Localization of Classical Waves in Weakly Scattering Two-Dimensional Media with Anisotropic Disorder

We study the localization of classical waves in weakly scattering 2D systems with anisotropic disorder. The analysis is based on a perturbative path-integral technique combined with a spectral filtering that accounts for the first-order Bragg scattering only. It is shown that in the long-wavelength limit the radiation is always localized, and the localization length is independent of the direction of propagation, the latter in contrast to the predictions based on an anisotropic tight-binding model. For shorter wavelengths that are comparable to the correlation scales of the disorder, the transport properties of disordered media are essentially different in the directions along and across the correlation ellipse. There exists a frequency-dependent critical value of the anisotropy parameter, below which waves are localized at all angles of propagation. Above this critical value, the radiation is localized only within some angular sectors centered at the short axis of the correlation ellipse and is extended in other directions.Comment: 10 pages, 5 figure

Space-Time Evolution of the Oscillator, Rapidly moving in a random media

We study the quantum-mechanical evolution of the nonrelativistic oscillator, rapidly moving in the media with the random vector fields. We calculate the evolution of the level probability distribution as a function of time, and obtain rapid level diffusion over the energy levels. Our results imply a new mechanism of charmonium dissociation in QCD media.Comment: 32 pages, 13 figure

Mobility Edge in Aperiodic Kronig-Penney Potentials with Correlated Disorder: Perturbative Approach

It is shown that a non-periodic Kronig-Penney model exhibits mobility edges if the positions of the scatterers are correlated at long distances. An analytical expression for the energy-dependent localization length is derived for weak disorder in terms of the real-space correlators defining the structural disorder in these systems. We also present an algorithm to construct a non-periodic but correlated sequence exhibiting desired mobility edges. This result could be used to construct window filters in electronic, acoustic, or photonic non-periodic structures.Comment: RevTex, 4 pages including 2 Postscript figure

Depression, Executive Dysfunction, and Prior Economic and Social Vulnerability Associations in Incarcerated African American Men

Low executive function (EF) and depression are each determinants of health. We examined the synergy between deficits in EF (impaired cognitive flexibility; >75th percentile on the Wisconsin Card Sorting Test perseverative error score) and depressive symptoms (modified CES-D) and pre-incarceration well-being among incarcerated African American men (N=189). In adjusted analyses, having impaired EF and depression was strongly associated with pre-incarceration food insecurity (OR=3.81, 95% CI: 1.35, 10.77), homelessness (OR=3.00, 95% CI: 1.02, 8.80), concern about bills (OR=3.76, 95% CI: 1.42, 9.95); low significant other support (OR=4.63, 95% CI: 1.62, 13.24), low friend support (OR=3.47, 95% CI: 1.30, 9.26), relationship difficulties (OR=2.86, 95% CI: 1.05, 7.80); and binge drinking (OR=3.62, 95% CI: 1.22, 10.80). Prison-based programs to treat depression and improve problem-solving may improve post-release success

Radon-to-Helmholtz mappings and nonlinear diffraction tomography

This paper addresses a number of approximate, analytically invertible solutions of the scalar Helmholtz equation. Primary attention is devoted to the Glauber approximation (GA) derived for the far-field pattern. It is shown that the GA has the form of a nonlinear Radon-to-Helmholtz (RtH) mapping, which transforms a sinogram of the scattering potential into an approximate solution of the Helmholtz equation. A proposal of how to construct a position space counterpart of the GA is formulated. Also, it is established that a paraxial version of the Glauber model coincides, up to an inessential constant factor, with a momentum-space representation of the Mazar–Felsen propagator, which describes forward-scattered waves. For weakly scattering objects, these solutions are reduced to the conventional Born/Rytov approximations, which may, however, preserve the parametrization and sampling formats of the original nonlinear models. Since all RtH mappings are analytically invertible, they can be applied to the (nonlinear) diffraction tomography of penetrable objects. In particular, the Glauber model, which has been largely ignored for years, is shown to provide efficient inversion of synthetic data. The resulting tomograms clearly outperform the Born inversions, even for moderately scattering potentials.</jats:p