scholarly journals The C-eigenvalue of third order tensors and its application in crystals

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Yannan Chen ◽  
Antal Jákli ◽  
Liqun Qi
Keyword(s):  
Piezoelectric Effect ◽  
Displacement Vector ◽  
Electric Displacement ◽  
Strain Tensor ◽  
Uniaxial Stress ◽  
Field Vector ◽  
Third Order ◽  
Rank One ◽  
Piezoelectric Coupling ◽  
Converse Piezoelectric Effect

<p style='text-indent:20px;'>In crystallography, piezoelectric tensors of various crystals play a crucial role in piezoelectric effect and converse piezoelectric effect. Generally, a third order real tensor is called a piezoelectric-type tensor if it is partially symmetric with respect to its last two indices. The piezoelectric tensor is a piezoelectric-type tensor of dimension three. We introduce C-eigenvalues and C-eigenvectors for piezoelectric-type tensors. Here, "C'' names after Curie brothers, who first discovered the piezoelectric effect. We show that C-eigenvalues always exist, they are invariant under orthogonal transformations, and for a piezoelectric-type tensor, the largest C-eigenvalue and its C-eigenvectors form the best rank-one piezoelectric-type approximation of that tensor. This means that for the piezoelectric tensor, its largest C-eigenvalue determines the highest piezoelectric coupling constant. We further show that for the piezoelectric tensor, the largest C-eigenvalue corresponds to the electric displacement vector with the largest 2-norm in the piezoelectric effect under unit uniaxial stress, and the strain tensor with the largest 2-norm in the converse piezoelectric effect under unit electric field vector. Thus, C-eigenvalues and C-eigenvectors have concrete physical meanings in piezoelectric effect and converse piezoelectric effect. Finally, by numerical experiments, we report C-eigenvalues and associated C-eigenvectors for piezoelectric tensors corresponding to several piezoelectric crystals.</p>

scholarly journals QED Response of the Vacuum

Physics ◽  
2020 ◽  
Vol 2 (1) ◽  
pp. 14-21 ◽  
Author(s):  
Gerd Leuchs ◽  
Margaret Hawton ◽  
Luis L. Sánchez-Soto
Keyword(s):  
Electromagnetic Field ◽  
Quantum Electrodynamics ◽  
Displacement Vector ◽  
Electric Displacement ◽  
Structure Constant ◽  
Universal Constant ◽  
Field Vector ◽  
Fine Structure Constant ◽  
Source Current ◽  
New Perspective

We present a new perspective on the link between quantum electrodynamics (QED) and Maxwell’s equations. We demonstrate that the interpretation of the electric displacement vector D = ε 0 E , where E is the electric field vector and ε 0 is the permittivity of the vacuum, as vacuum polarization is consistent with QED. A free electromagnetic field polarizes the vacuum, but the polarization and magnetization currents cancel giving zero source current. The speed of light is a universal constant, while the fine structure constant, which couples the electromagnetic field to matter runs, as it should.

3-D simulation of GPR surveys over pipes in dispersive soils

Geophysics ◽  
2000 ◽  
Vol 65 (5) ◽  
pp. 1560-1568 ◽  
Author(s):  
Tsili Wang ◽  
Michael L. Oristaglio
Keyword(s):  
Electrical Properties ◽  
Time Domain ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Displacement Vector ◽  
Electric Displacement ◽  
Field Vector ◽  
Dispersive Media ◽  
Dispersive Soils ◽  
Dispersive Soil

The finite‐difference time‐domain method is adapted to simulate radar surveys of objects buried in dispersive soils whose complex permittivity depends on frequency. The method treats dispersion through the constitutive relation between the electric field vector and the electric displacement vector, which is a convolution in the time domain. This convolution is updated recursively, along with Maxwell’s equations, after approximating the dispersion with a Debye (exponential) relaxation model. A novel feature of our work is the inclusion of dispersion in the perfectly‐matched layer formulation of Maxwell’s equations, which gives an absorbing boundary condition for dispersive media. We simulate 200-MHz ground‐penetrating radar surveys over metallic and plastic pipes buried at a depth of 2 m in soils whose electrical properties model are those of clay loams of different moisture contents. Radar reflections modeled for pipes in dispersive soil differ from those for pipes in soils whose electrical properties are constant (at the values of dispersive soil at the central frequency of the radar pulse). Because the permittivity decreases at higher frequencies in the soils modeled, energy in the reflections shifts toward the front of the waveform, and the amplitudes of trailing lobes in the waveform are suppressed. The effects are subtle, but become more pronounced in models of soils with 10% moisture content by weight.

Structural dynamics of PZT thin films at the nanoscale

2005 ◽  
Vol 902 ◽  
Author(s):  
Alexei Grigoriev ◽  
Dal-Hyun Do ◽  
Dong Min Kim ◽  
Chang-Beom Eom ◽  
Bernhard Adams ◽  
...  
Keyword(s):  
Crystal Lattice ◽  
Lattice Distortion ◽  
Piezoelectric Effect ◽  
Polarization Switching ◽  
X Rays ◽  
Time Resolved ◽  
X Ray ◽  
Converse Piezoelectric Effect ◽  
Ferroelectric Capacitors ◽  
Crystal Lattice Distortion

AbstractWhen an electric field is applied to a ferroelectric the crystal lattice spacing changes as a result of the converse piezoelectric effect. Although the piezoelectric effect and polarization switching have been investigated for decades there has been no direct nanosecond-scale visualization of these phenomena in solid crystalline ferroelectrics. Synchrotron x-rays allow the polarization switching and the crystal lattice distortion to be visualized in space and time on scales of hundreds of nanometers and hundreds of picoseconds using ultrafast x-ray microdiffraction. Here we report the polarization switching visualization and polarization domain wall velocities for Pb(Zr0.45Ti0.55)O3 thin film ferroelectric capacitors studied by time-resolved x-ray microdiffraction.

The Displacement Characteristics of Piezoelectric Ceramic Micro Actuators Evaluated by Laser Interferometer

2015 ◽  
Vol 645-646 ◽  
pp. 920-925 ◽  
Author(s):  
Hong Wu ◽  
Long Biao He ◽  
Jing Lin Zhou ◽  
Ping Yang
Keyword(s):  
Piezoelectric Ceramic ◽  
Piezoelectric Coefficient ◽  
Laser Interferometer ◽  
Piezoelectric Effect ◽  
Influence Factors ◽  
Energy Transformation ◽  
Measurement Results ◽  
Loading Sequence ◽  
Converse Piezoelectric Effect ◽  
Key Parameter

Understanding and measuring the displacement characteristics of piezoelectric ceramic with electric field exciting are particularly important. The piezoelectric coefficient d33 as the indication of its displacement characteristics, is the key parameter of its energy transformation. In this paper, the characteristics of two kinds of piezoelectric ceramics, PZT4 and PZT5 were studied by the laser interferometer measurement. The influence factors of d33 were studied, including the frequency and amplitude of the exciting signal, the ways of holding, and the loading sequence. Then the measurement results of piezoelectric ceramic with laser interferometer and the quasi-static method were compared, the results showed they had consistence and the analysis of the piezoelectric coefficient d33 measurement by converse piezoelectric effect and by piezoelectric effect was discussed.

Features of determining the deformed state of a particle material during hot stamping of porous moldings

2021 ◽  
pp. 21-30
Author(s):  
B. G. Gasanov ◽  
A. A. Aganov ◽  
P. V. Sirotin
Keyword(s):  
Displacement Vector ◽  
Hot Stamping ◽  
Strain Tensor ◽  
Particle Material ◽  
Software Algorithms ◽  
Deformed State ◽  
Metal Strain ◽  
Scalar Products ◽  
Analytical Expressions ◽  
Kinetics Of

The paper describes main methods for assessing the deformed state of porous body metal frames developed by different authors based on the analysis of yield conditions and governing equations, using the principle of equivalent strains and stresses, and studying the kinetics of metal strain during pressing. Formulas were derived to determine the components of the powder particle material strain tensor through dyads, as scalar products of the basis vectors of the convected coordinate system at each moment of porous molding strain. The expediency of using the analytical expressions developed to determine the deformed state of the particle material was experimentally substantiated subject to the known displacement vector parameters of representative elements (macrostrains) of porous billets. The applications of well-known analytical expressions were established, and the proposed formulas proved applicable for the deformed state assessment of particle metal during the pressure processing of powder products of different configurations and designing billets with a defined porosity and geometric parameters as a basis for compiling software algorithms for the computer simulation of porous molding hot stamping.

Kinetic theory of surface wave propagation along a hot plasma column

1976 ◽  
Vol 16 (1) ◽  
pp. 47-55 ◽  
Author(s):  
V. Atanassov ◽  
I. Zhelyazkov ◽  
A. Shivarova ◽  
Zh. Genchev
Keyword(s):  
Dispersion Relation ◽  
Plasma Column ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Displacement Vector ◽  
Electric Displacement ◽  
Wave Dispersion ◽  
Axially Symmetric ◽  
Surface Wave Propagation ◽  
Hot Plasma

In this paper we propose an exact solution of Vlasov and Maxwell's equations for a bounded hot plasma in order to derive the dispersion relation of the axially-symmetric surface waves propagating along a plasma column. Assuming specular reflexion of plasma particles from the boundary, expressions for the components of the electric displacement vector are obtained on the basis of the Vlasov equation. Their substitution in Maxwell's equations, neglecting the spatial dispersion in the transverse plasma dielectric function, allows us to determine the plasma impedance. The equating of plasma and dielectric impedances gives the wave dispersion relation which, in different limiting cases, coincides with the well-known results.

Analysis and Research of Piezoelectric Dynamic Weighing Sensor

2011 ◽  
Vol 483 ◽  
pp. 643-646 ◽  
Author(s):  
Li Bo Zhao ◽  
Jian Qiang Liang ◽  
Yu Long Zhao ◽  
Jian Zhu Wang ◽  
Wei Chen ◽  
...  
Keyword(s):  
Wall Thickness ◽  
Quartz Crystal ◽  
Piezoelectric Effect ◽  
Fem Simulation ◽  
Ansys Software ◽  
Critical Dimensions ◽  
Load Carrying ◽  
Piezoelectric Coupling ◽  
Influence Curve ◽  
Dynamic Weighing

The Kistler company has invented piezoelectric dynamic weighing sensors which are applied to determine dynamically axle load, speed and gross weight of the vehicle based on piezoelectric effect of quartz crystal. They mainly consist of load-carrying beams and sensitive elements. Focusing on the control of preload in design and fabrication, finite element method (FEM) is applied with ANSYS software to optimize structural sizes. The influence curve of the structural dimensions of load-carrying beam on the preload is analyzed. With the piezoelectric coupling analysis function, the preload influence on the sensor sensitivity is researched. FEM simulation results show that the critical dimensions of load-carrying beam as well as the deformation and wall thickness of cavity have significant impact on the preload. Further studies show that the sensor has the highest sensitivity with the reasonable deformation and wall thickness of the cavity. In this paper, a sensor with range of 150 kN has the highest sensitivity at the wall thickness of 2 mm and the deformation of 0.14 mm.

scholarly journals Determination of Lateral Modulation Apodization Functions Using a Regularized, Weighted Least Squares Estimation

2010 ◽  
Vol 2010 ◽  
pp. 1-7 ◽  
Author(s):  
Chikayoshi Sumi
Keyword(s):  
Least Squares ◽  
Spatial Resolution ◽  
Soft Tissues ◽  
Displacement Vector ◽  
Weighted Least Squares ◽  
Strain Tensor ◽  
Estimation Method ◽  
Modulation Method ◽  
Value Decomposition

Recently, work in this group has focused on the lateral cosine modulation method (LCM) which can be used for next-generation ultrasound (US) echo imaging and tissue displacement vector/strain tensor measurements (blood, soft tissues, etc.). For instance, in US echo imaging, a high lateral spatial resolution as well as a high axial spatial resolution can be obtained, and in tissue displacement vector measurements, accurate measurements of lateral tissue displacements as well as of axial tissue displacements can be realized. For an optimal determination of an apodization function for the LCM method, the regularized, weighted minimum-norm least squares (WMNLSs) estimation method is presented in this study. For designed Gaussian-type point spread functions (PSFs) with lateral modulation as an example, the regularized WMNLS estimation in simulations yields better approximations of the designed PSFs having wider lateral bandwidths than a Fraunhofer approximation and a singular-value decomposition (SVD). The usefulness of the regularized WMNLS estimation for the determination of apodization functions is demonstrated.

Converse Piezoelectric Effect in Cellulose I Revealed by Wide-Angle X-ray Diffraction

2010 ◽  
Vol 11 (5) ◽  
pp. 1281-1285 ◽  
Author(s):  
Wolfgang Gindl ◽  
Gerhard Emsenhuber ◽  
Johannes Plackner ◽  
Johannes Konnerth ◽  
Jozef Keckes
Keyword(s):  
Piezoelectric Effect ◽  
Wide Angle ◽  
X Ray Diffraction ◽  
Cellulose I ◽  
X Ray ◽  
Converse Piezoelectric Effect

A note on Kolmogorov's third-order structure-function law, the local isotropy hypothesis and the pressure–velocity correlation

1996 ◽  
Vol 326 ◽  
pp. 343-356 ◽  
Author(s):  
Erik Lindborg
Keyword(s):  
Structure Function ◽  
Strain Tensor ◽  
Inertial Range ◽  
Order Structure ◽  
Two Dimensional ◽  
Mean Flow ◽  
Velocity Correlation ◽  
Third Order ◽  
The Third ◽  
Point Pressure

We show that Kolmogorov's (1941b) inertial-range law for the third-order structure function can be derived from a dynamical equation including pressure terms and mean flow gradient terms. A new inertial-range law, relating the two-point pressure–velocity correlation to the single-point pressure–strain tensor, is also derived. This law shows that the two-point pressure–velocity correlation, just like the third-order structure function, grows linearly with the separation distance in the inertial range. The physical meaning of both this law and Kolmogorov's law is illustrated by a Fourier analysis. An inertial-range law is also derived for the third-order velocity–enstrophy structure function of two-dimensional turbulence. It is suggested that the second-order vorticity structure function of two-dimensional turbulence is constant and scales with$\epsilon ^{2/3}_\omega$in the enstrophy inertial range, εωbeing the enstrophy dissipation. Owing to the constancy of this law, it does not imply a Fourier-space inertial-range law, and therefore it is not equivalent to thek−1law for the enstrophy spectrum, suggested by Kraichnan (1967) and Batchelor (1969).

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