Building Scattering Cross Sections from Resonance Wave Functions

A comparative discussion is presented for methods to evaluate simultaneously both resonance and background contributions to scattering.Permanent address: Inst. of Physics, St. Petersburg State University, St. Petersburg, Russia     

Wave processes in media with hysteretic nonlinearity. Part I

Two phenomenological models of hysteretic equations of state for media with imperfect elasticity are described and compared. On the basis of these equations, a theoretical study of nonlinear effects caused by the acoustic wave propagation in an unbounded medium is performed. The profiles, parameters, and spectra of waves are determined. The distinctive features of nonlinear wave processes in such media are revealed, so that these features can be used to choose the appropriate hysteretic equation of state for analytically describing the experimental data.     

Detection of weak signals against the background of artificial noise fields scattered by an inhomogeneous medium. I. Gaussian approximation

We consider an optimal procedure for weak signal detection against the background of scattered artificial noise fields within the framework of a Gaussian approximation. We focus on the specific problems of detection and adaptive recovery of the primary wave field at the inputs of a multichannel detector. Antiaircraft Command High School, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 41, No. 9, pp. 1177–1194, September, 1998.     

Exponential tail estimates in the law of ordinary logarithm (LOL) for triangular arrays of random variables

We derive exponential bounds for the tail of the distribution of normalized sums of triangular arrays of random variables, not necessarily independent, under the law of ordinary logarithm.

Furthermore, we provide estimates for partial sums of triangular arrays of independent random variables belonging to suitable grand Lebesgue spaces and having heavy-tailed distributions.

     

Local correlations of different eigenfunctions in a disordered wire

The correlation of the local density of states 〈ρ_ɛ(r ₁)ρ_{ɛ + ω}(r ₂)〉 in quasi-one-dimensional disordered wires in a magnetic field is calculated under the assumption that |r ₁ − r ₂| is much smaller than the localization length. This amounts to finding the zero mode of the transfer-matrix Hamiltonian for the supersymmetric σ model, which is done exactly by mapping to the three-dimensional Coulomb problem. Both the regimes of level repulsion and level attraction are obtained, depending on |r ₁ − r ₂|. We demonstrate that the correlations of different eigenfunctions in the quasi-one-dimensional and strictly one-dimensional cases are dissimilar. The text was submitted by the authors in English.     

Short-wave asymptotics for weak shock waves and solitons in mechanics

Some recent applications of the theory of non-linear waves in smoothly inhomogeneous and weakly dissipative media are discussed in the paper. The possibilities of “linear-ray” approximation when the non-linear self-refraction effects may be neglected in comparison with the non-linear wave distortion along the rays are demonstrated for weak acoustic shocks in stratified atmospheres and ocean, the solitary waves in shallow water of variable depth and the solitons in elastic rods.     

Quantum criticality and minimal conductivity in graphene with long-range disorder

We consider the conductivity sigma of graphene with negligible intervalley scattering at half filling. We derive the effective field theory, which, for the case of a potential disorder, is a symplectic-class sigma model including a topological term with theta=pi. As a consequence, the system is at a quantum critical point with a universal value of the conductivity of the order of e(2)/h. When the effective time-reversal symmetry is broken, the symmetry class becomes unitary, and sigma acquires the value characteristic for the quantum Hall transition.     

Radiation force and shear motions in inhomogeneous media

An action of radiation force induced by ultrasonic beam in waterlike media such as biological tissues (where the shear modulus is small as compared to the bulk compressibility) is considered. A new, nondissipative mechanism of generation of shear displacement due to a smooth (nonreflecting) medium inhomogeneity is suggested, and the corresponding medium displacement is evaluated. It is shown that a linear primary acoustic field in nondissipative, isotropic elastic medium cannot excite a nonpotential radiation force and, hence, a shear motion, whereas even smooth inhomogeneity makes this effect possible. An example is considered showing that the generated displacement pulse can be significantly longer than the primary ultrasound pulse. It is noted that, unlike the dissipative effect, the nondissipative action on a localized inhomogeneity (such as a lesion in a tissue) changes its sign along the beam axis, thus stretching or compressing the focus area.     

Free-Space Propagation of the Generalized Radiance Defined in Terms of the Coherent-Mode Representation of Cross-Spectral Density Function

The equation for free-space propagation of the generalized radiance defined formerly by the authors in terms of the coherent-mode representation of the cross-spectral density function is derived within the accuracy of the paraxial approximation. It is shown that, in the short-wavelength limit, this generalized radiance obeys in a good approximation the fundamental radiative transfer law of classical radiometry.     

Fluorescence emission and excitation spectra of fluorophores of lipofuscin granules isolated from retinal pigment epithelium of human cadaver eyes

Visible light-induced changes in fluorescence characteristics of lipofuscin granules (LG) isolated from retinal pigment epithelium of human cadaver eyes are compared with the analogous age-related changes and correlated with the content and photooxidation of LG main fluorophore, A2E. We used HPLC to examine changes of LG fluorophore composition with donor age, as well as before and after visible-light irradiation (the latter HPLC tests were also done with synthetic A2E). Visible light induces oxidation of LG fluorophores. As a result, their fluorescence characteristics change: the emission spectrum is blue-shifted by 25–40 nm. The observed age-dependent changes in the relative content of LG fluorophores and their oxidized derivatives were qualitatively similar with those caused by irradiation. To improve the accuracy of a new noninvasive diagnostic method, fundus autofluorescence imaging, it is important to know the ratio of nonoxidized and oxidized fluorophore derivatives depending on age and eye pathology.