Exact and approximate symmetries for light propagation equations with higher order nonlinearity

For the first time exact analytical solutions to the eikonal equations in (1+1) dimensions with a refractive index being a saturated function of intensity are constructed. It is demonstrated that the solutions exhibit collapse; an explicit analytical expression for the self-focusing position, where the intensity tends to infinity, is found. Based on an approximated Lie symmetry group, solutions to the eikonal equations with arbitrary nonlinear refractive index are constructed. Comparison between exact and approximate solutions is presented. Approximate solutions to the nonlinear Schrodinger equation in (1+2) dimensions with arbitrary refractive index and initial intensity distribution are obtained. A particular case of refractive index consisting of Kerr refraction and multiphoton ionization is considered. It is demonstrated that the beam collapse can take place not only at the beam axis but also in an off-axis ring region around it. An analytical condition distinguishing these two cases is obtained and explicit formula for the self-focusing position is presented.Comment: 25 pages, 5 figure

All-electron theory of the coupling between laser-induced coherent phonons in bismuth

Using first principles, all-electron calculations and dynamical simulations we study the behavior of the A_1g and E_g coherent phonons induced in Bi by intense laser pulses. We determine the potential landscapes in the laser heated material and show that they exhibit phonon-softening, phonon-phonon coupling, and anharmonicities. As a consequence the E_g mode modulates the A_1g oscillations and higher harmonics of both modes appear, which explains recent isotropic reflectivity measurements. Our results offer a unified description of the different experimental observations performed so far on bismuth.Comment: 3 figure

GC₃ Biology in Eukaryotes and Prokaryotes

We describe the distribution of Guanine and Cytosine (GC) content in the third codon position (GC3) distributions in different species, analyze evolutionary trends and discuss differences between genes and organisms with distinct GC3 levels. We scrutinize previously published theoretical frameworks and construct a unified view of GC3 biology in eukaryotes and prokaryotes

Creep and damage in shells of revolution under cyclic loading and heating

Creep of cyclically loaded thin shells of revolution and their fracture due to creep and fatigue mechanisms are studied. Creep-damage equations for steels and nickel-based alloys are built by the use of scalar damage parameter. Constitutive equations were derived using the method of asymptotic expansions and averaging over a period of cyclic loading. The cases of fast and slow varying of temperature and loading are regarded. General problem statement and method for solution of creep problems at cyclic loading are presented. Strain–stress state in shell structures is determined by the use of homemade FEM creep–damage code, where the finite element of conical shell is used. Results of creep–damage problem for conical panel are discussed

Differential Evolution Approach to Detect Recent Admixture

The genetic structure of human populations is extraordinarily complex and of fundamental importance to studies of anthropology, evolution, and medicine. As increasingly many individuals are of mixed origin, there is an unmet need for tools that can infer multiple origins. Misclassification of such individuals can lead to incorrect and costly misinterpretations of genomic data, primarily in disease studies and drug trials. We present an advanced tool to infer ancestry that can identify the biogeographic origins of highly mixed individuals. reAdmix is an online tool available at http://chcb.saban-chla.usc.edu/reAdmix/.Comment: presented at ISMB 2014, VariSI

Creep and damage in shells of revolution under cyclic loading and heating

Creep of cyclically loaded thin shells of revolution and their fracture due to creep and fatigue mechanisms are studied. Creep-damage equations for steels and nickel-based alloys are built by the use of scalar damage parameter. Constitutive equations were derived using the method of asymptotic expansions and averaging over a period of cyclic loading. The cases of fast and slow varying of temperature and loading are regarded. General problem statement and method for solution of creep problems at cyclic loading are presented. Strain–stress state in shell structures is determined by the use of homemade FEM creep–damage code, where the finite element of conical shell is used. Results of creep–damage problem for conical panel are discussed

DEFORMATION TRANSVERSE SHEAR BENDING STATE OF A THIN PLATE LAYER OF AN ANISOTROPIC GEOLOGICAL MEDIUM FROM THE ACTION OF CONCENTRATED ENERGY IMPULSES

A method is proposed for study the structural stability of the deformation state of structural blocks of the earth's crust, approximated in the form of plate layers of the geological medium when transverse shear bending from the action of concentrated energy impulses. Advances here are carried out in the two directions. First, in contrast to the previous article, the physical and mechanical model of the geological medium is endowed with anisotropic properties, which makes it possible to increase the adequacy of the obtained numerical results to the specifics of the real problem. Secondly, instead of the simplest bilinear 4-node finite elements, the special spectral non-algebraic 8-node finite iso-parametric finite elements are used, the use of which significantly increases both the accuracy of calculations and their reliability in the sense of ensuring the robustness of calculations for relatively small values of the plate thickness. It should be noted that the Finite Element Method uses exclusively only algebraic finite elements (power polynomials in the h-version and orthogonal polynomials in the p-version). It is known from approximation theory that the use of spectral non-algebraic approximations improves the quality of approximations. Therefore, their introduction into the structure of finite element calculations can improve the quality of modeling in the study of the strain-stress-state (SSS) of the geological medium. A structural block (SB) is understood as a plate layer with plan dimensions exceeding the thickness by more than 10 times. The identification of hazardous zones in the rock massive due to stress concentration is complemented by the development of mechanical, mathematical and computational tools for modeling the curvature of the earth's crust during bending based on the classical theory of Kirchhoff and refined Reissner-Mindlin theory. Test calculations have shown that the accuracy of the calculation and the quality of geometric modeling of fragments of an anisotropic geological environment based on the refined 8-node spectral finite element is significantly better than for the 8-node algebraic finit

MODEL OF EMOTIONALLY-VALUABLE COMPONENT OF THE CONTENT OF ELEMENTARY FOREIGN LANGUAGE EDUCATION

Introduction. The component structure of the content of modern foreign language education involves the inclusion of the emotionally-valuable component (EVC), the main purpose of which is the formation of students’ axiological attitude to educational material and the world around them; the acquisition of individual system of national and universal values. The process of implementing the EVC of the content of foreign language education involves the construction of its models at all levels of school foreign language education. The aim of this article is to present the invariant of the model which enables to make a selection of foreign texts of emotionally-valuable contents at the junior stage of foreign language education. Methodology and research methods. The methods of theoretical analysis (systemic-structural, organizational, functional, comparative, typological) were used in order to define basic theoretical and methodological concepts of the research. When projecting the model of the EVC of the content of foreign language education, adapted to the conditions of teaching foreign languages in elementary school, methods of designing and modelling were used. Scientific novelty and results. In the article the subcomponent structure of the EVC of the content of foreign language education is presented. It was proved that all the system subcomponents of the EVC are functional, and each of them has its own special role in elementary foreign language education. The concept of a foreign language text of emotionally-valuable contents is proposed. The choice of the form of such texts, and also the selection of an emotionally-valuable technique of work with, including conditions, means and methods, allowed us to design the invariant of the model of the EVC of the content of elementary foreign language education. Practical significance. The research materials can be useful in implementing scientifically-based selection of speech material within the discipline “Foreign Language” and the development of adequate techniques of working with texts of emotionally-valuable contents in primary school.Введение. Содержание современного иноязычного образования в массовой школе включает эмоционально-ценностный компонент (ЭЦК), главным назначением которого являются приобщение учащихся к общенациональным и общечеловеческим ценностям и формирование у них аксиологического отношения к учебному материалу и окружающему миру. Реализация ЭЦК требует разработки инвариантов моделей обучения иностранному языку для всех ступеней школьного иноязычного образования. Цель данной статьи – представить авторскую модель, позволяющую осуществить отбор иноязычных текстов эмоционально-ценностного содержания на младшей ступени школьного иноязычного образования. Методология и методики. Для того чтобы определить базовые теоретические и методологические положения исследования, были использованы методы теоретического системно-структурного, организационно-функционального, сравнительно-сопоставительного и типологического анализа. При создании модели ЭЦК, адаптированной к условиям начальной школы, использовались методы проектирования и моделирования.Научная новизна и результаты исследования. Представлен субкомпонентный состав ЭЦК содержания иноязычного образования. Показаны функционал каждого системного компонента и его особая роль в обучении иностранному языку. Предложено определение иноязычного текста эмоциональноценностного содержания. Выбор вида таких текстов, а также приемов работы с ними, включающих условия, средства, способы учебной деятельности, позволили построить инвариант модели ЭЦК содержания начального иноязычного образования. Практическая значимость. Материалы исследования могут быть востребованы при осуществлении в рамках дисциплины «Иностранный язык» научно-обоснованного отбора учебного речевого материала и при разработке адекватных приемов работы с младшими школьниками