Numerical method for unsteady compressible boundary layers driven by compression or expansion wave

A numerical analysis is presented for the unsteady compressible laminar boundary layer driven by a compression or expansion wave. Approximate or series expansion methods have been used for the problems because of the characteristics of the governing equations, such as non-linearity, coupling with the thermal boundary layer equation and initial conditions. Here a transformation of the governing equations and the numerical linearization technique are introduced to deal with the difficulties. First, the governing equations are transformed for the initial conditions by Howarth and semisimilarity variables. These transformations reduce the number of independent variables from three to two and the governing equations from partial to ordinary differential equations at the initial point. Next, the numerical linearization technique is introduced for the non-linearity and the coupling with the thermal boundary layer equation. Because the non-linear terms are linearized without sacrifice of numerical accuracy, the solutions can be obtained without numerical iterations. Therefore the exact numerical solution, not approximate or series expansion, can be obtained. Compared with the approximate or series expansion method, this method is much improved. Results are compared with the series expansion solutions.     

Asymptotic Integration of Parabolic Problems with Large High-Frequency Summands

We develop the averaging method theory for parabolic problems with rapidly oscillating summands some of which are large, i.e., proportional to the square root of the frequency of oscillations. In this case the corresponding averaged problems do not coincide in general with those obtained by the traditional averaging, i.e., by formally averaging the summands of the initial problem (since the principal term of the asymptotic expansion of a solution to the latter problem is not in general a solution to the so-obtained problem). In this article we consider the question of time periodic solutions to the first boundary value problem for a semilinear parabolic equation of an arbitrary order 2k whose nonlinear terms, including the large, depend on the derivatives of the unknown up to the order k-1. We construct the averaged problem and the formal asymptotic expansion of a solution. When the large summands depend on the unknown rather than its derivatives we justify the averaging method and the complete asymptotic expansion of a solution.Original Russian Text Copyright © 2005 Levenshtam V. B.The author was supported by the Russian Foundation for Basic Research (Grant 01-01-00678) and the Program “ Universities of Russia” (UR.04.01.029).__________Translated from Sibirskii Matematicheskii Zhurnal, Vol. 46, No. 4, pp. 805–821, July–August, 2005.     

The Effect of Adhesion Interaction on the Mechanical Properties of Thermoplastic Basalt Plastics

The effect of temperature, adhesion time, and surface treatment of a reinforcing filler on the mechanical properties of thermoplastic basalt plastics based on a high-density polyethylene and a copolymer of 1,3,5-trioxane with 1,3-dioxolan is investigated. An extreme dependence for the adhesive strength in a thermoplastic-basalt fiber system is established and its effect on the mechanical properties of basalt plastics and the influence of the adhesion contact time on the adhesive strength in the system are clarified. The surface modification of basalt fibers in acidic and alkaline media intensifies the adhesion of thermoplastics to them owing to a more developed surface of the reinforcing fibers after etching. It is found that the treatment in the acidic medium is more efficient and considerably improves the mechanical properties of basalt plastics.     

State of Water in Hydration Spheres of Potassium Iodide

Ion hydration has been studied for potassium iodide solutions with concentrations from 0 to 51 wt.% at temperatures from 288.15 to 308.15 K based on ultrasonic measurements and molar adiabatic compressibility data. For hydration complexes, structural characteristics have been determined. The structure of noncoordinated water plays a significant role even in concentrated solutions. An electrostatic ion field has a strong effect on the temperature dependence of the molar volume of hydration water. A method for the precise determination of the total solvation boundary is presented.     

Uniform energy decay of Schrodinger equations with variable coefficients

This paper establishes the exponential decay of the solutionsof the Schrödinger equation with variable coefficientsin the principal part subject to dissipative feedback actingin the Dirichlet boundary condition. The approach adopted usesa lifting argument in the topology of the solution along withRiemannian geometry method.     

奇异非线性二阶三点边值问题正解的存在唯一性

本文研究了一类奇异非线性二阶三点边值问题，通过摄动技巧和比较原理获得了所论问题正解的存在唯一性。     

带有非线性边界条件的非线性抛物型方程组的爆破速率估计

In this paper, the estimate on blow-up rate of the following nonlinear parabolic system is considered: We will prove that there exist two positive constants such that: where l_1= l_(21)α／α_2 l_(22),r=α_1／α_2＞1,α_1≤α_2＜0.     

三维调和问题的自然积分方程及其数值解

1．引言许多椭圆型偏微分方程边值问题可以通过不同途径归化为边界积分方程，由此发展出各种边界元方法．由我国学者冯康和余德浩首创并发展的自然边界元方法便是其中之一山．这一方法与经典边界元法相比有其独特的优点，它有着较高的数值稳定性，能与传统的有限元方法基于同一变分原理自然而直接地耦合［2］．近年来，无界区域问题倍受关注［2－71，其中，基于自然边界归化的耦合算法及区域分解算法是处理无界区域问题的一种有效手段．但是，迄今为止关于自然边界归化的研究仅仅局限于二维问题．而三维问题显然更需要发展相应方法且其结果…     

热处理和紫外辐射对DNA影响的拉曼光谱研究

检测了鲕鱼精ＤＮＡ纤维和经过４０℃，９１℃，２００℃加热处理的拉曼光谱。研究结果表明，在熔融温度以下热处理对ＤＮＡ构象的影响是轻微的，在熔融温度以上则随温度的升高，对ＤＮＡ分子结构的影响有破坏也逐渐加剧，首先受影响的是腺嘌呤和脱氧核糖。     

ON NUMEROV SCHEME FOR NONLINEAR TWO-POINTS BOUNDARY VALUE PROBLEM

1.IntroductionInstudyingsomeproblemsarisinginelectromagnetism,biology)astronomy,bound-arylayerandothertopics,weoftenmeetnonlineartwo--pointsboundaryproblem,i.e.,findingyECo[0,11nC2(0,1)suchthatwhereor,garecertainconstants,andf(x,z)EC'(0,1)xC'(--co,co).Undersomeconditionsonf(x,z),wecanusetheframeworkof[1]toinvestigatetheexistenceanduniquenessofitssolutions.Alsotherearealotofliteratureconcerningitsnumericalsolutio.s[2--'].Inparticular,N..ero.15]proposedafamousfinitedifferenceschemewiththeaccu…