Electromagnetic Excitation of a Spherical Medium by an Arbitrary Dipole and Related Inverse Problems

A piecewise homogeneous spherical medium is excited by an external or internal electric dipole with arbitrary location and polarization. The dyadic Green's function of the medium is determined analytically. Then, the vector electric fields and far‐field patterns are obtained. Low‐frequency approximations of the far‐field patterns are subsequently derived, which encode the dipole's locations coordinates and polarization components in the different orders of the associated expansions. This fact enables the establishment of far‐field inverse scattering algorithms referring to the electromagnetic interior or exterior excitation of a small sphere by an arbitrary dipole. Inverse medium and inverse source problems are considered concerning, respectively, the determination of the scatterer's material parameters and the dipole's characteristics. The developed inverse algorithms determine exactly the unknown parameters of problems fulfilling the low‐frequency assumption, which is indeed the case in most relevant applications, like, e.g., in biomedical imaging.     

The Doppler Effect in a Warm Uniaxial Plasma

In this paper we consider the character of the radiation emittedby a radiator moving with uniform velocity through a warm, uniaxialplasma. It is shown that the dispersive and anisotropic natureof the plasma plays an important role in determining both theDoppler shift in frequency and the power spectrum of the radiation.The power spectrum and the Doppler relation between the frequencyand the direction of the emitted radiation are calculated when(a) the motion is parallel to the magnetic field, and (b) themotion is perpendicular to the magnetic field. It is shown thatthe Doppler shift and the power spectrum are substantially differentin these two cases. The formulae for the {caron}erenkov radiationemitted by a moving charged particle may be obtained from thosefor Doppler radiation. In the last section we show that a particlemoving parallel to the axis of symmetry excites a power spectrumwhich is linear with frequency, whereas a particle moving perpendicularto that axis excites a power spectrum that is sharply peakednear the plasma frequency.     

A Reproducible Excitation Mechanism for Analyzing Electric Guitars

This contribution presents the excitation mechanism of an experimental set-up for measuring the structural behavior of an electric guitar body using Laser-Doppler-Vibrometers, to be compared to the generated sound. It is the aim of this investigation to gain insight into the influence on the sound of materials and designs of the large variety of commercially available electric guitars. The core of the experimental set-up is the excitation mechanism, which has been developed to guarantee a well-defined and absolute reproducible excitation of the guitar string in order to detect even small differences in sound. This mechanism has been constructed making use of the methods of multibody dynamics and optimization. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Scattering Theorems for Acoustic Excitation of a Layered Obstacle by an Interior Point Source

Interesting scientific and technological applications motivate the study of scattering problems, where a layered scatterer is excited by a spherical acoustic wave generated by a point-source located in its interior. The scatterer's core may be acoustically soft, hard, resistive, or penetrable. This paper initiates the investigation of scattering theorems, corresponding to the excitation of a layered scatterer by a point source in its interior. Reciprocity and general scattering theorems are established, relating the total fields and the corresponding far-field patterns. The optical theorem, relating the scattering cross-section with the field in the layer containing the source, is recovered as a corollary of the general scattering theorem. Furthermore, for a scatterer excited by a spherical and a plane wave, mixed scattering theorems are derived. Numerical implementations of the optical theorem in concrete scattering applications are analyzed.     

楔型向错偶极子和裂纹的干涉效应

研究了晶体材料中一个楔型向错偶极子与裂纹的弹性干涉效应．运用复变函数方法获得了复势函数和应力场的封闭形式解答,导出了裂纹尖端应力强度因子和作用在向错偶极子中心点像力的解析表达式．获得了向错偶极子的位置、方向和偶臂长度对裂纹尖端应力强度因子的影响规律,并讨论了裂纹附近向错偶极子的平衡位置．结果表明向错偶极子靠近裂纹尖端时,对应力强度因子有明显的屏蔽或反屏蔽作用．     

具有热储备可修复平行系统本征值问题

针对具有热储备可修复平行系统模型,得出了一个本征值对应一个本征元的结论并证了除0本征值外还存在另外非零实本征值.     

随机激励下结构的非线性分析

针对随机时间序列载荷激励下的非线性系统,提出一种基于Z变换的递归方法．对于所获得的响应时间序列的识别,建议了一种离散小波变换（DWT）的技术．     

Fast Solvers for an Elliptic Problem from Dipole Localization

The model‐based reconstruction of electrical brain activity from electroencephalographic measurements is of constantly growing importance in the fields of Neurology and Neurosurgery. Algorithms for this task involve the solution of a 3D Poisson problem on a complicated geometry and with non‐continuous coefficients for a considerable number of different right hand sides. Thus efficient solvers for this subtask are required. We will report on our experiences with different iterative solvers for a discretization based on cell‐centered finite‐differences.     

提高水分子流出纳米碳管速度的特殊水分子偶极排布研究

使用分子动力学的方法,研究了水分子进出狭窄碳纳米管的过程．发现管口处水分子的偶极垂直于碳管时容易流出碳管．根据碳管中与之相邻的水分子的偶极方向可以把这种特殊构型分为2类．虽然,这2类特殊结构的出现概率非常小,但是它们对净流过碳管水分子的贡献与其它结构的贡献基本相同．这2种偶极排布中水分子比较接近管壁、远离Lennard-Jones势的平衡位置,导致这2种偶极排布中水分子能量升高,处于相对不稳定的状态,容易流出碳管．这个发现表明可以通过调控碳纳米管内的水分偶极方向控制管内的水分子流动．     

Excitation of normal modes of a weakly inhomogeneous waveguide by a point source

An asymptotic expansion of the Green function is constructed for a weakly inhomogeneous waveguide. Matching of asymptotic expansions is used.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 140, pp. 174–178, 1984.The author thanks V. M. Babich for posing the problem.     

The Excitation of a Fluid-loaded Plate Stiffened by a Semi-infinite Array of Beams

The excitation of an infinite, fluid-loaded plate with parallel,equally spaced stiffening beams reinforcing one half of it isstudied. The problem is formulated in terms of a discrete convolutionequation for the displacement at the beam positions and is solvedby discrete Fourier transforms coupled with the Wiener-Hopftechnique. The basic ideas are introduced through a reconsiderationof the excitation of an infinite, fluid-loaded plate, stiffenedby a periodic array of beams. As an example, asymptotic expressionsare derived for the reflected, transmitted and scattered fieldsgenerated when a free wave in the unstiffened half of the plateimpinges upon the semi-infinite array. It is shown, in particular,that the far-field motion in the stiffened half of the platehas the form of a Floquet wave. Numerical results for reflectionand transmission coefficients, and for the pressure field radiatedinto the fluid, are presented graphically. Finally, a briefoutline is given of a number of related problems that are solubleby similar techniques.     

Justification of Dipole Approximation in the Problem of Nonlinear Wave Generation by a Submerged Sphere

Some nonlinear dipole approximation is constructed for the nonstationary problem of a solid sphere motion under a free surface. The approximation is justified in the class of analytic functions decaying at infinity.Original Russian Text Copyright © 2005 Pyatkina E. V.The author was supported by the State Maintenance Program for the Leading Scientific Schools (Grant NSh-440.2003.1) and the Russian Foundation for Basic Research (Grant 05-01-00250).__________Translated from Sibirskii Matematicheskii Zhurnal, Vol. 46, No. 4, pp. 907–927, July–August, 2005.     

Resonant Excitation of a Composite Beam

Phase–locked loops are widely used within communication technology for synchronizing signals by tracking their phases. Their functional principle can be applied for maintaining the resonant excitation of a beam whose eigenfrequency changes over time and, thus, representing an alternative excitation method for the adaptronic strut for machine tools shown in [1]. In this contribution an experimental set–up for resonant excitation of a composite beam is introduced. A particle is mounted on the beam, its position and mass are are adjustable to modify the eigenfrequency of the beam. The simulation results of the analytical examination of the test–rig are compared with the experimental results. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Plasma formation in solid deuterium by an ultrashort laser prepulse

A calculation is carried out to determine plasma formation by laser light during the first few picoseconds, using a microscopic model for the interaction between laser beam and solid deuterium target. Results show an initial rapid low density ionization throughout the target, followed during the next few picoseconds by the formation of a peak in electron density immediately behind the incident surface at a temperature of a few electron volts. Reflection occurs since the electron density in the peak exceeds the critical value. Rapid expansion of the outer layer within the next 0.1–0.3 nsec will, however, reduce the high electron density to below the critical value, readying the target for absorption of the next laser pulse.

---

Zusammenfassung Eine Rechnung zur Bestimmung der Plasmabildung mittels Laserstrahlen währen der ersten Picosekunden wurde mit Hilfe eines mikroskopischen Modells der Wechselwirkung zwischen Laserstrahl und einer festen Deuteriumprobe ausgeführt. Das Resultat zeigt, dass die ganze Probe als erstes in sehr kurzer Zeit schwach ionisiert wird, worauf sich in den folgenden Picosekunden eine hohe Elektronendichte bei einer Temperatur von einigen eV unmittelbar hinter der Eintrittsoberfläche bildet. Da die Elektronendichte dort über dem kritischen Wert liegt, wird sie weiterhin einfallendes Laserlicht reflektieren. Die schnelle Expansion der äusseren Schicht während der nächsten 0.1–0.3 Nanosekunden bewirkt aber einen Abfall der Elektronendichte unter den kritischen Wert, wodurch die Probe für die Absorption des nächsten Laserpulses bereit gemacht wird.

     

热偶极子与圆形界面裂纹的作用

热偶极子由热源和热汇组成.应用解析延拓方法、广义Liouville 定理及Muskhelishvili 边值问题理论,研究了在热源偶极子作用下含圆形夹杂复合材料的界面裂纹问题.导出温度场和应力场之后,分析了温度场和夹杂对界面断裂的效应.作为实例,针对若干种组合材料及热偶极子处于不同位置,给出了界面裂纹热应力强度因子的数值变化曲线.结果表明,界面裂纹特性取决于材料的弹性常数和热学性能及偶极子的情况.     

Excitation of nuclei by nonrelativistic heavy ions

The scattering of nonrelativistic heavy ions is considered. Differential scattering cross sections are obtained on the basis of Feynman path integrals. The path integral with respect to the internal variables is calculated exactly along the trajectory of the relative motion in the semiclassical approximation. Equations of motion that take into account excitation of the nucleus are derived.Joint Institute for Nuclear Research. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 100, No.1, pp. 24–32, July, 1994.