Natural frequency analysis of laminated piezoelectric beams with arbitrary polarization directions

Piezoelectric devices exhibit unique properties that vary with different vibration modes,closely influenced by their polarization direction.This paper presents an analysis on the free vibration of laminated piezoelectric beams with varying polarization directions,using a state-space-based differential quadrature method.First,based on the electro-elasticity theory,the state-space method is extended to anisotropic piezoelectric materials,establishing state-space equations for arbitrary polarized piezoelectric beams.A semi-analytical solution for the natural frequency is then obtained via the differential quadrature method.The study commences by examining the impact of a uniform polarization direction,and then proceeds to analyze six polarization schemes relevant to the current research and applications.Additionally,the effects of geometric dimensions and gradient index on the natural frequencies are explored.The numerical results demonstrate that varying the polarization direction can significantly influence the natural frequencies,offering distinct advantages for piezoelectric elements with different polarizations.This research provides both theoretical insights and numerical methods for the structural design of piezoelectric devices.

Complete-basis-reprogrammable coding metasurface for generating dynamicallycontrolled holograms under arbitrary polarization states

Reprogrammable metasurfaces,which establish a fascinating bridge between physical and information domains,can dynamically control electromagnetic(EM)waves in real time and thus have attracted great attentions from researchers around the world.To control EM waves with an arbitrary polarization state,it is desirable that a complete set of basis states be controlled independently since incident EM waves with an arbitrary polarization state can be decomposed as a linear sum of these basis states.In this work,we present the concept of complete-basis-reprogrammable coding metasurface(CBR-CM)in reflective manners,which can achieve independently dynamic controls over the reflection phases while maintaining the same amplitude for left-handed circularly polarized(LCP)waves and right-handed circularly polarized(RCP)waves.Since LCP and RCP waves together constitute a complete basis set of planar EM waves,dynamicallycontrolled holograms can be generated under arbitrarily polarized wave incidence.The dynamically reconfigurable metaparticle is implemented to demonstrate the CBR-CM’s robust capability of controlling the longitudinal and transverse positions of holograms under LCP and RCP waves independently.It’s expected that the proposed CBR-CM opens up ways of realizing more sophisticated and advanced devices with multiple independent information channels,which may provide technical assistance for digital EM environment reproduction.

Least Square Finite Element Model for Analysis of Multilayered Composite Plates under Arbitrary Boundary Conditions

Laminated composites are widely used in many engineering industries such as aircraft, spacecraft, boat hulls, racing car bodies, and storage tanks. We analyze the 3D deformations of a multilayered, linear elastic, anisotropic rectangular plate subjected to arbitrary boundary conditions on one edge and simply supported on other edge. The rectangular laminate consists of anisotropic and homogeneous laminae of arbitrary thicknesses. This study presents the elastic analysis of laminated composite plates subjected to sinusoidal mechanical loading under arbitrary boundary conditions. Least square finite element solutions for displacements and stresses are investigated using a mathematical model, called a state-space model, which allows us to simultaneously solve for these field variables in the composite structure’s domain and ensure that continuity conditions are satisfied at layer interfaces. The governing equations are derived from this model using a numerical technique called the least-squares finite element method (LSFEM). These LSFEMs seek to minimize the squares of the governing equations and the associated side conditions residuals over the computational domain. The model is comprised of layerwise variables such as displacements, out-of-plane stresses, and in- plane strains, treated as independent variables. Numerical results are presented to demonstrate the response of the laminated composite plates under various arbitrary boundary conditions using LSFEM and compared with the 3D elasticity solution available in the literature.

Arbitrary Decode-Forward Relaying with Re-Encoded Bits Selection Strategy for Polar Codes

In this paper,we propose an arbitrary decode-forward single-relay scheme for finite blocklength polar codes,which can be applied to the general symmetric discrete memoryless relay channel with orthogonal receiver components.The relay node decodes the received message.The relay node selectively re-encodes the message and transmits it to the destination node.Furthermore,in order to minimize the upper-bound of the block error probability,we propose a selection strategy to decide the proper re-encoded bit set by the relay.Simulation results are presented to illustrate the improvement in decoding performance of the proposed scheme compared to conventional relay schemes in both additive white Gaussian noise(AWGN)channel and Rayleigh fading channel(RFC).

Optimized nonhyperbolic moveout correction equation of long-offset seismic data for TI media with an arbitrary spatial orientation

The conventional long-offset nonhyperbolic moveout equation is derived for the transverse isotropic media with a vertical symmetric axis（VTI）.It cannot be extended to the transverse isotropic media with an arbitrary spatial orientation of symmetry axis（ATI）.In this paper,we optimize a modified long-offset nonhyperbolic moveout equation for ATI media based on the conventional nonhyperbolic moveout equation and the exact analytical solution of the quartic moveout coefficient（A_4） and NMO velocity for ATI media that were derived in our previous work.Compared with the exact traveltimes of the ray-tracing algorithm for anisotropic media,this optimized equation can be used to calculate the traveltime varying with survey line azimuth in arbitrary strong or weak ATI media.It can replace the time-consuming, multi-offset,and multi-azimuth ray tracing method for forward modeling of long-offset reflection traveltimes in ATI media,which is useful to further anisotropic parameter inversion using long-offset nonhyperbolic moveout.

A New Method for Locating Calculation of Arbitrary Spatial Straight Line or Plane in NC Machining

In the manufacturing process, we often encounter so me location machining of space arbitrary straight lines and planes that are not on ly unparalleled but also not vertical with the machine tool spindle or the cutti ng tool. In the past, we can do the location machining through the methods of dr awing line and making level in the ordinary machine tool. In the numerical contr ol machining of the CNC machine tool and manufacturing center, however, the spac e location and angle of the arbitrary straight lines and planes must be precisel y calculated in advance. So that precisely locating can be guaranteed in machini ng. Therefore, how to work out the space location angle of the arbitrary straigh t lines and planes to be machined both conveniently and precisely, turns out to be the must-be-solved chief problem in the numerical control machining. In thi s paper, through the deeply research of this problem, a new kind of calculating formula that calculates and defines the space location angle of the arbitrary st raight lines and planes by using the methods of analytic calculating. The formul a has been applied in the practical manufacturing calculation. It is proved that the new space angle calculating methods of arbitrary straight lines and planes is convenient in calculating and precise in locating. And it provides us a n ew, brief and precise calculating method in the numerical control machining of t he numerical control machine tool and manufacturing center.

Photonic generation of arbitrary waveforms based on incoherent wavelength-to-time mapping

We demonstrate experimentally a radio frequency arbitrary waveform generator using the incoherent wavelength-to-time mapping technique. The system is implemented by amplitude modulation of a broadband optical resource whose spectrum is reshaped by a programmable optical pulse shaper and transmitted over a single mode fiber link. The shape of the generated waveform is controlled by the optical pulse shaper, and the fiber link introduces a certain group velocity delay to implement wavelength-to-time mapping. Assisted by the flexible optical pulse shaper, we obtain different shapes of optical waveforms, such as rectangle, triangle, and sawtooth waveforms. Furthermore, we also demonstrate ultra-wideband generation, such as Gaussian monocycle, doublet, and triplet waveforms, using the incoherent technique.

High-Order Models of Nonlinear and Dispersive Wave in Water of Varying Depth with Arbitrary Sloping Bottom

High-order models with a dissipative term for nonlinear and dispersive wave in water of varying depth with an arbitrary sloping bottom are presented in this article. First, the formal derivations to any high order of mu(= h/lambda, depth to deep-water wave length ratio) and epsilon(= a/h, wave amplitude to depth ratio) for velocity potential, particle velocity vector, pressure and the Boussinesq-type equations for surface elevation eta and horizontal velocity vector (U) over right arrow at any given level in water are given. Then, the exact explicit expressions to the fourth order of mu are derived. Finally, the linear solutions of eta, (U) over right arrow, C (phase-celerity) and C-g (group velocity) for a constant water depth are obtained. Compared with the Airy theory, excellent results can be found even for a water depth as large as the wave legnth. The present high-order models are applicable to nonlinear regular and irregular waves in water of any varying depth (from shallow to deep) and bottom slope (from mild to steep).

Probabilistic teleportation of an arbitrary three-particle state

A scheme for teleporting an arbitrary and unknown three-particle state from a sender to either one of two receivers is proposed. The quantum channel is composed of a two-particle non-maximally entangled state and two three-particle non-maximally entangled W states. An arbitrary three-particle state can be perfectly teleported probabilistically if the sender performs three generalized Bell-state measurements and sends to the two receivers the classical result of these measurements, and either one of the two receivers adopts an appropriate unitary transformation conditioned on the suitable measurement outcomes of the other receiver. All kinds of unitary transformations are given in detail.

Probabilistic Teleportation of an Arbitrary Two-particle State

A scheme for the teleportation of an arbitrary two-particle state via two non-maximally entangled particle pairsis proposed. We show that teleportation can be successfully realized with a certain probability if the receiveradopts an appropriate unitary-reduction strategy. A specific strategy is provided in detail The probability of successful teleportation is determined by the smaller coefficients of the two entangled pairs.

Computing Streamfunction and Velocity Potential in a Limited Domain of Arbitrary Shape.Part I:Theory and Integral Formulae

The non-uniqueness of solution and compatibility between the coupled boundary conditions in computing velocity potential and streamfunction from horizontal velocity in a limited domain of arbitrary shape are revisited theoretically with rigorous mathematic treatments.Classic integral formulas and their variants are used to formulate solutions for the coupled problems.In the absence of data holes,the total solution is the sum of two integral solutions.One is the internally induced solution produced purely and uniquely by the domain internal divergence and vorticity,and its two components（velocity potential and streamfunction） can be constructed by applying Green＇s function for Poisson equation in unbounded domain to the divergence and vorticity inside the domain.The other is the externally induced solution produced purely but non-uniquely by the domain external divergence and vorticity,and the non-uniqueness is caused by the harmonic nature of the solution and the unknown divergence and vorticity distributions outside the domain.By setting either the velocity potential（or streamfunction） component to zero,the other component of the externally induced solution can be expressed by the imaginary（or real） part of the Cauchy integral constructed using the coupled boundary conditions and solvability conditions that exclude the internally induced solution.The streamfunction（or velocity potential） for the externally induced solution can also be expressed by the boundary integral of a double-layer（or singlelayer） density function.In the presence of data holes,the total solution includes a data-hole-induced solution in addition to the above internally and externally induced solutions.

Teleportation of an Arbitrary Three-Particle State via Three EPR Pairs

A scheme of teleportation of an arbitrary three-particle state is presented when three pairs of entangled particles are used as quantum channels. After the Bell state measurements are operated by the sender, the original state with deterministic probability can be reconstructed by the receiver when a corresponding unitary transformation is followed.

The scattering fields for a spherical target irradiated by a plane electromagnetic wave in an arbitrary direction

The relation between corresponding trigonometric functions in two rotating coordinate systems is presented. The transformation formula for a vector in the two rotating spherical coordinate systems is obtained. The scattering fields for a spherical target irradiated by a plane electromagnetic wave in an arbitrary direction are derived. These fields in a particular case retrogress to those available in the literature. The obtained results have great potential in practical applications.

Teleportation of an Arbitrary Two-Particle State by Two Partial Entangled Three-Particle GHZ States

We present a scheme for teleporting an unknown arbitrary two-particle state from a sender to either one of two receivers. The quantum channel is composed of two partial entangled three-particle GHZ states. An unknown arbitrary two-particle state can be perfectly teleported probabilistically if the sender performs two generalized Bell-state measurements and each receiver introduces an appropriate unitary transformation with the help of the other receiver's Hadamard operations and simple measurements.

A new representation and probabilistic teleportation of an arbitrary and unknown N-particle state

A new representation of an arbitrary and unknown N-particle state is presented at first. As an application, a scheme for teleporting an arbitrary and unknown N-particle state is proposed when N pairs of two-particle non- maximally entangled states are utilized as quantum channels. After Alice （sender） makes Bell-state measurement on her particles, Bob （recipient） introduces an auxiliary particle and carries out appropriate unitary transformation on his particle and the auxiliary particle depending on classical information from Alice. Then, von Neumann measurement that confirms whether the teleportation succeeds or not is performed by Bob on the auxiliary particle. In order to complete the teleportation, another N-1 times operations need to be performed which are similar to the above ones. It can be successfully realized with a certain probability which is determined by the product of the smaller coefficients of non-maximally entangled pairs. All possible unitary transformations are given in detail.

Probabilistic Teleportation of an Arbitrary Two-Particle State and Its Quantum Circuits

Two simple schemes for probabilistic teleportation of an arbitrary unknown two-particle state using a non-maximally entangled EPR pair and a non-maximally entangled GHZ state as quantum channels are proposed. After receiving Alice＇s Bell state measurement results, Bob performs a collective unitary transformation on his inherent particles without introducing the auxiliary qubit. The original state can be probabilistically teleported. Meanwhile, quantum circuits for realization of successful teleportation are also presented.

Coupling dynamic analysis of a liquid-filled spherical container subject to arbitrary excitation

Using spherical coordinates, the coupling nonlinear dynamic system of a liquid-filled spherical tank, which can be excited discretionarily, is deduced by the H-O varia- tional principle, and the viscous damping is introduced via the liquid dissipation function. The kinetic equations of the coupling system are deduced by the relationship between the velocity of liquid particles and the disturbed liquid surface equation. Normal differential equations are obtained through the Galerkin method. An equivalent mechanical model is developed for liquid sloshing in a spherical tank subject to arbitrary excitation. The fixed and slosh masses, as well as the spring and damping constants, are determined in such a way as to satisfy the principle of equivalence. Numerical simulations illustrate the theoretical results in this paper as well.

An efficient algorithm to compute transient pressure responses of slanted wells with arbitrary inclination in reservoirs

Compared with vertical and horizontal wells, the solution and computation of transient pressure responses of slanted wells are more complex. Vertical and horizontal wells are both simplified cases of slanted wells at particular inclination, so the model for slanted wells is more general and more complex than other models for vertical and horizontal wells. Many authors have studied unsteady-state flow of fluids in slanted wells and various solutions have been proposed. However, until now, few of the published results pertain to the computational efficiency. Whether in the time domain or in the Laplace domain, the computation of integration of complex functions is necessary in obtaining pressure responses of slanted wells, while the computation of the integration is complex and time-consuming. To obtain a perfect type curve the computation time is unacceptable even with an aid of high-speed computers. The purpose of this paper is to present an efficient algorithm to compute transient pressure distributions caused by slanted wells in reservoirs. Based on rigorous derivation, the transient pressure solution for slanted wells of any inclination angle is presented. Assuming an infinite-conductivity wellbore, the location of the equivalent-pressure point is determined. More importantly, according to the characteristics of the integrand in a transient pressure solution for slanted wells, the whole integral interval is partitioned into several small integral intervals, and then the method of variable substitution and the variable step-size piecewise numerical integration are employed. The amount of computation is significantly reduced and the computational efficiency is greatly improved. The algorithm proposed in this paper thoroughly solved the difficulty in the efficient and high-speed computation of transient pressure distribution of slanted wells with any inclination angle.

Computing Streamfunction and Velocity Potential in a Limited Domain of Arbitrary Shape.Part II:Numerical Methods and Test Experiments

Built on the integral formulas in Part I,numerical methods are developed for computing velocity potential and streamfunction in a limited domain.When there is no inner boundary（around a data hole） inside the domain,the total solution is the sum of the internally and externally induced parts.For the internally induced part,three numerical schemes（grid-staggering,local-nesting and piecewise continuous integration） are designed to deal with the singularity of the Green＇s function encountered in numerical calculations.For the externally induced part,by setting the velocity potential（or streamfunction） component to zero,the other component of the solution can be computed in two ways：（1） Solve for the density function from its boundary integral equation and then construct the solution from the boundary integral of the density function.（2） Use the Cauchy integral to construct the solution directly.The boundary integral can be discretized on a uniform grid along the boundary.By using local-nesting（or piecewise continuous integration）,the scheme is refined to enhance the discretization accuracy of the boundary integral around each corner point（or along the entire boundary）.When the domain is not free of data holes,the total solution contains a data-hole-induced part,and the Cauchy integral method is extended to construct the externally induced solution with irregular external and internal boundaries.An automated algorithm is designed to facilitate the integrations along the irregular external and internal boundaries.Numerical experiments are performed to evaluate the accuracy and efficiency of each scheme relative to others.

Probabilistic teleportation of an arbitrary GHZ-class state with a pure entangled two-particle quantum channel and its application in quantum state sharing

This paper presents a scheme for probabilistic teleportation of an arbitrary GHZ-class state with a pure entangled two-particle quantum channel. The sender Alice first teleports the coefficients of the unknown state to the receiver Bob, and then Bob reconstructs the state with an auxiliary particle and some unitary operations if the teleportation succeeds. This scheme has the advantage of transmitting much less particles for teleporting an arbitrary GHZ-class state than others. Moreover, it discusses the application of this scheme in quantum state sharing.