Selected properties of optical spatial solitons in photorefractive media and their important applications

Some selected important properties of photorefractive spatial solitons and their applications have been reviewed in the present paper. Using band transport model, the governing principle of photorefractive nonlinearity has been addressed and nonlinear dynamical equations of spatial solitons owing to this nonlinearity have been discussed. Mechanisms of formation of screening and photovoltaic solitons of three different configurations i.e., bright, dark and grey varieties have been examined. Incoherently coupled vector solitons due to single and two-photon photorefractive phenomena have been highlighted. Modulation instability, which is precursor to soliton formation has been also discused briefly. Finally possible applications of photorefractive spatial solitons have been highlighted.Comment: 17 pages, 3 figures. arXiv admin note: text overlap with arXiv:1209.221

Competence amplification of correctness result verification in mathematical disciplines

The ability to verify the correctness and effectiveness of the result is an important competence for all areas of training. Checking the correctness of the decision should be a mandatory final stage of solving mathematical problems. On the example of differentiation and integration of functions shown that when tested using simple numerical algorithms that can be implemented using the basic features package Excel. Assimilation of natural competence easier to implement with the help of numerical methods, which are fixed in the process of constant testingУмение осуществлять проверку корректности и эффективности полученного результата является важной компетенцией для всех направлений подготовки. Проверка правильности решения должна являться обязательным завершающим этапом решения математической задачи. На примере дифференцирования и интегрирования функций показано, что при тестировании используются простые численные алгоритмы, которые можно реализовать с помощью базовых возможностей пакета Excel. Усвоение естественнонаучных компетенций легче реализовать с помощью численных методов, которые закрепляются в процессе постоянного тестировани

About the Applicability of Bone and Cartilage Acid-free Staining for Anura

The article describes the first use of acid-free alcian-alizarin staining for tailless amphibians in comparison with the standard method of acid staining on the example of the moor frog. The acid-free protocol is applicable for Anura and it has a number of advantages, such as the absence of decalcification, safety for the researcher andothers. However, this method also has limitations, such as the binding of alcian blue with soft tissues

Quantitative modeling of \textit{in situ} x-ray reflectivity during organic molecule thin film growth

Synchrotron-based x-ray reflectivity is increasingly employed as an \textit{in situ} probe of surface morphology during thin film growth, but complete interpretation of the results requires modeling the growth process. Many models have been developed and employed for this purpose, yet no detailed, comparative studies of their scope and accuracy exists in the literature. Using experimental data obtained from hyperthermal deposition of pentane and diindenoperylene (DIP) on SiO$_2$, we compare and contrast three such models, both with each other and with detailed characterization of the surface morphology using ex-situ atomic force microscopy (AFM). These two systems each exhibit particular phenomena of broader interest: pentacene/SiO$_2$ exhibits a rapid transition from rough to smooth growth. DIP/SiO$_2$, under the conditions employed here, exhibits growth rate acceleration due to a different sticking probability between the substrate and film. In general, \textit{independent of which model is used}, we find good agreement between the surface morphology obtained from fits to the \insitu x-ray data with the actual morphology at early times. This agreement deteriorates at later time, once the root-mean squared (rms) film roughness exceeds about 1 ML. A second observation is that, because layer coverages are under-determined by the evolution of a single point on the reflectivity curve, we find that the best fits to reflectivity data --- corresponding to the lowest values of $\chi_\nu^2$ --- do not necessarily yield the best agreement between simulated and measured surface morphologies. Instead, it appears critical that the model reproduce all local extrema in the data. In addition to showing that layer morphologies can be extracted from a minimal set of data, the methodology established here provides a basis for improving models of multilayer growth by comparison to real systems.Comment: 34 pages (double-spaced, including figures and references), 10 figures, 3 appendice

Scattering of neutrinos on a polarized electron target as a test for new physics beyond the Standard Model

In this paper, we analyze the scattering of the neutrino beam on the polarized electron target, and predict the effects of two theoretically possible scenarios beyond the Standard Model. In both scenarios, Dirac neutrinos are assumed to be massive. First, we consider how the existence of CP violation phase between the complex vector V and axial A couplings of the Left-handed neutrinos affects the azimuthal dependence of the differential cross section. The future superbeam and neutrino factory experiments will provide the unique opportunity for the leptonic CP violation studies, if the large magnetized sampling calorimeters with good event reconstruction capabilities are build. Next, we take into account a scenario with the participation of the exotic scalar S coupling of the Right-handed neutrinos in addition to the standard vector V and axial A couplings of the Left-handed neutrinos. The main goal is to show how the presence of the R-handed neutrinos, in the above process changes the spectrum of recoil electrons in relation to the expected Standard Model prediction, using the current limits on the non-standard couplings. The interference terms between the standard and exotic couplings in the differential cross section depend on the angle $\alpha$ between the transverse incoming neutrino polarization and the transverse electron polarization of the target, and do not vanish in the limit of massless neutrino. The detection of the dependence on this angle in the energy spectrum of recoil electrons would be a signature of the presence of the R-handed neutrinos in the neutrino-electron scattering. To make this test feasible, the polarized artificial neutrino source needs to be identified.Comment: 11 pages, 3 eps figures, revtex, submitted to publicatio

Optimization of complex functions and the algorithm for exact geometric search for complex roots of a polynomial

The paper describes an application for visualization of four-dimensional graphs of a complex variable function. This application allowed us to construct an exact geometric algorithm for finding the real and complex roots of a polynomial on the same plane. A graph of an n-th order polynomial on the real plane allows us to define geometrically all the real roots. Number of real roots varies from 0 to n. The rest of the roots are complex and not determined by the graph. In the article, in addition to the graph of the basic polynomial, two auxiliary graphs are constructed, which allow us to represent all complex roots on the same real plane. Realization of this method is considered in detail for the solution of a cubic polynomial. In this case the method has exceptional features in comparison with polynomials of other degrees. We also propose an algorithm for constructing auxiliary functions for the general case of a polynomial of order n which have exact formulas for polynomials with order n ≤ 10. The algorithm for the first time builds the exact hodograph of poles for the control systems with feedback. We generalize the concepts of stationary and extremal points to the case of a complex function. The absence of the possibility of comparing the complex values of the objective function is compensated by an analysis of the behavior of the stationary point under small perturbations of the polynomial by linear functions. Optimality criteria are proposed using complex trajectories of stationary points. © 201