Related papers: Asymptotic Theory of Particle Trapping in Coherent…
In this paper we discuss some aspects of the theory of wave packets. We consider a popular non-covariant Gaussian model used in various applications and show that it predicts too slow a longitudinal dispersion rate for relativistic…
We develop a stability theory for two-dimensional periodic traveling waves of general parabolic systems, possibly including conservation laws. In particular, we identify a diffusive spectral stability assumption and prove that it implies…
We consider a simple model of an open partially expanding map. Its trapped set K in phase space is a fractal set. We first show that there is a well defined discrete spectrum of Ruelle resonances which describes the asymptotics of…
We propose, as an alternative theory of quantum mechanics, a relativistically covariant variational principle (VP) capable of describing both wavefunction collapse and, as an appropriate limiting case, evolution of the wavefunction…
Evolution of a Langmuir wave is studied numerically for finite amplitudes slightly above the threshold which separates damping from nondamping cases. Arrest of linear damping is found to be a second-order effect due to ballistic evolution…
Acoustic fields effect steady transport of suspended particles by rectifying the inertia of primary oscillations. We develop a fully analytic theory that relates this steady particle motion to incident oscillatory (acoustic) flow and the…
We investigate invariant random fields on the sphere using a new type of spherical wavelets, called needlets. These are compactly supported in frequency and enjoy excellent localization properties in real space, with quasi-exponentially…
The relationship between anomalous superdiffusive behavior and particle trapping probability is analyzed on a rocking ratchet potential with spatially correlated weak disorder. The trapping probability density is shown, analytically and…
We consider non-stationary oscillations of an infinite string with time-varying tension. The string lies on the Winkler foundation with a point inhomogeneity (a concentrated spring of negative stiffness). In such a system with constant…
We develop a diagrammatic theory for transport of waves in disordered media with weak nonlinearity. We first represent the solution of the nonlinear wave equation as a nonlinear Born series. From this, we construct nonlinear ladder and…
Our aim in this paper is to investigate the asymptotic behavior of solutions of the perturbed linear fractional differential system. We show that if the original linear autonomous system is asymptotically stable then under the action of…
The one-dimensional motion of $N$ particles in the field of many incoherent waves is revisited numerically. When the wave complex amplitudes are independent, with a gaussian distribution, the quasilinear approximation is found to always…
We introduce the notion of relative volatility/intermittency and demonstrate how relative volatility statistics can be used to estimate consistently the temporal variation of volatility/intermittency when the data of interest are generated…
We deduce the asymptotic error distribution of the Euler method for the nonlinear filtering problem with continuous-time observations. Previous works by several authors have shown that the error structure of the method is characterized by…
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,…
We derive the asymptotic distribution of ordinal-pattern frequencies under weak dependence conditions and investigate the long-run covariance matrix not only analytically for moving-average, Gaussian, and the novel generalized coin-tossing…
While there are many well-known and extensively tested results involving diffusion-limited binary reactions, reactions involving subdiffusive reactant species are far less understood. Subdiffusive motion is characterized by a mean square…
We consider waves propagating in a randomly layered medium with long-range correlations. An example of such a medium is studied in \citeMS and leads, in particular, to an asymptotic travel time described in terms of a fractional Brownian…
In this paper, we develop a model to describe the generalized wave-particle instability in a quasi-neutral plasma. We analyze the quasi-linear diffusion equation for particles by expressing an arbitrary unstable and resonant wave mode as a…
Turbulence in space and astrophysical plasmas is governed by the nonlinear interactions between counterpropagating Alfven waves. Here we present the theoretical considerations behind the design of the first laboratory measurement of an…