Free vibrations of a simply supported,rectangular plate: An exact elasticity solution

An exact, three-dimensional solution for the free vibrations of simply supported, rectangular plates of arbitrary thickness within the linear theory of elastodynamics is given in this paper. The solution, obtained in a semi-inverse fashion as was the solution of the elastostatic problem for such plates, satisfies all of the boundary conditions of the problem in a pointwise manner. It is found that there are two types of modes of oscillation possible which are consistent with the kinematic assumptions made to find the semi-inverse solution. Other modes of oscillation may exist in the three-dimensional theory of elastodynamics for such plates but our kinematic assumptions would not be consistent with such modes. The two types of modes found are analogous to the flexural modes of classical plate theory and the thickness-twist modes, here called breathing modes, of Mindlin plate theory. Some numerical results are given which indicate that the predictions of Mindlin plates are uncannily good approximations to the flexural frequencies given by the present, three-dimensional analysis even for very thick plates. However, the predictions of Mindlin plate theory for the thickness-twist, or breathing, frequencies are not nearly so good. These discrepancies are discussed briefly in an appendix.     

Ratio of a strange quark mass ms to up or down quark mass mu,d predicted by a quark propagator in the frameworkof the chiral perturbation theory

Based on the fully dressed quark propagator and chiral perturbation theory, we study the ratio of the strange quark mass m_s to up or down quark mass m_u,d. The ratio is related to the determination of quark masses which are fundamental input parameters of QCD Lagrangian in the Standard Model of particle physics and can not be directly measured since the quark is confined within a hadron. An accurate determination of these QCD free parameters is extremely important for both phenomenological and theoretical applications. We begin with a brief introduction to the non-perturbation QCD theory, and then study the mass ratio in the framework of the chiral perturbation theory (χ PT) with a parameterized fully dressed quark propagator which describes confining fully dressed quark propagation and is analytic everywhere in the finite complex p²-plane and has no Lehmann representation so there are no quark production thresholds in any theoretical calculations of observable data. Our prediction for the ratio m_s/m_u,d is consistent with other model predictions such as Lattice QCD, instanton model, QCD sum rules and the empirical values used widely in the literature. As a by-product of this study, our theoretical results, together with other predictions of physical quantities that used this quark propagator in our previous publications, clearly show that the parameterized form of the fully dressed quark propagator is an applicable and reliable approximation to the solution of the Dyson-Schwinger Equation of quark propagator in the QCD.     

Analysis of Raman gain for focussed Gaussian pump beams

Several theoretical and numerical models have been published which describe the evolution of a Stokes beam in a Raman medium excited by a focussed pump beam. Generally, the published theoretical departures from the plane-wave theory of Raman scattering are based on assumptions about the power of the pump beam. In this paper we present a theoretical model which is shown to be in excellent agreement with an exact numerical treatment, and which is valid without restrictions on the pump power. Its predictions are used to indicate the range of validity of earlier theories.     

Non-perturbative Aspects of QCD and Parameterized Quark Propagator

Based on the Global Color Symmetry Model, the non-perturbative Q, CD vacuum is investigated in the parameterized fully dressed quark propagator. Our theoretical predictions for various quantities characterized the QCD vacuum are in agreement with those predicted by many other phenomenologieal QCD inspired models. The successful predictions clearly indicate the extensive validity of our parameterized quark propagator used here. A detailed discussion on the arbitrariness in determining the integration cut-off parameter ofμ in calculating QCD vacuum condensates and a good method, which avoided the dependence of calculating results on the cut-off parameter is also strongly recommended to readers.     

Dynamical Running Mass of Quark in the Dyson-Schwinger Equation Approach

Based on the Dyson-Schwinger equations of QCD in the "rainbow" approximation, the fully dressed quarkpropagator Sf(p) is investigated, and then an algebraic parametrization form of the propagator is obtained as a solutionof the equations. The dressed quark amplitudes Af and Bf built up the fully dressed quark propagator and the dynamicalrunning masses Mf defined by Af and Bf for light quarks u, d and s are calculated, respectively. Using the predictedrunning masses Mf, quark condensates <0|q(0)q(0)|0> = -(0.255 GeV)a for u, d quarks, and <0|s s|0> = 0.8<0|q(0)q(0)]0)for s quark, and experimental pion decay constant fπ = 0.093 GeV, the masses of Goldstone bosons K, π, and η are alsoevaluated. The numerical results show that the masses of quarks are dependent on their momentum p2. The fully dressedquark amplitudes Af and Bf have correct behaviors which can be used for many purposes in our future researches onnonperturbative QCD.     

Artifacts,assumptions, and ambiguity: Pitfalls in comparing experimental results to numerical simulations when studying electrical stimulation of the heart

Insidious experimental artifacts and invalid theoretical assumptions complicate the comparison of numerical predictions and observed data. Such difficulties are particularly troublesome when studying electrical stimulation of the heart. During unipolar stimulation of cardiac tissue, the artifacts include nonlinearity of membrane dyes, optical signals blocked by the stimulating electrode, averaging of optical signals with depth, lateral averaging of optical signals, limitations of the current source, and the use of excitation-contraction uncouplers. The assumptions involve electroporation, membrane models, electrode size, the perfusing bath, incorrect model parameters, the applicability of a continuum model, and tissue damage. Comparisons of theory and experiment during far-field stimulation are limited by many of these same factors, plus artifacts from plunge and epicardial recording electrodes and assumptions about the fiber angle at an insulating boundary. These pitfalls must be overcome in order to understand quantitatively how the heart responds to an electrical stimulus. (c) 2002 American Institute of Physics.     

Tensor Susceptibilities of QCD Vacuum and Parameterized Quark Propagator

Based on the parameterized fully dressed quark propagator proposed by us, the tensor susceptibilities of QCD vacuum and quark vacuum condensates are investigated. Our predicted values of the tensor susceptibilities are in agreement with those predicted by many other theoretical models with QCD feature. The results also show that the tensor susceptibility of QCD vacuum strongly depends on flavor of quark but not sensitive to variation of quark vacuum condensates. However, the quark vacuum condensate is very sensitive to the change of cut-off-parameter μ^2 of the integration, that is, it depends on the separation point of perturbative and non-perturbative QCD region. The successful predictions clearly indicate the extensive validity of our parameterized fully dressed quark propagator used here.     

The theory of long waveguide structures radiating lower hybridwaves into a plasma

It is shown that the radiation into a plasma from the structures composed of many waveguides is well described by the theory of the infinite structures. This theory results in the efficient numerical code which is appropriate for the study of the nonlinear response of the plasma ill front of the grill. Both the infinite conventional grill and the structure built up from the infinite series of identical N-waveguide multijunction sections are investigated. It is proved that the spectrum of the last structure is the superposition of N spectra of the infinite conventional grills with the specially selected phase shifts. The theoretical results for three long structures (24-waveguide conventional grill on ASDEX and two multijunction arrays, namely a 32-waveguide grill on JET and a 30-waveguide grill proposed for T15) are compared with the predictions of the theory for the corresponding infinite structures. and the agreement is good     

Spontaneously broken Lorentz invariance from the dynamics of a heavy sterile neutrino

A relativistic theory for neutrino superluminality is presented (in principle, the same mechanism applies also to other fermions). The theory involves the standard-model particles and one additional heavy sterile neutrino with an energy-scale close to or above the electroweak one, all particles propagating in the usual 3 + 1 spacetime dimensions. Lorentz violation results from spontaneous symmetry breaking in the sterile-neutrino sector. The theory tries, as far as possible, to be consistent with the existing experimental data from neutrino physics and to keep the number of assumptions minimal. There are clear experimental predictions which can be tested.     

Quark mass and the masses of Goldstone bosons

Based on the Dyson-Schwinger Equations (DSEs) of QCD in the “rainbow” approximation, the fully dressed quark propagator S _f (p) is investigated, and then an algebraic parametrization form of the propagator is obtained as a solution of the equations. The dressed quark amplitudes A _f and B _f which built up the fully dressed quark propagator, and the dynamical running masses M _f , which is defined by A _f and B _f for light quarks u, d and s, are calculated, respectively. Using the predicted current masses m _f , quark local vacuum condensates, and our predicted value of pion decay constant, the masses of Goldstone bosons K, π and η and their in-medium values are also evaluated. Our predictions fit to data and to many other different calculations quite well. The numerical results show that the mass of quark is dependent of its momentum p ². The fully dressed quark amplitudes A _f and B _f have correct behaviors and can be used for many purposes in our future researches on non-perturbative QCD.      

Photoemission and Auger CVV spectra of partially filled bands: A cluster approach

A theory of XPS and Auger lineshapes from almost completely filled bands, that had previously been proposed in the context of a graph-theoretical expansion, is applied to a finite cluster and solved exactly. The new method avoids the calculation of complex vertex corrections and reveals the full potential of the theory. We find that while the holes observed in photoemission are dressed quasi-holes, those observed in Auger CVV spectra are essentially bare. This explains certain discrepancies between calculated and experimental spectra, that had been attributed to intrinsic limitations of the theoretical set-up, but actually were due to the mathematical approximations. A simple analytic approach based on the use of bare propagators is found to agree closely with the exact numerical results.     

Focusing of electromagnetic waves into a biaxial crystal, experimental results

We present experimental results for focusing of an electromagnetic wave from air into a biaxial crystal. These results are compared with numerical results, and good agreement is found. The experimental results show distinct tangential and sagittal foci, whose positions agree with numerical predictions. The theory is outlined both for the exact solution, which includes extra-paraxial geometries and double refraction, and for the paraxial solution, in which double refraction is ignored. We also present a simple ray-optical interpretation of the results, which allows us to predict the positions of the sagittal and tangential foci.     

梯型四能级系统中超窄电磁感应透明与无反转增益

研究了两个光场作用下梯型四能级系统中Rabi频率及多通道辐射对电磁感应透明的影 响-在梯型四能级系统中上驱动场的Rabi频率对于超窄电磁感应透明及无反转增益的获得起 重要作用-不同的激发方式可改变电磁感应透明的位置-研究了偶极矩关联度在量子干 涉效应中所起的作用-利用缀饰态理论对数值计算结果给出了解释- 关键词： 梯型四能级系统 量子干涉效应 电磁感应透明 无反转增益     

吸收型光学双稳性和自脉动

本文主要是详细评述了吸收型光学双稳性的缀饰模式(dressed mode)理论的进展。但对双稳性理论的基础也给予了一定的注意,重点在这里是要提出,Benza-Lugiato理论怎样能够给出自脉动(self-pulsing)不稳性和高阶分歧的完整的半解析性的描述。我们相信这一评述的价值主要在于缀饰模式方法的普遍性,它的概念框架使它在感兴趣的现象是用非线性微分方程来描述的物理学的许多其它分支中是有价值的。     

Dynamics of a nonlinear parametrically excited partial differential equation

We investigate a parametrically excited nonlinear Mathieu equation with damping and limited spatial dependence, using both perturbation theory and numerical integration. The perturbation results predict that, for parameters which lie near the 2:1 resonance tongue of instability corresponding to a single mode of shape cos nx, the resonant mode achieves a stable periodic motion, while all the other modes are predicted to decay to zero. By numerically integrating the p.d.e. as well as a 3-mode o.d.e. truncation, the predictions of perturbation theory are shown to represent an oversimplified picture of the dynamics. In particular it is shown that steady states exist which involve many modes. The dependence of steady state behavior on parameter values and initial conditions is investigated numerically. (c) 1999 American Institute of Physics.     

Monte Carlo study of the step flow to island nucleation transition for close packed structures

Using joined super-lattice Kinetic Monte Carlo and continuous simulations we study the transition between step flow and two-dimensional island nucleation growth on stepped surfaces for close packed crystalline structures. The numerical analysis is performed in terms of misorientation cut, deposition rate and temperature. We compare the results of the atomistic approach with the predictions of the standard and generalized Burton-Cabrera-Frank (BCF) continuous model. The generalization consists in the explicit inclusion in the theory of the formation and dissolution of mobile dimers on the terraces. We show that the BCF-like continuous theories break down for low temperatures, large off-angle cuts and high deposition rates. In view of these results we critically discuss the basic assumptions of the continuous models.     

Elastic contact mechanics: Percolation of the contact area and fluid squeeze-out

The dynamics of fluid flow at the interface between elastic solids with rough surfaces depends sensitively on the area of real contact, in particular close to the percolation threshold, where an irregular network of narrow flow channels prevails. In this paper, numerical simulation and experimental results for the contact between elastic solids with isotropic and anisotropic surface roughness are compared with the predictions of a theory based on the Persson contact mechanics theory and the Bruggeman effective medium theory. The theory predictions are in good agreement with the experimental and numerical simulation results and the (small) deviation can be understood as a finite-size effect. The fluid squeeze-out at the interface between elastic solids with randomly rough surfaces is studied. We present results for such high contact pressures that the area of real contact percolates, giving rise to sealed-off domains with pressurized fluid at the interface. The theoretical predictions are compared to experimental data for a simple model system (a rubber block squeezed against a flat glass plate), and for prefilled syringes, where the rubber plunger stopper is lubricated by a high-viscosity silicon oil to ensure functionality of the delivery device. For the latter system we compare the breakloose (or static) friction, as a function of the time of stationary contact, to the theory prediction.     

Validity of Parametrized Quark Propagator

Based on an extensively study of the Dyson-Schwinger equations for a fully dressed quark propagator in the “rainbow”approximation, a parametrized fully dressed quark propagator is proposed in this paper. The parametrized propagator describes a confining quark propagator in hadron since it is analytic everywhere in complex p2-plane and has no Lemmann representation. The validity of the new propagator is discussed by comparing its predictions on selfenergy functions A/(p2), Bl(p2) and effective mass M$(p2) of quark with flavor f to their corresponding theoretical results produced by Dyson-Schwinger equations. Our comparison shows that the parametrized quark propagator is a good approximation to the fully dressed quark propagator given by the solutions of Dyson-Schwinger equations in the rainbow approximation and is convenient to use in any theoretical calculations.     

Comments on the linear theory of the gyrotron

The authors present alternative methods for the calculation of the starting current in a gyrotron, and an analysis of the excitation of parasitic modes in gyrotrons operating in a given mode. Numerical examples are presented which check the validity of some of the assumptions made, and the extension of the formalism to the investigation of the stability of an operating mode when parasitic modes can be excited (mode competition) is also discussed. Results from the problem formulation, which is based on the cold-cathode model of Borie and Jodicke (1987), are compared with both linear and fully nonlinear models. These results illustrate the importance of using a correct model for the field profile and the influence of numerical uncertainties on the results obtained using a linear theory for mode competition. It is noted that the results obtained using the nonlinear theory of mode competition are usually numerically more stable and easier to interpret     

Higher-order inertial Alfvén wave dressed solitons,quasiperiodic structures,and chaos in plasmas

The higher-order, low-amplitude inertial Alfvén wave (IAW) dressed soliton and chaos are investigated in a magnetized plasma. In the linear limit, the dispersion relation for propagation of IAWs in plasmas is also obtained in the presence of electron thermal effects and illustrated numerically. It is found that the electron inertial length plays an important role for wave dispersion effects and its phase speed is increased on including the electron temperature in the model. The reductive perturbation method is employed to obtain the first-order IAW Korteweg–de Vries (KdV) soliton and second-order dressed soliton solutions analytically, which gives electron density dip (or rarefactive) structure and moves with super Alfvénic speed in plasmas. The numerical illustrations of the KdV and dressed IAW solitons are also presented by using the laboratory and space plasma parameters given in the literature. Furthermore, a numerical study of quasi-periodicity and chaotic behaviour of IAWs in the presence of external periodic force is also discussed in detail. The effects of plasma beta (which depends on plasma density, electron temperature, and magnetic field intensity) and obliqueness of the wave propagation on the formation of nonlinear Alfvénic wave structures have also been presented.