Detection and location of cracks using loss of reciprocity in ultrasonic waves propagation

The reciprocity theorem is a general statement valid for elastic media, and it has been applied to the solution of elastic wave equations, transducers calibration, time reversal acoustics, etc. However, localized nonlinear scatterers are expected to break reciprocity even though the effect is, in several cases, negligible. Here the dependence of the reciprocity break on the presence of a localized damage and the influence of its relative position has been experimentally investigated. It will be shown that the break of reciprocity, usually considered a disadvantage, can be exploited as an imaging tool for localized cracks detection.     

Electron-ion interference and Onsager reciprocity in mixed ionic-electronic transport in TiO2

Onsager's reciprocity theorem has been extensively discussed for fluid systems and its validity generally accepted. The application of the theorem to solid state, however, is not always transparent due to additional complications that have no counterparts in fluids, and its validity has not been so exhaustively examined experimentally either. Here we show that in the phenomenon of mixed ionic-electronic conduction in TiO2 (rutile), the theorem is verified experimentally, and the Onsager cross coefficient can be even larger than a direct one, contrary to the conventional belief.     

Receiving Antenna in a Magnetoplasma in the Resonance Frequency Band

We find the rms voltage on a receiving dipole antenna in the electromagnetic field of a quasipotential-wave packet in a magnetoplasma in the resonance frequency band. It is shown that this voltage can be determined as a product of the electromagnetic-field amplitude of the incident wave by the effective length L_eff of the receiving antenna. For a short dipole whose length is much smaller than the electromagnetic-mode wavelength, the antenna effective length is proportional to the product of the dipole effective length in free space by the excitation coefficient of quasielectrostatic waves (non-normalized electric-field pattern of a dipole). In the case where the receiving antenna is located in proximity to the resonance cone on the lighted side, this excitation coefficient is much greater than unity. Therefore, the determined voltage differs significantly from the conventional estimate which is based on formulas valid for antennas in free space. We perform our derivations using the reciprocity theorem and the fluctuation-dissipation theorem applied to a regular electromagnetic field and a receiving antenna, which constitute the special case of a system which is not in equilibrium but allows an equilibrium (stationary state) to be reached between the incident radiation field and the electromagnetic field reemitted by the antenna. The emphasis is placed on the universal nature of the applied calculation procedure which is valid for arbitrary antennas and matters.     

Mackey Theorem and Two-Electron Wave Function of a Multi-Centre System

The two-electron wave function in a system of many equivalent atoms is investigated group-theoretically. It is shown that the classification of different types of two-electron (two-hole) localizations can be made by the double-coset decomposition of the symmetry group with respect to the local subgroup, and that the group appearing in the Mackey theorem can be used for the additional classification of states. The Mackey theorem on symmetrized squares and the generalized Frobenius reciprocity theorem are applied to the construction of two-electron states in octahedral symmetry. Received October 23, 1995; revised June 21, 1996; accepted for publication July 1, 1996     

Reciprocity in the wave reflection and transmission problem: Part 1. Symmetry of the matrices of reflection coefficients

The reciprocity theorem in Lyamshev’s formulation is used to derive a general symmetry relationship for the matrices of reflection coefficients in homogeneous media and one-dimensional waveguides. This relationship is shown to be equivalent to the normalization of the amplitudes by the cross power flux of the forward and backward waves. The relationship is valid for both propagating and evanescent waves, and all the symmetry relationships known from the literature represent its particular cases.     

Cherenkov radiation in biaxial crystals—II

By a series of transformations the integral for the radiated energy in the general case is brought into a form which facilitates its evaluation. Two results follow from this. First, it is seen that a generalized uniaxiality condition can be formulated even when the electric and the magnetic anisotropy axes do not coincide. Secondly, a theorem is established which enables one to deduce the results for double anisotropy from those for anisotropy in ? only by means of certain simple substitutions.     

Calculation of surface wave motions due to a subsurface point force: an application of elastodynamic reciprocity

The elastodynamic reciprocity theorem for two time-harmonic elastodynamic states of the same body is used to determine the surface wave motions generated by a subsurface point load of arbitrary direction in an isotropic, homogeneous, elastic half-space. The actual surface wave motions due to the point load expressed in a suitably general form represent one of the states, while the other one is an appropriately selected auxiliary solution consisting of incoming and outgoing surface waves. A direct application of the reciprocity theorem yields the desired information on the generated surface wave motion.     

永磁轨道上方高温超导块材各向异性对悬浮力弛豫特性的影响

采用顶部熔融织构生长法制备的高温超导块材YBCO通常有5个生长区域．通过捕获磁通实验研究,人们发现高温超导块材内部生长区域及边界的捕获磁通能力不同,存在明显的各向异性．面向高温超导磁悬浮应用,本文比较研究了3块不同的高温超导块材YBCO组合在永磁轨道上方悬浮力弛豫特性．实验结果表明,无论场冷还是零场冷情况,块材籽晶生长...     

Quantum thermodynamics of nonequilibrium. Onsager reciprocity and dispersion-dissipation relations

A generalized Onsager reciprocity theorem emerges as an exact consequence of the structure of the nonlinear equation of motion of quantum thermodynamics and is valid for all the dissipative nonequilibrium states, close and far from stable thermodynamic equilibrium, of an isolated system composed of a single constituent of matter with a finite-dimensional Hilbert space. In addition, a dispersion-dissipation theorem results in a precise relation between the generalized dissipative conductivity that describes the mutual interrelation between dissipative rates of a pair of observables and the codispersions of the same observables and the generators of the motion. These results are presented together with a review of quantum thermodynamic postulates and general results.     

格林互易定理在求解均匀带电圆环的静电势分布中的应用

对于静电场,由普遍的格林互易定理得出特殊情形下的格林互易定理.应用该定理推导出均匀带电圆环的数种在形式上互不相同的静电势分布解式.     

Brillouin's theorem and the Hellmann-Feynman theorem for Hartree-Fock wave functions

It is shown that there is an intimate relation between the Hellmann-Feynman theorem and Brillouin's theorem. A more general form of Brillouin's theorem is provided, which applies to excited states of arbitrary symmetry and multiplicity. This new form leads to a simple proof of the Hellmann-Feynman theorem. This theorem is valid when all the orbitals that occur in the wave function are determined by a complete, and not a partial, variational procedure. Arguing in the opposite direction it is shown that the complete satisfaction of the generalized Brillouin's theorem provides an alternative scheme for obtaining the Hartree-Fock orbitals.     

On the coupling impedance for particles with opposite velocities

As already shown by several authors, the reciprocity theorem can be rewritten as a simple formula connecting the longitudinal coupling impedances of a particle travelling in the positive and negative directions of an infinitely long vacuum chamber crossing a scattering structure (cavity, step junction, iris, etc.) of general shape. The formula is valid for any particle velocity. As an example, we consider the case of two semi-infinite circular vacuum chambers with different radii; for this case we give the explicit difference between the coupling impedances and the wake potentials. Received: 27 March 2002 / Revised version: 5 December 2002 / Published online: 26 February 2003     

两个相邻目标对平面波、高斯波束的光散射

基于等效原理和互易性定理研究了两个靠近目标对平面波、高斯波束的光散射问题,给出了这一复合光散射模型的二阶散射结果。通常一阶散射结果容易求解,但由于耦合效应的复杂性,很难给出二阶散射结果的解析形式。为了解决这一问题,应用互易性定理给出了求解任意相邻介质目标二阶散射场的公式,同时借助等效原理将求解散射场公式中的体积分简化为面积分的形式,从而降低了求解难度。求解了两相邻球形粒子的复合散射场,并将求解结果与应用时域积分方程法求得的结果进行了比较。同时,还讨论了束腰半径、目标位置对散射截面及偏振度的影响。     

Generalized Brillouin theorem and generalized forces in SCF and MC SCF theories and their Hartree-Fock limits

A formula for the change of energy is derived, valid for any infinitesimal change of the hamiltonian and the wave function in CI, SCF and MC SCF theories. A general form of MC Hartree-Fock equations is derived in a somewhat new form. A closed MC theory is defined and a condition of self-consistency is derived for this theory. The role of deorthogonalization of spin orbitals is discussed. The Hellmann-Feynman theorem and the generalized Brillouin theorem are rederived in a unique and simple way. It is shown that in the case of the closed MC SCF theory the Brillouin theorem derived by Levy and Berthier can be strengthened.

Formulae for generalized forces are derived, valid for closed-shell, openshell and multiconfigurational SCF theories also far from the Hartree-Fock limit.     

等效原理和互易性定理在两个相邻球形目标电磁散射中的应用

基于等效原理和互易性定理研究了两个相邻目标的电磁散射问题，给出了这一复合电磁散射模型的二阶散射结果. 通常平面入射波的一阶散射结果容易求解，但由于耦合效应的复杂性，很难给出二阶散射结果的解析形式. 应用互易性定理给出了求解任意相邻导体/介质目标二阶电磁散射场的公式，并利用等效原理将求解散射场公式中的体积分简化为面积分的形式，从而降低了求解难度. 同时还推导了两个目标的二次散射场之间的关系. 最后应用给出的公式，求解了两相邻球形目标的复合散射场，对双站散射结果进行了讨论，同时与应用时域积分方程法求得的结果进行了比较. 关键词： 等效原理 互易性定理 电磁散射 相邻圆球     

电磁理论中算符的一些性质

在本文中,把在不均匀各向异性介质中的麦克斯韦方程看作算符,它定义在一个有界区域,可以被理解为微波技术中的谐振腔。但在这腔中充填着铁氧体,等离子体或其他各向异性介质,这些介质在应用中日益重要。文中证明了在某些μ、ε和边界条件下,算符成为对称。而对称性和自伴性在本征函数展开中带来很多方便;此外我们推导了本征振动的正变性和互易定理。如果不满足对称性,引入伴谐振腔的概念,所谓伴谐振腔在几何形状上和原来的腔相同,但ε、μ和边界条件不一样。它和自伴谐振腔在正交性和互易定理上有某些相似之处。     

Apparent transducer non-reciprocity in an ultrasonic flow meter

This paper investigates the effects of non-identical ultrasonic transducers on reciprocity and zero-flow calibration in transit time flow meters. According to the theorem of reciprocity, there should not be any difference between the up- and downstream acoustic times of flight in a zero-flow situation. This would thus eliminate zero-flow estimation drifts. The flow meter is modeled as a one dimensional system with equivalent electrical circuits and simulated with simulation program with integrated circuits emphasis. The work shows that variations between the two transducers cause false estimates of flow and indicate which parameters have the largest influence. It indicates that reciprocity holds only for identical transducers.     

Levitation performance of the magnetized bulk high-Tc superconducting magnet with different trapped fields

To a high-T_c superconducting (HTS) maglev system which needs large levitation force density, the magnetized bulk high-T_c superconductor (HTSC) magnet is a good candidate because it can supply additional repulsive or attractive force above a permanent magnet guideway (PMG). Because the induced supercurrent within a magnetized bulk HTSC is the key parameter for the levitation performance, and it is sensitive to the magnetizing process and field, so the magnetized bulk HTSC magnets with different magnetizing processes had various levitation performances, not only the force magnitude, but also its force relaxation characteristics. Furthermore, the distribution and configuration of the induced supercurrent are also important factor to decide the levitation performance, especially the force relaxation characteristics. This article experimentally investigates the influences of different magnetizing processes and trapped fields on the levitation performance of a magnetized bulk HTSC magnet with smaller size than the magnetic inter-pole distance of PMG, and the obtained results are qualitatively analyzed by the Critical State Model. The test results and analyses of this article are useful for the suitable choice and optimal design of magnetized bulk HTSC magnets.     

A METHOD TO PREDICT ACOUSTIC RADIATION FROM AN ENCLOSED MULTICAVITY STRUCTURE

The acoustical reciprocity theorem can be used to solve the problem of vibroacoustic coupling. However, the theorem can be used only on the presupposition that the scattered sound field of the elastic surface concerned is known. This is the key point and the most difficult point for many complicated surfaces, such as a multicavity structure. A new method, covering-domain method, which transforms the calculation of scattered sound field of an arbitrary-shaped closed shell into that of a series of simply closed spherical shells, is applied in this paper to calculate the scattered sound field of a multicavity structure with elastic surfaces. So the radiated sound pressure of an elastic multicavity structure excited by an external force can be predicted by using the acoustical reciprocity theorem. It is verified to be correct by a corresponding test in this paper.