Nonlinear acoustics in Nizhni Novgorod (A review)

This article reviews the development of nonlinear acoustics in Nizhni Novgorod from the days when the idea of parametric transmission and reception was conceived until the present time.     

A highly anisotropic cobalt(II)-based single-chain magnet: exploration of spin canting in an antiferromagnetic array

In this article we report for the first time experimental details concerning the synthesis and full characterization (including the single-crystal X-ray structure) of the spin-canted zigzag-chain compound [Co(H2L)(H2O)]infinity [L = 4-Me-C6H4-CH2N(CPO3H2)2], which contains antiferromagnetically coupled, highly magnetically anisotropic Co(II) ions with unquenched orbital angular momenta, and we also propose a new model to explain the single-chain magnet behavior of this compound. The model takes into account (1) the tetragonal crystal field and the spin-orbit interaction acting on each Co(II) ion, (2) the antiferromagnetic Heisenberg exchange between neighboring Co(II) ions, and (3) the tilting of the tetragonal axes of the neighboring Co units in the zigzag structure. We show that the tilting of the anisotropy axes gives rise to spin canting and consequently to a nonvanishing magnetization for the compound. In the case of a strong tetragonal field that stabilizes the orbital doublet of Co(II), the effective pseudo-spin-1/2 Hamiltonian describing the interaction between the Co ions in their ground Kramers doublet states is shown to be of the Ising type. An analytical expression for the static magnetic susceptibility of the infinite spin-canted chain is obtained. The model provides an excellent fit to the experimental data on both the static and dynamic magnetic properties of the chain.     

Internal solitons in the ocean and their effect on underwater sound

Nonlinear internal waves in the ocean are discussed (a) from the standpoint of soliton theory and (b) from the viewpoint of experimental measurements. First, theoretical models for internal solitary waves in the ocean are briefly described. Various nonlinear analytical solutions are treated, commencing with the well-known Boussinesq and Korteweg-de Vries equations. Then certain generalizations are considered, including effects of cubic nonlinearity, Earth's rotation, cylindrical divergence, dissipation, shear flows, and others. Recent theoretical models for strongly nonlinear internal waves are outlined. Second, examples of experimental evidence for the existence of solitons in the upper ocean are presented; the data include radar and optical images and in situ measurements of wave forms, propagation speeds, and dispersion characteristics. Third, and finally, action of internal solitons on sound wave propagation is discussed. This review paper is intended for researchers from diverse backgrounds, including acousticians, who may not be familiar in detail with soliton theory. Thus, it includes an outline of the basics of soliton theory. At the same time, recent theoretical and observational results are described which can also make this review useful for mainstream oceanographers and theoreticians.     

Effect of UV radiation and hydrogen peroxide on the antiradical and antioxidant activities of DOPA-melanin and melanosomes from retinal pigment epithelial cells

The effect of continuous UV radiation and hydrogen peroxide on destruction and antioxidant properties of synthetic DOPA-melanin (prepared by oxidation of 3,4-dihydroxyphenylalanine (DOPA)) and melanosomes isolated from cells of the retinal pigment epithelium (RPE) was investigated. The kinetics of melanin destruction was recorded based on the accumulation of fluorescent low-molecular-weight reaction products, the antiradical activity of melanin was determined by chemiluminescence method, the concentration of free radical products was measured by electron paramagnetic resonance, and the antioxidant activity of melanins was estimated by their inhibitory effect on lipid peroxidation. It was shown that UVC—UVA irradiation (up to 5 hours) of DOPA-melanin and melanosomes of retinal pigment epithelium decreased neither the latency period of luminol chemiluminescence nor the inhibitory action of pigments on Fe²⁺- and UV-induced peroxidation of cardiolipin liposomes. However, very long UV irradiation gave rise to fluorescent destruction products, decreased the concentration of paramagnetic centers in the pigment (especially light-dependent ones), and decreased the antiradical and antioxidant activities. For example, UV irradiation of DOPA-melanin during 52 h resulted in approximately a 2-fold decrease in the concentration of paramagnetic centers and decline of antiradical and antioxidant activities. However, even with such a hard irradiation the pigment retained significant inhibitory activity against lipid peroxidation. The oxidative destruction of DOPA-melanin in the presence of hydrogen peroxide in the dark resulted in complete destruction of the polymer and loss of its protective properties. It is assumed that destruction of RPE cell melanin is caused mainly by oxidative processes.     

Dynamics of Strongly Nonlinear Kinks and Solitons in a Two‐Layer Fluid

Perturbation theory is developed for interaction of strongly nonlinear solitary waves close to the limiting, tabletop solitons (Π‐solitons). The method is based on representing each soliton as a compound of two kinks so that the interaction of N solitons is treated as the interaction of 2N kinks. As an example the Miyata–Choi–Camassa equations for a two‐layer fluid is considered. Equations for kink coordinates are obtained and analyzed. Some nontrivial features of two‐soliton interaction characteristic of the strongly nonlinear case are established.     

Mellin Transform of the Limit Lognormal Distribution

The technique of intermittency expansions is applied to derive an exact formal power series representation for the Mellin transform of the probability distribution of the limit lognormal multifractal process. The negative integral moments are computed by a novel product formula of Selberg type. The power series is summed in general by means of its small intermittency asymptotic. The resulting integral formula for the Mellin transform is conjectured to be valid at all levels of intermittency. The conjecture is verified partially by proving that the integral formula reproduces known results for the positive and negative integral moments of the limit lognormal distribution and gives a valid characteristic function of the Lévy-Khinchine type for the logarithm of the distribution. The moment problem for the logarithm of the distribution is shown to be determinate, whereas the moment problems for the distribution and its reciprocal are shown to be indeterminate. The conjecture is used to represent the Mellin transform as an infinite product of gamma factors generalizing Selberg’s finite product. The conjectured probability density functions of the limit lognormal distribution and its logarithm are computed numerically by the inverse Fourier transform.     

The problems of nonlinear acoustics which seem to be the most important and interesting today

The material of the correlated report delivered at the 18th International Symposium on Nonlinear Acoustics (ISNA-18) in July 2008 (Stockholm, Sweden) [1] is presented in a more comprehensive form [1]. These results have also been partially reported on in the lectures given at the 12th and 13th “Nonlinear Waves“ schools in Nizhni Novgorod [2, 3]. The aim of the paper is to briefly consider the directions of the development of nonlinear acoustics and its successes which have been at the center of attention lately.     

A note on moments of limit log-infinitely divisible stochastic measures of Bacry and Muzy

A multiple integral representation of single and joint moments of the total mass of the limit log-infinitely divisible stochastic measure of Bacry and Muzy (Commun Math Phys 236:449–475, 2003) is derived. The covariance structure of the total mass of the measure is shown to be logarithmic. A generalization of the Selberg integral corresponding to single moments of the limit measure is proposed and shown to satisfy a recurrence relation. The joint moments of the limit lognormal measure, classical Selberg integral with \(\lambda _1=\lambda _2=0,\) and Morris integral are represented in the form of multiple binomial sums. For application, low moments of the limit log-Poisson measure are computed exactly and low joint moments of the limit lognormal measure are considered in detail.     

Molecular physiology of rhodopsin: Computer simulation

Computer simulation is used for comparative investigation of the molecular dynamics of rhodopsin containing the chromophore group (11-cis-retinal) and free opsin. Molecular dynamics is traced within a time interval of 3000 ps; 3 × 10⁶ discrete conformational states of rhodopsin and opsin are obtained and analyzed. It is demonstrated that the presence of the chromophore group in the chromophore center of opsin influences considerably the nearest protein environment of 11-cis-retinal both in the region of the β-ionone ring and in the region of the protonated Schiff base bond. Based on simulation results, a possible intramolecular mechanism of keeping rhodopsin as a G-protein-coupled receptor in the inactive state, i.e., the chromophore function as an efficient ligand antagonist, is discussed.     

Optical classification of random image fields using spectral synthetic discriminant functions

It is shown that the problem of classification of images that have the perfectly random nature may be solved with the help of synthetic discriminant functions being synthesized by least-squares technique to separate linearly the power spectra of the corresponding random image fields. The realization of the proposed method by means of an optical technique is discussed, and its efficiency is illustrated by two examples of real-life texture classification.