Acoustic scattering of a plane wave by a circular penetrable cone

The paper is devoted to the diffraction of a plane wave by an acoustically transparent semi-infinite cone. The problem of diffraction is reduced to a singular integral equation in the framework of the incomplete separation of variables. The Fredholm property and regularization of the integral equation are discussed. Some important integral representations of the wave field are considered. The detailed study of the far-field asymptotics is given. Expressions for the diffraction coefficient of the spherical wave scattered from the vertex of the cone are considered. The reflected from the conical surface waves and those transmitted across the surface are also discussed.     

二维位势边界元法高阶单元几乎奇异积分半解析算法

准确计算几乎奇异积分是边界元法难题之一。目前,对于一般的高阶单元的几乎奇异积分尚缺乏通用高效的计算方法。本文在单元局部坐标系中表征了二维高阶单元的几何特征,提出了源点相对高阶单元的接近度概念。针对二维位势边界元法的3节点二次等参单元,构造出与单元积分核具有相同几乎奇异性的近似奇异核函数。从二维位势几乎奇异积分单元积分核中扣除近似奇异核函数,把几乎奇异积分项转换为规则积分和奇异积分两部分之和,规则积分部分用常规Gauss数值积分计算,奇异积分部分由导出的解析公式计算,从而建立了二维位势问题高阶单元几乎强奇异和超奇异积分的半解析算法。算例结果表明了本文半解析算法的有效性和计算精度。     

An improved exponential transformation for nearly singular boundary element integrals in elasticity problems

This paper presents an improved exponential transformation for nearly singular boundary element integrals in elasticity problems. The new transformation is less sensitive to the position of the projection point compared with the original transformation. In our work, the conventional distance function is modified into a new form in the polar coordinate system. Based on the refined distance function, an improved exponential transformation is proposed in the polar coordinate system. Moreover, to perform integrations on irregular elements, an adaptive integration scheme considering both the element shape and the projection point associated with the improved transformation is proposed. Furthermore, when the projection point is located outside the integration element, another nearest point is introduced to subdivide the integration elements into triangular or quadrilateral patches of fine shapes. Numerical examples are presented to verify the proposed method. Results demonstrate the accuracy and efficiency of our method.     

Approximate First Integrals of Weakly Nonlinear,Damped-Driven Oscillators with One Degree of Freedom

First-order approximate symmetries of weaklynonlinear, damped-driven oscillators have been determined.First-order approximate first integrals have been obtained byemploying an approximate version of Noether's theorem for the conservativecase. Furthermore, approximate first integrals of the damped case have been obtained based on the first integrals of the conservative case.Approximate first integrals enabled us to identify three types of genericbifurcations. Analytical results have been verified by numerical experiments.     

Preferential Solvation in Mixed Solvents X. Completely Miscible Aqueous Co-Solvent Binary Mixtures at 298.15 K

Summary.  The Kirkwood-Buff integrals for 18 completely miscible aqueous co-solvent binary mixtures have been recalculated from thermodynamic data, and the volume-corrected preferential solvation parameters derived from them are presented. Also presented are these latter quantities for 15 additional such mixtures, for which the volume correction has not been applied previously. The self-interaction of the water, the mutual interaction of the water and the co-solvent, and the self-interaction of the co-solvent at infinite dilution derived from these integrals and parameters are then discussed. The systems studied include aqueous hydrogen peroxide, methanol, ethanol, 1- and 2-propanol, 2-methyl-2-propanol, 2,2,2-trifluoroethanol, 1,1,1,3,3,3-hexafluoro-2-propanol, ethane-1,2-diol, glycerol, 2-methoxyethanol (at 313 and 343 K), 2-ethoxyethanol, 2-butoxyethanol, 2-aminoethanol, N-methyl- and N,N-dimethyl-2-aminoethanol, tetrahydrofuran, 1,4-dioxane, acetone, formic, acetic, and propanoic acids, piperidine, pyridine, acetonitrile, formamide, N-methyl- and N,N-dimethylformamide, N-methylacetamide, N-methylpyrrolidin-2-one (at 303 K), hexamethyl phosphoric triamide, dimethylsulfoxide, and tetramethylenesulfone (at 303 K). Received January 10, 2001. Accepted (revised) February 20, 2001     

On Information Processes in Statistical Experiments with Distributed Observations

Using stochastic integration theory in topological vector spaces general formulas for the Hellinger processes are derived. Feynman–Kac type formulas are obtained for the related Hellinger integrals in terms of the Hellinger processes and the geometric mean measures. The expected logarithmic utility from data, characterized as the Shannon information, is also considered.     

Numerical evaluation of hypersingular integrals

Boundary integral equations which employ integrals which exist only if defined in the Cauchy principal value sense or as the Hadamard finite part are currently used with success to solve many two- and three-dimensional problems of applied mechanics. We will recall definitions and main properties of these integrals, examine some numerical approaches for their evaluation and present several new results.