Sound radiation from rectangular baffled and unbaffled plates

The radiation efficiency of a flat rectangular plate is often used as a basis on which to represent the sound radiation from more complex plate-like structures. The solution for a plate set in a rigid baffle is well known, including the radiation efficiency for multi-modal response of the plate. In this case the assumption is usually made that each mode within a given frequency band has equal modal vibration energy. This paper explores a number of limitations of this simple result. First, the extent to which the radiation efficiency for a particular forcing point deviates from the modal-average result is investigated. Second, the difference is shown between the results for a baffled plate and an unbaffled plate. For a multi-modal response, an empirical formula is also presented which allows the radiation efficiency to be estimated for the unbaffled case. Finally, the effect of different boundary conditions on both baffled and unbaffled results is demonstrated by comparing the results for guided boundaries with those for simply supported boundaries.     

On detonation initiation by a temperature gradient for a detailed chemical reaction models

The evolution from a temperature gradient to a detonation is investigated for combustion mixture whose chemistry is governed by a detailed chemical kinetics. We show that a detailed chemical reaction model has a profound effect on the spontaneous wave concept for detonation initiation by a gradient of reactivity. The evolution to detonation due to a temperature gradient is considered for hydrogen-oxygen and hydrogen-air mixtures at different initial pressures. It is shown that the minimal length of the temperature gradient for which a detonation can be ignited is much larger than that predicted from a one-step chemical model.     

On statistical mechanics of systems with highly singular two-body potentials

A finite volume statistical mechanics for highly singular two-body potentials is studied. The case of “point” hard-core particles (Lennard-Jones type two-body potentials) is discussed and the mathematical background for this physical idealization is given. Firstly the definition of a self-adjoint Hamiltonian for such a system is considered. Then a natural cutoff procedure for two-body highly singular potentials is proposed. The main result is the proof of a convergence theorem for partition sums (or free energies) when the cutoff parameter is removed to infinity. The question of stability of the cutoff interactions is also discussed. These results are illustrated by a consideration of the Lennard-Jones potential (12-6). Our results are valid in all dimensions greater than two and for potentials being not inevitably spherically symmetric.     

Effect of Finite Spectral Width on the Modulational Instability of Langmuir Waves described by a Nonlinear Schrödinger Equation

By using the two-point space correlation function an equation for the power spectral density for a random Langmuir field has been derived. The dispersion relation for a monochromatic wave is regained for a delta spectrum. For a Gaussian spectrum, the maximum growth rate is less than that for a monochromatic wave. For a “meander spectrum”, the growth rate is increased with the width of the spectrum in the first stage then decreased for further increase of the width.     

基于一组Kalman滤波器信息融合的故障诊断

为了能及时准确地诊断发动机的传感器和执行机构故障,本文提出了基于一组Kalman滤波器信息融合的方法进行故障诊断。首先根据传感器特性设计了一组滤波器用于传感器故障诊断、隔离,每个滤波器针对一个传感器进行设计;其次根据执行机构故障特性设计了一组Kalman滤波器进行执行机构偏差估计,从而对执行机构进行故障诊断、隔离;接着给出了传感器、执行机构信息融合的诊断方案;最后分别给传感器、执行机构添加故障进行方案验证,仿真结果得出在传感器或者执行机构任意部件出故障的情况下,该融合方法可以有效地诊断并隔离出有故障的传感器或者执行机构。     

A path integral approach to inclusive processes

The single-particle inclusive differential cross-section for a reaction is written as the imaginary part of a correlation function in a forward scattering amplitude for in a modified effective theory. In this modified theory the interaction Hamiltonian equals in the original theory up to a certain time. Then there is a sign change and becomes nonlocal. This is worked out in detail for scalar field models and for QED plus the abelian gluon model. A suitable path integral for direct calculations of inclusive cross sections is presented. Received: 8 March 2000 / Published online: 6 July 2000     

Diffusion over a saddle with a langevin equation

The diffusion problem over a saddle is studied using a multidimensional Langevin equation. An analytical solution is derived for a quadratic potential and the probability to pass over the barrier deduced. A very simple solution is given for the one-dimensional problem and a general scheme is shown for higher dimensions.     

On the Gribov ambiguity in the Faddeev-Popov procedure

The standard Faddeev-Popov procedure for quantization of a gauge theory is modified so as to be valid even when the Gribov problem is present. The hamiltonian is employed and a definite expression for the path integral is obtained for a wide class of gauges.     

Rigorous solution to a quantum statistical mechanical laser model

A quantum mechanical laser model with relaxation and pumping mechanisms is solved rigorously. A basic equation for the density matrix is derived by the damping theory and is transformed into a corresponding c-number equation for a (quasi-) probability density. This is done with the aid of the quantum phase space method. The probability density is expanded in terms of orthogonal polynomials. The expansion coefficients are solved to give a continued fraction. A complete solution is obtained, namely, time evolution of the probability density is determined as well as that for certain physical quantities. The solution is valid even for strong coupling between photons and atoms: it is free from restriction on system parameters. Detailed studies on dynamics are performed for typical values of the system parameters. This is a prototype of interacting quantum nonequilibrium systems. Relevance to systems other than a laser is briefly mentioned.     

Variational principles for scattering in the generator coordinate method

The generator coordinate method (GCM) wave function is used as a trial function in a Kohn type variational principle for scattering phase shifts. It is shown that a GCM trial function is a solution of the variational equations if the Hill-Wheeler integral equation is satisfied subject to an appropriate boundary condition. A new method for introducing the scattering boundary condition is presented. There is a uniqueness theorem for the phase shift.     

Resonance oscillation damping of a scanning microscope probe by a near-surface viscous liquid layer

Viscous liquid layer motion between a probe with a tip shaped as a paraboloid of revolution and a surface is considered for semicontact-mode operation of a scanning probe microscope. The presence of a viscous liquid layer leads to energy dissipation and is one of the factors responsible for the decrease in the probe oscillation amplitude. The Reynolds equation for viscous liquid motion is used to obtain an analytic solution to the problem. The formula derived for the loss is compared with experimental data obtained for probes and layers with various curvature radii and viscosities.     

Image potential for a medium with wavevector and frequency dependent dielectric function

The equation for the quasistatic image potential induced by a charge is derived for a semiinfinite medium with wavevector and frequency dependent dielectric function. The equation is solved exactly for a dielectric function which is local in the direction perpendicular to the surface. This result is applied to the case of a metal, semiconductor and insulator; the Schottky effect is discussed.     

Cross sections for the photodisintegration of a deuteron and neutron capture by a proton calculated for the case of nonlocal potential

The processes of deuteron photodisintegration by a gamma-quantum and the radiative capture of a neutron by a proton with the emission of a gamma-quantum are considered. Interaction between nucleons is described by a nonlocal potential of the Yamaguchi type but allowing for repulsion due to the nucleon cores. In contrast to other potentials, the Schroedinger equation is solved exactly for the proposed potential. The potential is more exactly defined in comparison with the previously obtained values for the parameters; information on this potential is important in solving certain fundamental problems in nuclear theory. The effective cross sections for photodisintegration of a deuteron and for radiative capture are computed. Calculations show that the proposed potential makes it possible to describe the photodisintegration processes quite accurately for intermediate (up to 20 MeV) energies. The cross section computed for radiative capture is in somewhat better agreement with experiment than is the same cross section determined for other potentials.     

Revisiting the moving force problem

The problem of the vibration of a beam subject to a travelling force is considered. The purpose of the study is to develop simple tools for finding the maximum deflection of a beam for any given velocity of the travelling force. It is shown that, for given boundary conditions, there exists a unique response-velocity dependence function. A technique to determine this function is suggested, which is based on the assumption that the maximum beam response can be adequately approximated by means of the first beam mode. To illustrate this, the maximum response function is calculated analytically for a simply supported (SS) beam and constructed numerically for a clamped-clamped beam. The effect of the higher modes on the maximum response is investigated, and the relative error of the one-mode approximation for a SS beam is constructed. The estimates obtained substantiate the assumption about adequacy of the one-mode approximation in a wide range of velocities; in particular, the relative error in the neighborhood of the velocity that results in the largest response is less than one percent.     

Simulation of a quantum NOT gate for a single qutrit system

A three-level system based an a three-level atom interacting with a detuned cavity is considered. Because of the fact that the three-level atom defines a total normalized state composed of superposition of three different single-level states, it is assumed that such a system implements a qutrit. In order to achieve a quantum NOT gate for a single qutrit, the respective Schrödinger equation is solved numerically within a two-photon rotating wave approximation. For small values of one-photon detuning, there appear decoherence effects. Meanwhile, for large values of one-photon detuning, an ideal quantum NOT gate for a single qutrit is achieved. An expression for the execution time of the quantum NOT gate for a single qutrit as a function of the one-photon detuning is found.     

Gravitational stability of a massless scalar field

A solution is obtained to the Einstein equations for a static, spherically symmetric, massless scalar field. The stability of a static, massless scalar field for a point source is studied. It is found that the field is unstable for small ratios of the scalar charge of the source to its mass but is stable for large ratios. It is proven that there exists a dimensionless number which limits the region of stability for the field.Translated from Izvestiya Vysshikh Uchebnyk Zavedenii, Fizika, No. 7, pp. 79–83.     

Generalized Noether theorems in canonical formalism for field theories and their applications

A generalization of Noether's first theorem in phase space for an invariant system with a singular Lagrangian in field theories is derived and a generalization of Noether's second theorem in phase space for a noninvariant system in field theories is deduced. A counterexample is given to show that Dirac's conjecture fails. Some preliminary applications of the generalized Noether second theorem to the gauge field theories are discussed. It is pointed out that for certain systems with a noninvariant Lagrangian in canonical variables for field theories there is also a Dirac constraint. Along the trajectory of motion for a gauge-invariant system some supplementary relations of canonical variables and Lagrange multipliers connected with secondary first-class constraints are obtained.     

Numerical reconstruction stability of fiber Bragg gratings

Traditional algorithms for solving the inverse scattering problem for a fiber Bragg grating are described, and a new numerical method for this problem is developed. The method is based on the fast inversion of a matrix using its Toeplitz symmetry and on a special “inner-bordering” procedure. It is shown that the method is equally efficient as the well-known discrete layer peeling method but exceeds the latter in accuracy, especially for high-reflectance gratings. The stability of the proposed method with respect to initial data errors is demonstrated.     

Monte Carlo analysis of the internal structure of light scattering particles with slit-scan illumination

An algorithm based upon a Monte Carlo procedure for calculating the scattering and absorption by a host particle containing a distribution of particulate inclusions is described. The host particle is sufficiently large so that ray optics can be applied. The inclusions are too small for ray optics but sufficiently large so that the full boundary-value formalism must be used. A major consideration is to determine whether the internal structure is better resolved when slit-scan illumination is utilized rather than plane wave illumination. The algorithm is tested for a layered sphere for which the boundary value solution is available.