MULTIDIMENSIONAL COUPLED VIBRATIONS OF PIEZOELECTRIC VIBRATORS——COMPOSITE PIEZOELECTRIC VIBRATORS

This paper presents an analysis of the three-dimensional coupled vibrations of a compositepiezoelectric vibrator by using the apparent elasticity method. A very simple analytic formula for the resonant frequency of the vibrator is obtained and withit the variation of the frequency constant with the geometric size of the vibrator is calculated. A satisfactory agreement is obtained as compared with the published results calculated by thefinite element method. Because the formula is quite simple the resonant frequency of the vibrator can be quickly cal-culated by using a scientific calculator,without having to use a computer,and so this method ismore convenient than the finite element method for engineeing design and estirmation. In addition,a dispersion relation of the phase velocity of "longitudinal"waves in the finiteisotropic solid cylinder is given and a comparison between this relation and those in an infinitecylinder is made. This method may also be used to calculate the resonant frequencies of other     

Strange—Nonchaotic—Attractor—Like Behaviors in Coupled Map SYstems

In a coupled map system,an attractor which seems to be strange nonchaotic attractor(SNA)is discovered for nonzero measure in parameter range,The attractor has nonpositive Lyapunov exponent(LE) and discrete structure.We call it strange-nonchaotic-attractor-like(SNA-like) behavior because the size of its size of its discrete structure decreases with the computing precision increasing and the true SNA does not change.The SNA-like behavior in the autonomous system is born when the truncation error of round-off is amplified to the size of the discrete part of the attractor during the long time interval of positive local LE.The SNA-like behavior is easily mistaken for a true SNA judging merely from the largest LE and the phase portrait in double precision computing.In non-autonomous system an SNA-like attractor is also found.     

Application of adaptive filter in time delay estimation——generalized quadratic interpolation method

The time delay estimation(TDE)of two different received sig-nals from the same source has attracted many interests of researchers inthe field of signal processing.A method described for precisely estimatingtime delay in this paper is based on the assumption that little prioriknowledge on statistical characteristics is available for the received signals.The variance of the estimate is derived.The basic architecture of thismethod is to use the adaptive noise canceller,in the steady state,andto interpolate the weight coefficients by using a generalized quadratic inter-polation matrix.The formula of the time delay estimation is presented.The method proposed by F.A.Reed is a special case of this method.The hardware implementation is much easier than that of theconventional time delay estimation method.The results of the systemsimulation and the experimental results at sea show a good agreementwith the theoretical analysis.     

An Almost—Poisson Structure for Autoparallels on Riemann—Cartan Spacetime

An almost-Poisson bracket is constructed for the regular Hamiltonian formulation of autoparallels on Riemann-Cartan spacetime, which is considered to be the motion trajectory of spinless particles in the space. This bracket satisfies the usual properties of a Poisson bracket except for the Jacobi identity. There does not exist a usual Poisson structure for the system although a special Lagrangian can be found for the case that the contracted torsion tensor is a gradient of a scalar field and the traceless part is zero. The almost-Poisson bracket is decomposed into a sum of the usual Poisson bracket and a “Lie-Poisson“ bracket, which is applied to obtain a formula for the Jacobiizer and to decompose a non-Hamiltonian dynamical vector field for the system. The almost-Poisson structure is also globally formulated by means of a pseudo-symplectic two-form on the cotangent bundle to the spacetime manifold.     

Einstein——Podolsky——Rosen entanglement in time-dependent periodic pumping non-degenerate optical parametric amplifier

The solution of the time-dependent periodic pumping non-degenerate optical parametric amplifier (NOPA) is derived when the pump depletion is considered both above and below thresholds. Based on this solution, the quantum fluctuation calculated shows that a high entanglement and a good squeezing degree of the parametric light beams are achieved near and above thresholds. We adopt two kinds of pump fields: (i) a continuously modulated pump with a sinusoidal envelope; (ii) a sequence of laser pulses with Gaussian envelopes. We analyse the time evolution of continuous variable entanglement by analytical and numerical calculations, and show that the periodic driven pumping also improves the degree of entanglement. The squeezing and Einstein-Podolsky-Rosen (EPR) entanglement by using the two pumping driven functions are investigated from below to above the threshold regions, the tendencies are nearly the same, and the Gaussian driven function is superior to that of the sine driven function, when the maximum squeezing and the minimum variance of quantum fluctuation are considered. In the meantime, the generalization of frequency degenerate OPA to frequency non-degenerated OPA problem is investigated.     

Electronic confinement in quasi—one—dimensional triblock copolymers

A tight-binding calculation to describe the triblock copolymer xPA(polyacetylene)/nPPP (poly(p-phenylene))/yPA or xPPP/nPA/yPPP is presented. The interfacial coupling between homopolymer segments is attributed to the hopping of π-electrons and the coupling of σ-bonds. The dependence of the band gap of triblock copolymers on the interfacial couplings or on the composite segment lengths is studied. The influence of composite segment lengths on the electron density is also studied. For nPPP/xPA/nPPP structures, the band gap varies with PA segment length over a wide range of 1.32－2.74eV. For nPA/xPPP/nPA structures,the band gap is invariant with PPP segment length. It is found that a spontaneous tunnelling phenomenon could take place in nPA/xPPP/nPA structures. Furthermore, the polaron caused by doping an electron into nPA/xPPP/nPA will tend to be confined in one of the well (PA) parts. This kind of confinement may increase the electron－hole recombination probability.     

Evolution and Collision of Bose—Condensed Gas in One—Dimensional Optical Lattices and a Far—Off Resonant Laser Beam

Evolution of a Bose-condensed gas in one-dimensional optical lattices is investigated in the presence of a potentialbarrier created by a far-off resonant laser beam. After the magnetic trap and optical lattices are switched off,by using the propagator method, the analytical result of the evolution of the density distribution of the Bose-condensed gas is given. In particular, the collision between the condensate and the potential barrier is shown inthis paper.     

Chaos in Einstein—Maxwell—Dust System

We study the dynamics of the Einstein-Maxwell-dust system and find that the system presents a critical point of a centre-centre-type structure in the phase space. By performing the numerical experiments, we find that the dynamics of the Einstein-Maxwell-dust system is unstable and its chaotic behaviour is obvious when the Hamiltonian becomes smaller.     

Entropy and topology of the Kerr—de Sitter black hole

By using the path integral method of Gibbons and Hawking, the entropy of the Kerr-de Sitter black hole is investigated under the microcanonical ensemble. We find that the entropy is one eighth the sum of the products of the Euler number of its cosmological horizon and event horizon with their respective areas. It is shown that the origin of the entropy of the black hole is related to the topology of its instanton.     

Moving Compacton—like Kink in a Purely Anharmonic Lattice with Symmetric On—Site Potential

We study the moving compacton-like kink in the system of a purely anharmoinc lattice with symmetric onsite poential by a direct algebraic method.It is found that the localization of the compactons is related to the nonlinear coupling parameter Cnl and the potential barrier height V0 of the double well potential,and the velocity of the propagation of the compacton is determined by the localization parameter q and the potential barrier height V0.Numerical calculation results demonstrate that the compacton is stable when it moves along the lattice chain.     

Influence of Light Polarization States on Sum—Frequency Generation in a Chiral Medium with a Two—Coupled—Oscillator Model

Sum-frequency generation (SFG) is investigated using the two-coupled-oscillator molecular model.The influence of the polarization states and angles of two incident beams on reflected and transmitted sum-frequency lights is discussed by considering the circular birefringence in a chiral medium.The different response of media with two kinds of enantiomers to polarization states of incident beams is also discussed.Furthermore,the relations between the SFG spectrum and the polarization states are studied.The theoretical result is consistent with a known experimental fact.     

Failure of the Ott—Grebogi—York—Type Controllers for Nonhyperbolic Chaos

It is considered that nonhyperbolicity affects the achievement of Ott-Grebogi-York-type (OGY-type) controllers.The result shows that,without a priori analytical knowledge of the dynamics,it is impossible to estimate the local dynamics from an experimental time series due to the singularity of the corresponding least-squares problem which results from the nonhyperbolicity in the system.Thus,it is necessary to destroy chaos before obtaining the formation for attempting control by experimental time series.The result explains a physical experimental result in the failure of chaos control in a parametrically excited pendulum model.     

Read—out of a read—only super—resolution optical disc with a Si mask

A novel read-only super-resolution optical disc structure (substrate/mask layer/dielectric layer) is proposed in this paper. By using a Si thin film as the mask layer, the recording pits with a diameter 380nm and a depth 50nm are read out on the dynamic measuring equipment; the laser wavelength α is 632.8nm and the numerical aperture is 0.40. In the course of reproduction, the laser power is 5mW and the rotation velocity of the disc is 4m·s^-1. The optimum thickness of the Si thin film is 18nm and the signal-to-noise ratio is 32dB.     

Analysis of the low—lying spectrum of the He—tetramer

There is a type of nodal surface imposed by symmetry on wavefunctions.These surfaces are crucial to the ordering of low-lying states.Based on an analysis of this type of surface and based on existing theoretical results,the feature of the low-lying spectrum of the He-tetramer is studied,and the candidates of bound states and narrow resonances are suggested.     

Numerical Simulation of the Two—State Decoherence Model of Nano—Spin Systems

We have studied the two-state random decoherence model of the V15 system (Phys.Rev.Lett.84(2000)3458) with the k‘partial tracing of the environment’ method.The linearity relation between the averaged decoherence time and the random dipolar interaction amplitude is verified.The distribution function of decoherence time spreads more widely as the amplitude of the random field is decreased,hence it is difficult to define a decoherence time for the system.     

Statistical Entropy of Horowitz—Strominger Black Hole

The partition functions of bosonic and fermionic fields in Horowitz-Strominger black hole are derived directly by quantum statistical method.Then via the improved brick-wall method (membrane model),the statistical entropy of black hole is obtained.If a proper parameter is chosen in our result,it is found out that the entropy is proportional to the area of horizon.The stripped term and the divergent logarithmic term in the original brick-wall method no longer exist.The difficulty in solving the wave equations of scalar and Dirac fields is avoided.A new neat way of calculating the entropy of various complicated black holes is offered.     

Condition of Prequantization to Two—Dimensional Manifolds with Boundary

The Weil‘s integrality condition of prequantization is generalized to two-dimensional phase space with boundaries.It is shown that in the prequantization condition a term related to the symplectic potential on the boundary appears.The necessity of the generalized condition is proved by analyzing the isolated singularities of the Hermitian bundle while the sufficiency of the condition is proved via geometric construction on the space of equivalence class.     

Localization of Surface—exciton Polaritons

We develop a numerical model to investigate the localization of surface-exciton polaritons in the presence of random roughness and spatial dispersion.It is found that the localication occurs in a limited frequency range near the maximum frequency of surface-exciton polaritons.The decaying length in the extended region is much larger than that in the localized region.The localization of surface-exciton polaritons is due to the destructive interference between waves scattered from the rough surface.     

Fresnel incoherent correlation hologram—— a review （Invited Paper）

Holographic imaging offers a reliable and fast method to capture the complete three-dimensional （3D） information of the scene from a single perspective. We review our recently proposed single-channel optical system for generating digital Fresnel holograms of 3D real-existing objects illuminated by incoherent light. In this motionless holographic technique, light is reflected, or emitted from a 3D object, propagates through a spatial light modulator （SLM）, and is recorded by a digital camera. The SLM is used as a beamsplitter of the single-channel incoherent interferometer, such that each spherical beam originated from each object point is split into two spherical beams with two different curve radii. Incoherent sum of the entire interferences between all the couples of spherical beams creates the Fresnel hologram of the observed 3D object. When this hologram is reconstructed in the computer, the 3D properties of the object are revealed.