We discuss the production of induced noise by a pulse and the propagation of the noise in a dispersive medium. We present a simple model where the noise is the sum of pulses and where the mean of each pulse is random. We obtain explicit expressions for the standard deviation of the spatial noise as a function of time. We also formulate the problem in terms of a time-frequency phase space approa...

We develop a new approach to velocity averaging lemmas based on the dispersive properties of the kinetic transport operator. This method yields unprecedented sharp results, which display, in some cases, a gain of one full derivative. Moreover, the study of dispersion allows to treat the case of LxL p v integrability with r ≤ p. We also establish results on the control of concentrations in the d...

We prove optimal (that is, without loss of derivatives) dispersive estimates for the Schrödinger group e ) for a class of real-valued potentials V ∈ Ck(R), V (x) = O(〈x〉), where n = 4, 5, k > (n− 3)/2, δ > 3 if n = 4 and δ > 5 if n = 5.

Abstract: This paper aims at presenting a proof of the attractor for a class of viscous nonlinear dispersive wave equations. In this paper, the global existence of solution to this equation in L2 under the periodical condition is studied. By using the time estimate of this equation, we get the compact and bounded absorbing set and the existence of the global attractor for the viscous nonlinear ...

We derive the long-time decay in weighted norms for solutions of the discrete 3D Schrödinger and Klein-Gordon equations.

X-ray mass attenuation coefficients for polycrystalline samples of copper have been measured with a high-precision energy-dispersive method. Estimates of the scattering contributions to the attenuation coefficients are made. The photoelectric coefficients deduced from the experimental results are compared with theoretical calculations using screened hydrogen-like eigenfunctions as well as more ...

Non-typical transport phenomena may arise when randomly driven particles remain in an active relationship with the environment instead of being passive. If we attribute to Brownian particles an ability to induce alterations of the environment on suitable space-time scales, those in turn must influence their further movement. In that case a general feedback mechanism needs to be respected. By re...