wave localization at random locations and random…

In an attempt to determine the outer scale of turbulence driven by localized sources, such as supernova explosions in the interstellar medium, we consider a forcing function given by the gradient of gaussian profiles localized at random…

We consider solutions of a scalar reaction-diffusion equation of the ignition type with a random, stationary and ergodic reaction rate. We show that solutions of the Cauchy problem spread with a deterministic rate in the long time limit. We…

A theory of electromagnetic wave propagation in a weakly anisotropic smoothly inhomogeneous medium is developed, based on the quantum-mechanical diagonalization procedure applied to Maxwell equations. The equations of motion for the…

We establish a comprehensive probability theory for coherent transport of random waves through arbitrary linear media. The transmissivity distribution for random coherent waves is a fundamental B-spline with knots at the transmission…

The narrow and wide-angle parabolic equations for the quasi-monochromatic sound wave packets propagating in a waveguide with a non-stationary background flow are obtained. The results of numerical simulations are presented.

We study the simultaneous paraxial and white-noise limit of the Helmholtz equation in randomly layered media where the refractive index fluctuations are in the direction of propagation. We consider the regime in which the wavelength is of…

In this paper we discuss the uniaxial propagation of transient waves within a semi-infinite viscoelastic Bessel medium. First, we provide the analytic expression for the response function of the material as we approach the wave-front. To do…

The propagation of electromagnetic waves in a linearly-varying index of refraction is a fundamental problem in wave physics, being relevant in fusion science for describing certain wave-based heating and diagnostic schemes. Here, an exact…

We study Maxwell's equations in random media with small fluctuations of the electric permittivity. We consider a setup where the waves propagate toward a preferred direction, called range. We decompose the electromagnetic wave field in…

While wave-packet solutions for relativistic wave equations are oftentimes thought to be approximate (paraxial), we demonstrate that there is a family of such solutions, which are exact, by employing a null-plane (light-cone) variables…

We analyze the self-averaging properties of time-reversed solutions of the paraxial wave equation with random coefficients, which we take to be Markovian in the direction of propagation. This allows us to construct an approximate martingale…

The objective of this dissertation is to prove a scaling limit for the exit of a domain problem of a small noise system with underlying hyperbolic dynamics. In this case, Large Deviation kind of estimates fail to provide a complete picture…

The oscillations of ultrasound contrast agents are of particular importance to the understanding of the propagation of acoustic waves in the bubbly liquids (suspensions of ultrasound contrast agents). Acoustic waves propagating in bubbly…

We consider the propagation of Gaussian beams in a waveguide with gain and loss in the paraxial approximation governed by the Schr\"odinger equation. We derive equations of motion for the beam in the semiclassical limit that are valid when…