Casimir Interaction between a plate and a cylinder

We find the exact Casimir force between a plate and a cylinder, a geometry intermediate between parallel plates, where the force is known exactly, and the plate sphere, where it is known at large separations. The force has an unexpectedly weak decay approximately L/[H3 ln(H/R)] at large plate-cylinder separations H (L and R are the cylinder length and radius), due to transverse magnetic modes. Path integral quantization with a partial wave expansion additionally gives a qualitative difference for the density of states of electric and magnetic modes, and corrections at finite temperatures.     

An atomistic approach to the dielectric modes of BaTiO3 and SrTiO3

Recently, a clear long-sought Debye mode (D) in barium titanate (BT) was identified [J. Hlinka, T. Ostapchuk, D. Nuzhnyy, J. Petzelt, P. Kuzel, C. Kadlec, P. Vanek, I. Ponomareva, L. Bellaiche, Phys. Rev. Lett. 101 (2008) 167402] and this mode was shown to originate from the polar coordinate that also generates the so-called Slater mode (S). The inter-relations between the D mode and the normal A1-type phonon modes were studied by those authors using a four-mode phenomenological model. The present work is to offer an atomistic support of their work and to better illustrate the nature of and the couplings between these modes. In addition, we extend the as-obtained insights to the investigation of the nature of the low frequency Raman peaks that were found in ¹⁸O-substituted strontium titanate (ST) many years ago [M. Itoh, R. Wang, Y. Inaguma, T. Yamaguchi, Y.-J. Shan, T. Nakamura, Phys. Rev. Lett. 82 (1999) 3540]. Thus, our work provides important information on the connections between the lattice dynamics of BT and ST.     

Maxima and minima of the displacement components for the Lamb modes

This paper revisits the vanishing of the transverse component of the particle displacement vector in free surfaces of an isotropic homogeneous plate, for both symmetric and antisymmetric Lamb waves. Drawing on well-known analytical expressions from Viktorov's book [(1967) Rayleigh and Lamb Waves: Physical Theory Applications, Chap. II, pp. 67-121], two distinct frequency-thickness product expressions, in cases where this vanishing occurs, are derived: one for the symmetric modes and another for the antisymmetric modes. At these frequency-thickness products, phase and group velocities have appreciable values which are discussed herein. It appears that these velocities depend on the transverse bulk wave velocity only. This is the specific condition of the Lame? modes. Moreover, theoretical and experimental investigations of displacements in the surface of a plate in air have been carried out. The theoretical part shows that the normal and transverse displacements have, respectively, a local maximum and a local minimum in the vicinity of these frequency-thickness products. The experimental part corroborates the presence of the local maximum of the S(0) Lamb mode for various materials.     

Comparison between the dispersion curves calculated in complex frequency and the minima of the reflection coefficients for an embedded layer

Analytical solutions of Lamb functions for symmetric and antisymmetric elastodynamic modes propagating within a solid layer embedded in an infinite medium are presented. Alternative theoretical analyses of such modes are performed, first in terms of the usual approach of harmonic heterogeneous plane waves (real frequency and complex slowness) and then in terms of transient homogeneous plane waves (complex frequency and real slowness). An example structure of a 0.1-mm-thick "alpha case" (an oxygen-rich phase of titanium that is relatively stiff) plate embedded in titanium is used for the study. A large difference between the usual dispersion curves calculated in real frequency and complex slowness and those calculated in complex frequency and real slowness is shown. Thus the choice between a spatial and a temporal parameter to describe the imaginary part of the guided waves is shown to be significant. The minima and the zeros of the longitudinal and shear plane-wave reflection coefficients are calculated and are compared with the dispersion curves. It is found that they do not match with the dispersion curves for complex slowness, but they do agree quite well with the dispersion curves for complex frequency. This implies that the complex frequency approach is better suited for the comparison of the modal properties with near-field reflection measurements.     

High frequency waves in liquid metals

The inelastic scattering of long wavelength neutrons from coherently scattering metals has been used to examine the collective motions of atoms in the liquid state and to make comparisons with the polycrystalline solids. Well-defined peaks in the velocity spectra of the scattered neutrons have been found in both states for lead, rubidium, tin, bismuth and aluminium. These have been used to present parts of the dispersion curves for vibrational modes of motion in the frequency range 1 to 20 × 10¹² rad/sec and wave number range 1 to 3 Å^?1, and to estimate lifetimes of the modes of the order 0.4 × 10^?12 sec in the solid near the melting point and roughly half these values in the liquid.

In polycrystalline aluminium the major contribution to the observed intensity in the solid is due to transverse modes and the observed similarity of the liquid and solid spectra suggests that transverse motions are observed in the liquid also.     

On the “overlapping resonances” concept of acoustic transmission through an elastic plate,I: An examination of properties

The Fiorito, Madigosky and Überall approximate representation [1] of the acoustic transmission coefficient of an infinite, isotropic, elastic plate by resonances associated with Lamb modes is examined and clarification of its properties is obtained. Some theoretical extension is provided which validates coherent addition of these overlapping resonances. Minor limitations shown are that the theory is inapplicable near grazing incidence and that it gives only a partial solution at incidence beyond the second critical angle when the frequency thickness product is the variable. Existing overlapping resonances theory is shown not to yield a unique relationship between the incident wave and a set of physical motions within the plate, and an approach to overcome this non-uniqueness is suggested. An equivalence is demonstrated between the 3 dB resonance half-width of each Lamb mode and the imaginary part of the modal wavenumber per unit wavenumber of the fluid, and this facilitates the numerical checking of the theory which is carried out in a companion paper [2] and yields convincing proof of the applicability of the approach.     

Generalized thermoelastic extensional and flexural wave motions in homogenous isotropic plate by using asymptotic method

In this paper the asymptotic method has been applied to investigate propagation of generalized thermoelastic waves in an infinite homogenous isotropic plate. The governing equations for the extensional, transversal and flexural motions are derived from the system of three-dimensional dynamical equations of linear theories of generalized thermoelasticity. The asymptotic operator plate model for extensional and flexural free vibrations in a homogenous thermoelastic plate leads to sixth and fifth degree polynomial secular equations, respectively. These secular equations govern frequency and phase velocity of various possible modes of wave propagation at all wavelengths. The velocity dispersion equations for extensional and flexural wave motion are deduced from the three-dimensional analog of Rayleigh-Lamb frequency equation for thermoelastic plate. The approximation for long and short waves along with expression for group velocity has also been obtained. The Rayleigh-Lamb frequency equations for the considered plate are expanded in power series in order to obtain polynomial frequency and velocity dispersion relations and its equivalence established with that of asymptotic method. The numeric values for phase velocity, group velocity and attenuation coefficients has also been obtained using MATHCAD software and are shown graphically for extensional and flexural waves in generalized theories of thermoelastic plate for solid helium material.     

平头弹丸正撞击下延性金属靶板的破坏模式

 对延性金属靶板在刚性平头弹丸正撞击下的破坏模式进行了研究。一般而言,延性金属靶板的破坏模式可以分为两种：带有总体变形的局部简单剪切破坏和局部化的绝热剪切冲塞破坏。首先基于Bai-Johnson热塑性本构关系建立了一个局部化的绝热剪切冲塞模型,然后结合描述带有总体变形的局部简单剪切破坏的Wen-Jones模型,找出了两种模型之间转化的临界条件。理论预测与文献中的实验结果吻合得很好。     

Energy trapping in high-frequency vibrations of piezoelectric plates with partial mass layers under lateral electric field excitation

We study coupled face-shear (FS) and thickness-twist (TT) motions of a piezoelectric plate of monoclinic crystals with mass layers on the central parts of the plate surfaces. The plate is driven by a lateral electric field. Mindlin’s first-order theory of piezoelectric plates is used. An analytical solution is obtained. Numerical results are presented for an AT-cut quartz plate, including the motional capacitance of the plate as a resonator and the vibration modes trapped under the mass layers in the central portion of the plate. The relationship between the dimension of the mass layers and the number of trapped modes is examined.     

Magnetic resonance investigations of phase transitions and modulation wave motions in incommensurate solids

We measured⁸⁷Rb nuclear magnetic resonance (NMR) and³⁵Cl nuclear quadrupole resonance (NQR) Hahn spin-echo magnetization decays in the incommensurate (I) phase of Rb₂ZnCl₄ and, in each case, obtained a Hahn echo decay that was shorter than the Carr-Purcell-Meiboom-Gill decay and one which decayed with a time constant proportional to the cube of the echo time. From these measurements we obtained from both the⁸⁷Rb NMR and³⁵Cl NQR measurements values for the diffusion coefficients that are comparable in magnitude, a fact that strongly supports the existence of slow modulation wave diffusionlike motions in the I phase, since such motions should affect both Rb and Cl ions similarly. In addition, we used⁸⁷Rb two-dimensional exchange-difference NMR to study atomic motions in the incommensurate (I) and paraelectric (P) phases to elucidate the nature of the I-P transition. We measured as a function of the mixing time the frequency shifts of the cross peaks from the main diagonal and observed a gradual increase towards an asymptotic value in the I phase but a sudden jump to the final value in the P phase. We interpreted the motions observed in the P phase as normal modes arising from simultaneous reorientations of ZnCl₄ tetrahedra and corresponding Rb ions displacements between two sites. These normal modes freeze out in the I phase and change to the diffusionlike motion of the modulation wave. We also performed³⁵Cl NQR lineshape andT ₁ measurements in K₂ZnCl₄ and obtained conclusive evidence for the presence of a narrow 1q (singly modulated) I phase between 146 and 149 K.     

Experimental Investigation of Opposing Mixed Convection in a Channel with an open Cavity Below

Abstract

In this article, mixed convection in an open cavity with a heated wall bounded by a horizontal unheated plate is investigated experimentally. The heated wall is on the opposite side of the forced inflow. The results are reported in terms of wall temperature profiles of the heated wall and flow visualization. The range of pertinent parameters used in this experiment are Reynolds numbers (Re) from 100 to 2,000 and Richardson numbers (Ri) from 4.3 to 6,400. Also, the ratio between the length and the height of cavity (L/D) ranges from 0.5–2.0, and the ratio between the channel and cavity height (H/D) is equal to 1.0. The lack of experimental results on mixed convection in a channel with an open cavity below was an impetus for investigating this configuration when one cavity vertical wall is heated at uniform heat flux. The present results show that at the lowest investigated Reynolds number, the surface temperatures are lower than the corresponding surface temperatures for Re = 2,000 at the same ohmic heat flux. The flow visualization shows that for Re = 1,000, there are two nearly distinct fluid motions: a parallel forced flow in the channel and a recirculation flow inside the cavity. For Re = 100, the effect of a stronger buoyancy determines a penetration of thermal plumes from the heated plate wall into the upper channel. Moreover, the flow visualization shows that for lower Reynolds numbers, the forced motion penetrates inside the cavity, and a vortex structure is adjacent to the unheated vertical plate. At higher Reynolds numbers, the vortex structure has a larger extension while L/D is held constant.     

Guided wave modes in porous cylinders: Theory

The classical theory of wave propagation in elastic cylinders is extended to poro-elastic mandrel modes. The classical theory predicts the existence of undamped L modes and damped C, I, and Z modes. These waves also appear in poro-elastic mandrels, but all of them become damped because of viscous effects. The presence of the Biot slow bulk wave in the poro-elastic material is responsible for the generation of additional mandrel modes. One of them was already discussed by Feng and Johnson, and the others can be grouped together as so-called D modes. The damping of these D modes is at least as high as the damping of the free-field slow wave.     

Absorption Lineshapes in Two-Dimensional Electron Spin Resonance and the Effects of Slow Motions in Complex Fluids

A methodology for obtaining pure absorption two-dimensional electron spin resonance spectra is presented for the case of large inhomogeneous broadening and/or slow motions. For slow motions, the spectra consist of “complex Lorentzians” superimposed with complex weighting factors, presenting a challenge to obtaining absorption spectra. It is shown how absorption-type spectra can be recovered for the two-pulse COSY and SECSY experiments in such cases. For three-pulse 2D ELDOR experiments, absorption lineshapes can be obtained for the autopeaks, whereas the cross peaks would be of mixed-mode character, in general. However, for practical cases the dispersive components in the cross peaks will be relatively small. Theoretical and experimental absorption spectra are provided to illustrate the method and to show the improved resolution obtained from absorption lineshapes. In particular, the variation in linewidths across a SECSY spectrum, which is a key component in elucidating motional dynamics, is clearly rendered in the pure absorption mode. A convenient method for introducing the necessary phase corrections for the slow-motional spectra is also provided.     

Characterization of the crystallization behaviors in the PbTiO3 thin films on Si substrates by an infrared spectroscopy technique

PbTiO₃ thin films on silicon substrates derived from a modified sol–gel technique are characterized by IR reflectance spectroscopy for the first time. Seven infrared (IR) reflectance peaks modes have been observed in the crystallized perovskite PbTiO₃ thin films and are assigned to the corresponding phonon modes. Comparisons between the IR reflectance spectra of PbTiO₃ thin films obtained by different annealing processes, i.e., rapid thermal annealing (RTA) and conventional thermal annealing (CTA), have also been carried out. It is observed that the frequencies of most peaks in the RTA-derived PbTiO₃ films are lower than that in the CTA-derived films.     

物质纯重力场部分的能量-动量张量研究

认为物质的质量(能量)存在形式可分为两部分，一部分是以纯物质形式存在的，另一部分是以纯重力场形式存在的.物质质量(能量)这两种形式各自对应着相应的能量 动量张量，物质总的能量-动量张量可表示为Tμν=T(Ⅰ)μν+T(Ⅱ)μν,这里，T(Ⅰ)μν，T（Ⅱ）μν分别代表物质纯物质部分和纯重力场部分的能量-动量张量.通过类比电磁理论，定义：ωμ≡-c2gμ0/g00,并引入一个反对称张量Dμν=ωμ/xν-ων/xμ，则物质纯重力场部分的能量-动量张量为T(Ⅱ)μν=(DμρDρν-gμνDαβDαβ/4 关键词： 能量-动量张量 纯重力场 重力场方程 标量重力势 矢量重力势     

PTS单晶的介电性质

测量了一维聚合物PTS单晶从77K到273K沿分子链方向的介电性质。由介电常数的反常观察到在195K发生二级相变,从高温的非极性态转变为低温的极性态。发现介电损耗在150K和100K有两个峰。用侧链分子的三种运动方式解释了上述结果。 关键词：     

Study of second-harmonic generation of shear horizontal modes using modal analysis

In this work a modal analysis was employed to study generation of the second harmonics of shear horizontal (SH) modes in a solid plate. Under second order perturbation, second-harmonic generation will occur accompanying SH mode propagation due to the bulk elastic non-linearity of plate material. In solid plate the total second-harmonic fields of a SH mode propagation are regarded as sum of the fields of a series of double frequency Lamb modes (DFLMs). The contribution of each DFLM component to the total second-harmonic fields is dependent of the difference of phase velocities of the corresponding DFLM and SH mode. The analysis results show that the DFLM field component may have cumulative growth effect once its phase velocity exactly or approximately equals that of a SH mode. It is also found that the fields of the total second harmonics of a SH mode are only symmetrical. The examples of field distributions of several DFLMs on the plate surface are considered.     

Flexural and transversal wave motion in homogeneous isotropic thermoelastic plates by using asymptotic method

The present investigation is concerned with the flexural and transversal wave motion in an infinite, transversely isotropic, thermoelastic plate by asymptotic method. The governing equations for the flexural and transversal motions have been derived from the system of three-dimensional dynamical equations of linear theory of coupled thermoelasticity. The asymptotic operator plate model for free vibrations; both flexural and transversal, in a homogenous thermoelastic plate leads to fifth degree and cubic polynomial secular equations, respectively, that governs frequency and phase velocity of various possible modes of wave propagation at all wavelengths. All the coefficients of differential operator have been expressed as explicit functions of the material parameters. The velocity dispersion equations for the flexural and transversal wave motion have been deduced from the three-dimensional analog of Rayleigh-Lamb frequency equation for thermoelastic plate waves. The approximations for long and short waves and expression for group velocity have also been derived. The thermoelastic Rayleigh-Lamb frequency equations for the considered plate are expanded in power series in order to obtain polynomial frequency and velocity dispersion relations whose equivalence is established with that of asymptotic method. The dispersion curves for phase velocity, group velocity and attenuation coefficient of various flexural and transversal wave modes are shown graphically for aluminum-epoxy material elastic and thermoelastic plates.     

Pressure-induced transformations and optical properties of the two-dimensional tetragonal polymer of C60 at pressures up to 30 GPa

The Raman spectra of the two-dimensional tetragonal (2D(T)) polymeric phase of C₆₀ have been studied in situ at pressures up to 30 GPa and room temperature. The pressure dependence of the phonon modes shows an irreversible transformation of the material near 20 GPa into a new phase, most probably associated with the covalent bonding between the 2D polymeric sheets. The Raman spectrum of the high-pressure phase is intense and well resolved, and the majority of modes are related to the fullerene molecular cage. The sample recovered at ambient conditions is in a metastable phase and transforms violently under laser irradiation: the transformed material contains mainly dimers and monomers of C₆₀ and small inclusions of the diamond-like carbon phase. The photoluminescence spectra of the 2D(T) polymer of C₆₀ were measured at room temperature and pressure up to 4 GPa. The intensity distribution and the pressure-induced shift of the photoluminescence spectrum drastically differ from those of the C₆₀ monomer. The deformation potential and the Grüneisen parameters of the 2D(T) polymeric phase of C₆₀ have been determined and compared with those of the pristine material.