Analysis of Frequency Spectrum of Laser-Induced Vibration of Microbeam Resonators

The vibration phenomenon during pulsed laser heating of micro-beams is investigated. The beam is made of silicon and is heated by a laser pulse with a non-Gaussian temporal profile and with an ultrashort pulse duration of 2ps, which incites vibration due to the thermoelastic damping effect. This coupled thermoelastic problem is solved using an analytical-numerical technique based on the Laplace transformation. The damping ratio and resonant frequency shift ratio of beams due to the air damping effect and the thermoelastic damping effect are also examined and discussed.     

Teleportation of an arbitrary mixture of diagonal states of multiqudit

This paper proposes a scheme to teleport an arbitrary mixture of diagonal states of multiqutrit via classical correlation and classical communication. To teleport an arbitrary mixture of diagonal states of N qutrits, N classically correlated pairs of two qutrits are used as channel. The sender （Alice） makes Fourier transform and conditional gate （i.e., XOR（3） gate） on her qutrits and does measurement in appropriate computation bases. Then she sends N ctrits to the receiver （Bob）. Based on the received information, Bob performs the corresponding unitary transformation on his qutrits and obtains the teleported state. Teleportation of an arbitrary mixture of diagonal states of multiqudit is also discussed.     

Measurement of the decoherence of a mesoscopic superposition of motional states of a trapped ion

We propose a scheme to observe the decoherence of a mesoscopic superposition of two coherent states in the motion of a trapped ion. In the scheme the ion is excited by two perpendicular lasers tuned to the ion transition. The decoherence is revealed by the decrease of the correlation between two successive measurements of the internal state of the ion after relevant laser－ion interaction.     

Improvement of Synchronizability of Scale-Free Networks

We investigate the factors that affect synchronizability of coupled oscillators on scale-free networks. Using the memory Tabu search （MTS） algorithm, we improve the eigen-ratio Q of a coupling matrix by edge intercrossing. The numerical results show that the synchronizatlon-improved scale-free networks should have distinctive both small average distance and larger clustering coefficient, which are consistent with some real-world networks. Moreover, the synchronizability-improved networks demonstrate the disassortative coefficient.     

Analysis of the causes of formation of negative loss factors

I-IatroductionStatisticalEnergyAnalysis(SEA)isakindofeffective,simpleanddirectapproachforan-alyzingvibrationandsound,andithasbeenfoundwidelyapplicationsinanalysisofmechanicalnoiseandvibrationcolltrolsince198osl1-4].However,forgeneralindustrialmachineswhichalwayconsistofcomPlexandheaVystructures,thedeterminationmethodsofSEAparametersintheclassicalSEAtheoryareinapplicable[5]because:(1)SEAparametersofthesekindsofstructuresaredifficulttoobtainfromthetheory(2)theconditionofconservativeandweak…     

Observation of spontaeous Polarization of tourmaline

Since Tetsujiro kubo indirectly found the spontaneous polarization of tourmaline through absorbing copper ions in copper sulfate aqueous solutions in 1980s,there is no other evidence to demonstrate the existence of the spontaneous polarization in tourmaline.It was ound that after a tourmaline particle was bombarded by electron beams,a spot appeared on the surface of the sample,and that one half of the spot was brighter than the other half under scanning electron icroscope.After touraline was treated for 2h at 1223K and then bombarded by electron beams,the bombardment spot did not appear because the crystal structure of tourmaline is destroyed.The existence of the bombardment spot accounts for the spontaneous polarization.The shape and brightness of the bombardment spot not only shows the existence of a surface electric filed induced by spontaneous polarization.but also the relation with the direction of the crystal plane of tourmaline.     

Measurement of Eccentricity of the Centre of Mass from the Geometric Centre of a Sphere

The eccentricity of the centre of mass from the geometric centre of a spherical attracting mass in determining the Newtonian gravitational constant G is tested by means of an electronic balance. The experimental result shows that the eccentricity of the sample is about 0.31 μm with uncertainty of 0.05μm. Two density distribution models are discussed to estimate the uncertainty to G by the eccentricities of the attracting masses.     

Symmetry of Lagrangians of nonholonomic systems of non-Chetaev’s type

This paper studies the symmetry of Lagrangians of nonholonomic systems of non-Chetaev's type. First, the definition and the criterion of the symmetry of the system are given. Secondly, it obtains the condition under which there exists a conserved quantity and the form of the conserved quantity. Finally, an example is shown to illustrate the application of the result.     

Calibration of Membrane Viscosity of the Reconstituted Vesicles by Measurement of the Rotational DIffusion of Bacteriorhodopsin

Membrane viscosity of the reconstituted vesicles was calibrated by rotational diffusion of bacteriorhodopin(BR) in dimyristoylphosphatidylcholine(DMPC) and egg phosphatidylcholine(PC) vesicles.Rotational diffusion of BR in the vesicles was measured by flash-induced absorption anisotropy decay.BR was,for the first time ,reconstituted successfully into DMPC and egg PC vesicles,From the measurement of flash-induced absorption anisotropy decay of BR,the value of rotational diffusion coefficient D was obtained from each curve fitting by a global fitting procedure and ,in turn,membrane viscosity η was estimated from D.The results have shown that membrane viscosity is temperature-dependent,It was decreased as temperature increased,but a transition occurred in the region of the respective phase transition of DMPC and egg PC,respectively,The decrease of η was fast near the phase transition for DMPC and egg PC.Few effects of lipid/BR ratio and glycerol or sucrose in suspension medium on membrane viscosity were found.     

场方法的改进及其在积分Riemann-Cartan空间运动方程中的应用

和Hamilton-Jacobi方法类似,Vujanovi?场方法把求解常微分方程组特解的问题转化为寻找一个一阶拟线性偏微分方程(基本偏微分方程)完全解的问题,但Vujanovi?场方法依赖于求出基本偏微分方程的完全解,而这通常是困难的,这就极大地限制了场方法的应用.本文将求解常微分方程组特解的Vujanovi?场方法改进为寻找动力学系统运动方程第一积分的场方法,并将这种方法应用于一阶线性非完整约束系统Riemann-Cartan位形空间运动方程的积分问题中.改进后的场方法指出,只要找到基本偏微分方程的包含m(m≤ n,n为基本偏微分方程中自变量的数目)个任意常数的解,就可以由此找到系统m个第一积分.特殊情况下,如果能够求出基本偏微分方程的完全解(完全解是m=n时的特例),那么就可以由此找到≤系统全部第一积分,从而完全确定系统的运动.Vujanovi?场方法等价于这种特殊情况.     

Lie Group of Transformations for a KdV–Boussinesq Equation

We consider a combined Korteweg–deVries and Boussinesq equation governing long surface waves in shallow water. Considering traveling wave solutions, the basic equations will be reduced to a second order ordinary differential equation. Using the Lie group of transformations we reduce it to a first order ordinary differential equation and employ a direct method to derive its periodic solutions in terms of Jacobian elliptic functions and their corresponding solitary wave and explode decay mode solutions.     

The explicit secular equation for surface acoustic waves in monoclinic elastic crystals

The secular equation for surface acoustic waves propagating on a monoclinic elastic half-space is derived in a direct manner, using the method of first integrals. Although the motion is at first assumed to correspond to generalized plane strain, the analysis shows that only two components of the mechanical displacement and of the tractions on planes parallel to the free surface are nonzero. Using the Stroh formalism, a system of two second order differential equations is found for the remaining tractions. The secular equation is then obtained as a quartic for the squared wave speed. This explicit equation is consistent with that found in the orthorhombic case. The speed of subsonic surface waves is then computed for 12 specific monoclinic crystals.     

Potential method of integration for solving the equations of mechanical systems

This paper is intended to apply a potential method of integration to solving the equations of holonomic and nonholonomic systems. For a holonomic system, the differential equations of motion can be written as a system of differential equations of first order and its fundamental partial differential equation is solved by using the potential method of integration. For a nonholonomic system, the equations of the corresponding holonomic system are solved by using the method and then the restriction of the nonholonomic constraints on the initial conditions of motion is added.     

Formal study of a chemical reaction by Grad expansion of the Boltzmann equation. II

In a previous communication the Boltzmann equations for a bimolecular chemical reaction were transformed into an infinite system of quadratic differential equations. It is shown here that the reaction rate may be calculated approximately by using the first differential equation only, which is a generalization of the phenomenological law of chemical kinetics. Then, a general method for solving the expanded Boltzmann equations by successive approximations is proposed and studied to first order.     

Zur Theorie der Teilchenbewegung in zeitabhängigen elektromagnetischen Feldern

The Langevin equation – i.e. the equation of motion for a charged particle including a collision term proportional to the particle velocity – is solved for arbitrary time-dependent electric and magnetic fields by a new general method. Instead of the usual ansatz: particle velocity = cyclotron velocity + drift velocity the method given makes the ansatz: particle velocity = tensor = cyclotron velocity. The unknown tensor obeys a simple differential equation of the first order which can be generally solved at once. This method is a modification of the variation of constants method for inhomogeneous differential equations. The electromagnetic fields considered must be spatially homogeneous; for (weakly) inhomogeneous fields an iteration procedure of Pytte (1962) may be applied. Some examples are discussed shortly. The Langevin equation treated is completely equivalent to the equation of motion in a magnetohydrodynamic one-fluid theory.     

Remarks concerning the derivation and the expansion of the master equation

The present work consist of two parts: In the first part we apply the method of quasilinearization to the differential equation describing the time development of the quantum-mechanical probability density. In this way we derive the master equation without resorting to perturbation theory. In the second part of the paper, for a general form of the master equation which is an integro-differential equation, we test the accuracy of the Fokker-Planck approximation with the help of a solvable model. Then we study an alternative way of reducing the integro-differential equation to a partial differential equation. By expanding the transition probability W(q, q′), and the distribution function in terms of a complete set of functions, we show that for certain forms of W(q, q′), the master equation can be transformed exactly to partial differential equations of finite order.     

任意激励下一阶电路的积分解及三要素法

给出任意激励下一阶电路的积分解,并由此导出三要素法公式。     

Signs of life

Programmable electronic calculators provide a speedy means of performing scientific calculations, e.g. the evaluation of a given polynomial for many different x values and the performance of iterative procedures for the solution of polynomial equations. Both of these uses appear in variational calculations of the energy of simple quantum mechanical systems such as the perturbed harmonic oscillator. For this system the traditional perturbation method has some drawbacks, end so it is useful to find its energy levels directly by purely numerical methods. The electronic calculator can do this if the relevant Schrödinger differential equation is transformed into a difference equation. The diffusion equation is a partial differential equation, but can be converted to an ordinary differential equation and thence to a pair of difference equations which can be solved on the calculator. This applies even if the diffusion coefficient depends on the concentration, so that the associated ordinary differential equation is non-linear.     

The harmonic inversion of the field-swept fixed-frequency resonance spectrum

When the spin Hamiltonian is a linear function of the magnetic field intensity the resonance fields can be determined, in principle, by an eigenfield equation. In this report, we show a new technical approach to the resonance field problem where the eigenfield equation leads to a dynamic equation or, more specifically, to a first order differential equation of a variable L(x), where x is associated with the magnetic field h. Such differential equation has the property that: its stationary solution is the eigenfield equation and the spectral information contained in L(x) is directly related to the resonance spectrum. Such procedure, known as the "harmonic inversion problem" (HIP), can be solved by the "filter diagonalization method" (FDM) providing sufficient precision and resolution for the spectral analysis of the dynamic signals. Some examples are shown where the resonance fields are precisely determined in a single procedure, without the need to solve eigenvalue equations.