The use of the kramers-kronig relations in determining optical constants

The paper discusses some of the ways in which to avoid difficulties in applying dispersion relations to experimental data of the optical constants of solids, particularly with regard to measurements in a narrow frequency range.

---

-

.

     

The relations between the decay constants of pseudoscalar mesons and the residues of the pomeron

The relations between the decay constants of pseudoscalar mesons and the residues of the pomeron are given. Based on these relations, it is shown that the relative scale between the couplings of the zero-mass Nambu-Goldstone bosons to the pomeron is determined by the spontaneous chiral symmetry breaking of the vacuum.     

Equivalent circuit with complex physical constants and equivalent-parameters-expressed dissipation factors of piezoelectric materials

The equivalent circuit with complex physical constants for a piezoelectric ceramic in thickness mode is established. In the equivalent circuit, electric components (equivalent circuit parameters) are connected to real and imaginary parts of complex physical coefficients of piezoelectric materials. Based on definitions of dissipation factors, three of them (dielectric, elastic and piezoelectric dissipation factors) are represented by equivalent circuit parameters. Since the equivalent circuit parameters are detectable, the dissipation factors can be easily obtained. In the experiments, the temperature and the stress responses of the three dissipation factors are measured.     

The thermodynamical approach to the back reaction problem

A new approach to the back reaction of Hawking radiation on a Schwarzschild black hole (SBH), based on thermodynamics, is proposed, in which the thermodynamical system composed of SBH and thermal radiation in curved space is treated as a thermodynamical system composed of SBH, thermal radiation and a two-dimensional thermodynamical membrane (i.e. event horizon) in flat space.     

The thermodynamical history of the universe

A predestrian walk is offered in the early universe. It is argued that the universe has departed from its original thermal equilibrium as a consequence of its mechanical instability. This transient deviation from the state of maximum entropy has made the creation of protons and galaxies possible. It is shown that several puzzling astrophysical phenomena can be explained by assuming a nonvanishing rest mass for the heaviest stable neutrino in the region of 30 eV.     

Lagrangian effective material constants for the modeling of thermal behavior of acoustic waves in piezoelectric crystals. I. Theory.

After some necessary recalls on the nonlinear theory of thermoelectroelasticity in piezoelectric crystals, asserting the need of constitutive equations which derive from a rotationally invariant energy function, this paper presents the governing equations for a small vibration superimposed on a bias originated by a slow and homogeneous temperature variation from a well-defined reference state. Thereafter, the authors define the effective coefficients appearing in the linearized incremental dynamic balance equations for linear momentum and electrical charge in Lagrange configuration, not omitting associated boundary conditions. The main features of these coefficients are discussed and explicit relations with more conventionally defined coefficients are given. Determination of numerical values of the proposed effective coefficients and examples of their use in the higher order modeling of static frequency-temperature characteristics of either bulk acoustic wave or surface acoustic wave devices are given in a companion paper.     

A FEM-based method to determine the complex material properties of piezoelectric disks

Numerical simulations allow modeling piezoelectric devices and ultrasonic transducers. However, the accuracy in the results is limited by the precise knowledge of the elastic, dielectric and piezoelectric properties of the piezoelectric material. To introduce the energy losses, these properties can be represented by complex numbers, where the real part of the model essentially determines the resonance frequencies and the imaginary part determines the amplitude of each resonant mode. In this work, a method based on the Finite Element Method (FEM) is modified to obtain the imaginary material properties of piezoelectric disks. The material properties are determined from the electrical impedance curve of the disk, which is measured by an impedance analyzer. The method consists in obtaining the material properties that minimize the error between experimental and numerical impedance curves over a wide range of frequencies. The proposed methodology starts with a sensitivity analysis of each parameter, determining the influence of each parameter over a set of resonant modes. Sensitivity results are used to implement a preliminary algorithm approaching the solution in order to avoid the search to be trapped into a local minimum. The method is applied to determine the material properties of a Pz27 disk sample from Ferroperm. The obtained properties are used to calculate the electrical impedance curve of the disk with a Finite Element algorithm, which is compared with the experimental electrical impedance curve. Additionally, the results were validated by comparing the numerical displacement profile with the displacements measured by a laser Doppler vibrometer. The comparison between the numerical and experimental results shows excellent agreement for both electrical impedance curve and for the displacement profile over the disk surface. The agreement between numerical and experimental displacement profiles shows that, although only the electrical impedance curve is considered in the adjustment procedure, the obtained material properties allow simulating the displacement amplitude accurately.     

双变量厄米多项式递推关系与积分公式的简捷推导

基于正规乘积和反正规乘积性质与双变量厄米多项式的母函数形式,利用相干态表象完备性的高斯积分形式,系统而全面的导出双变量厄米多项式的算符恒等式、递推关系与积分公式,此推导方法简捷明了.     

Singular variation property of elastic constants of piezoelectric ceramics shunted to negative capacitance

Piezoelectric shunt damping has been widely used in vibration suppression, sound absorption, noise elimination, etc.In such applications, the variant elastic constants of piezoelectric materials are the essential parameters that determine the performances of the systems, when piezoelectric materials are shunted to normal electrical elements, i.e., resistance,inductance and capacitance, as well as their combinations. In recent years, many researches have demonstrated that the wideband sound absorption or vibration suppression can be realized with piezoelectric materials shunted to negative capacitance. However, most systems using the negative-capacitance shunt circuits show their instabilities in the optimal condition, which are essentially caused by the singular variation properties of elastic constants of piezoelectric materials when shunted to negative capacitance. This paper aims at investigating the effects of negative-capacitance shunt circuits on elastic constants of a piezoelectric ceramic plate through theoretical analyses and experiments, which gives an rational explanation for why negative capacitance shunt circuit is prone to make structure instable. First, the relationships between the elastic constants c_(11), c_(33), c_(55) of the piezoelectric ceramic and the shunt negative capacitance are derived with the piezoelectric constitutive law theoretically. Then, an experimental setup is established to verify the theoretical results through observing the change of elastic constant c_(55) of the shunted piezoelectric plate with the variation of negative capacitance.The experimental results are in good agreement with the theoretical analyses, which reveals that the instability of the shunt damping system is essentially caused by the singular variation property of the elastic constants of piezoelectric material shunted to negative capacitance.     

The temperature dependence of piezoelectric constants eiμ of μ-quartz

Measurements of the temperature dependence of e₁₁ and e₁₄ of α-quartz relative to room temperature based on thichkness mode resonances and antiresonances show that e₁₄ changes its sign at ≈360°C. Fair agreement of e₁₁ with values reported in earlier work was found.     

Connection between the thermodynamical and the percolation models of nuclear fragmentation

The connection is investigated between the percolation approach to nuclear fragmentation and the statistical multifragmentation model based on thermodynamical equilibrium concepts. The relation between the percolation parameter and the average excitation energy per nucleon of the fragmentating system has been investigated.     

用多目标遗传算法获取压电材料参数

多目标遗传算法是在遗传算法的基础上,利用在多个给定区域内的遗传优化性能,反演出这些特定区域内的优化特性。本文基于瑞利波的有效介电常数理论,将压电材料的弹性常数CE、压电常数e、介电常数εs看作特定区域的待优化参数,利用压电材料(本文用石英、铌酸锂晶体为例)的同一切割面不同传播方向的表面波速度,运用多目标遗传算法,通过概率分区优化,逐次逼近真值,成功地同时反演出了它们的弹性常数、压电常数与介电常数。证明了该方法同样适用于获取新材料的参数。     

Anisotropic contribution of magnetostriction to the elastic compliance constants in hexagonal materials: The Δs-effect

In this paper, we consider the single crystal analogue of the ΔE-effect in hexagonal materials with uniaxial magnetic anisotropy. We define Δs_ijld as the fractional change in the elastic compliance tensor s_ijkl in the demagnetized state relative to its value in the saturated state. The Δs-effect depends in general on the direction of the applied stress and the resulting magnetostrictive strain. We can show, however, that Δs_ijkl is always nonnegative when i=k and j=l. We then consider the measurements of the elastic constants in magnetic materials which have large magnetocrystalline anisotropy. The stresses applied in these measurements are not sufficient to rotate the magnetization away from the magnetically preferred direction, and hence cause no magnetostriction, and no Δs-effect. Therefore, it is not necessary to apply a saturating magnetic field along the easy axis in order to measure the true elastic constants in these materials.     

The structure of Heesch groups and its relation to material property tensors

The magnetic crystal point groups (Heesch groups) are classified according to their structure with respect to the three inversion operations: space, time, and total inversion. Accordingly the tensors are classified by the irreducible representations of the full inversion group. The groups and tensors are considered under the action of the elements A_i of the group of automorphisms of the full inversion group. The following correspondence theorem is proved: The matrix form of the tensor representation T of the group G coincides with the matrix form of the representation A_iT of the group A_iG. The theorem gives a clear explanation of the so-called “magic numbers” and provides a suitable short cut for the calculation and tabulation of material property tensors.     

Orientational contribution to the piezoelectric constants of BaTiO3 ceramic in ferroelectric phases with various symmetries

A self-consistent method based on the interaction of a piezoelectric sphere with a piezoelectric medium that has anisotropic elastic and dielectric properties is used to calculate the components of the tensor piezoelectric modulus of BaTiO₃ ceramic in all three ferroelectric modifications. A comparison of the calculated and measured piezoelectric moduli shows that at least 60–70% of the piezoelectric effect in BaTiO₃ ceramic is caused by domain boundary movement throughout the entire ferroelectric region. Fiz. Tverd. Tela (St. Petersburg) 41, 1080–1083 (June 1999)     

Investigation of the piezoelectric constants of polycrystalline ferroelectrics of the barium titanate type

A study has been made of the piezoelectric constants of polycrystalline ferroelectrics of the barium titanate type and of their dependence on temperature of sintering of the ceramic and on the constant voltage applied. The measurements were made under static and dynamic conditions. It is shown that the piezomoduli of certain solid solutions in the systems Ba(Ti, Zr, Sn)O₃ and Ba(Ti, Si, Sn)O₃ are somewhat greater than those of barium titanate.     

The origin dependence of the material constants: the permittivity and the inverse permeability

New derivations of origin-independent expressions for the electric permittivity are presented, starting either from the response function of the current density that defines the absorption coefficient, or from the off-resonance single-photon scattering amplitude that leads to the Kramers–Heisenberg dispersion formula. The resulting expression for the permittivity is compared with earlier work on the origin dependence of the material constants. Different origin-independent expressions for the permittivity, the inverse permeability and the magnetisability are calculated and discussed. By considering electromagnetic plane waves in the absence of external sources, the macroscopic Maxwell equations are used to describe the response of matter to external fields. In combination with the constitutive relations, a wave equation expressed in terms of the material constants is derived. It is shown that the different definitions of the material constants lead to the same wave equation. The non-uniqueness of the definitions of the material constants is discussed in this context. Finally, based on the discussions, we propose a possible unique, origin-independent definition of the material constants.     

Elastic constants of noble-gas crystals under pressure and the cauchy relations

Physics of the Solid State - The equations of state are solved and the elastic constants responsible for the propagation of sound in strongly compressed crystals of noble gases are calculated in...