The energy spectrum of fully developed turbulence generated by random stirring

For fully developed turbulence in an incompressible fluid described by the Navier-Stokes equations with Gaussian random forces the relation between the energy spectrum and the stirring mechanism is investigated within a variational approach. Therein, the effect of nonlinear mode coupling is approximated by a wave number dependent eddy viscosity determined via a nonlinear integral equation for the energy spectrum. For various stirring spectra analytic approximations are compared with the solution obtained numerically with a cutoff in the integral kernel which ensures in eddy relaxing processes that the stirring forces exert strain only on scales larger than the eddy size. The results are compared with renormalization group calculations and closure approximations. Random forces injecting energy at a ratek ^–1 into the wave number banddk aroundk lead to a Kolmogorov distribution of energy. The spectrum of small-scale velocity fluctuations is shown to be universal in the sense that it remains unchanged under variations of the long wavelength stirring spectra.     

Semiclassical stochastic trajectory investigation of vibrational-rotational-translational-phonon energy transfer: The role of attractive forces

A semiclassical stochastic trajectory (SST) approach to the study of collision induced transitions in gas molecule-solid surface scattering is used to investigate vibrational-rotational-transiational-phonon energy transfer in the H₂, D₂, HD-(smooth)Pt systems. State-to-state rotationally and ro-vibrationally inelastic transition probabilities are determined using interaction potentials with varying strength of the long-range attractive component. Rigid and non-rigid surfaces are considered, the latter via the generalized Langevin-ghost atom technique. The results demonstrate that addition of a significant attractive interaction broadens the rotationally and ro-vibralionally inelastic probability distributions. This leads in the latter case to the replacement of the near-resonant vibration-rotation mechanism for vibrational relaxation by a much more effective and uniform vibration-rotation, translation mechanism.     

Fluctuations in Derrida's random energy and generalized random energy models

The fluctuations of the finite-size corrections to the free energy per site of the random energy model (REM) and the generalized random energy model (GREM) are investigated. Almost sure behavior for the corrections of order (logN)/N is given. We also prove convergence in distribution for the corrections of order 1/N.     

Study of the performance of a thermoelectric generator transformation of the thermal energy conveyed by a heat transfer fluid into electrical energy

A mathematical model to predict the maximum energy conversion efficiency of the thermoelectric generator is developed to improve the performance and maximize the energy conversion efficiency of the thermoelectric power generator. The studied device corresponds to an original configuration of thermoelectric modules mounted on the peripheral surfaces of two channels, one of the channels is crossed by hot fluid and the other by a cold fluid. First, the effect of the flow rate was studied to choose the flow rate adapted to our study for three different configurations of the thermopile, the co-current configuration, the counter-current configuration, and the sandwich configuration. Then a comparison was made to choose the best configuration between these three studied configurations by addressing their thermoelectric performances. The results revealed that the sandwich configuration is much better than the co-current and counter-current configurations and reduces the surface area occupied by the TEG by half while generating more power than a solar panel.     

Waves and energy in random elastic guided media through the stochastic wave finite element method

Energy propagation in random viscoelastic media is considered in this Letter. The forced response of uncertain waveguide subject to time harmonic loading is treated. This energy model is based on a spectral approach called the “Stochastic Wave Finite Element” (SWFE) method which is detailed in this Letter. Assuming that the random properties are spatially homogeneous in the media, the SWFE is a hybridization of the deterministic wave finite element and a parametric probabilistic approach. The proposed model is applicable in a wide frequency band with reduced time consumption. Numerical examples show the effectiveness of the proposed approach to predict the statistics of kinematic and quadratic variables of guided wave propagation. The results are compared to Monte Carlo simulations.     

Vibration of a beam due to a random stream of moving forces with random velocity

The problem of dynamic response of a beam to the passage of a train of concentrated forces with random amplitudes and velocities is considered. Force arrivals at the beam are assumed to constitute the point stochastic process of events. Thus, the excitation process is an idealization of vehicular traffic loads on a bridge. An analytical technique is developed to determine the response of the beam. Explicit expressions for the expected value and the variance of the beam deflection are provided. As an example, the response of a beam to a stationary stream of forces is determined for some practical situations, and discussed.     

On the interpretation of random forces derived by projection operators

We study the derivation of a Langevin equation from a microscopic basis in order to elucidate the nature of the random force. We arrive at the conclusion that the consistent interpretation of the microscopic Langevin equation in terms of a stochastic differential equation (SDE) is according to I o rules. In addition, the random force is in general not Gaussian, and it is hence not completely characterized by its second moments.     

Chaotic stirring by a mesoscale surface-ocean flow

The horizontal stirring properties of the flow in a region of the East Australian Current are calculated. A surface velocity field derived from remotely sensed data, using the maximum cross correlation method, is integrated to derive the distribution of the finite-time Lyapunov exponents. For the region studied (between latitudes 36 degrees S and 41 degrees S and longitudes 150 degrees E and 156 degrees E) the mean Lyapunov exponent during 1997 is estimated to be lambda( infinity )=4x10(-7) s(-1). This is in close agreement with the few other measurements of stirring rates in the surface ocean which are available. Recent theoretical results on the multifractal spectra of advected reactive tracers are applied to an analysis of a sea-surface temperature image of the study region. The spatial pattern seen in the image compares well with the pattern seen in an advected tracer with a first-order response to changes in surface forcing. The response timescale is estimated to be 20 days. (c) 2002 American Institute of Physics.     

The random energy model in a magnetic field and joint source-channel coding

We demonstrate that there is an intimate relationship between the magnetic properties of Derrida’s random energy model (REM) of spin glasses and the problem of joint source-channel coding in Information Theory. In particular, typical patterns of erroneously decoded messages in the coding problem have “magnetization” properties that are analogous to those of the REM in certain phases, where the non-uniformity of the distribution of the source in the coding problem plays the role of an external magnetic field applied to the REM. We also relate the ensemble performance (random coding exponents) of joint source-channel codes to the free energy of the REM in its different phases.     

The stochastic collocation method for radiation transport in random media

Stochastic spectral expansions are used to represent random input parameters and the random unknown solution to describe radiation transport in random media. The total macroscopic cross section is taken to be a spatially continuous log-normal random process with known covariance function and expressed as a memoryless transformation of a Gaussian random process. The Karhunen-Loève expansion is applied to represent the spatially continuous random cross section in terms of a finite number of discrete Gaussian random variables. The angular flux is then expanded in terms of Hermite polynomials and, using a quadrature-based stochastic collocation method, the expansion coefficients are shown to satisfy uncoupled deterministic transport equations. Sparse grid Gauss quadrature rules are investigated to establish the efficacy of the polynomial chaos-collocation scheme. Numerical results for the mean and standard deviation of the scalar flux as well as probability density functions of the scalar flux and transmission function are obtained for a deterministic incident source, contrasting between absorbing and diffusive media.     

Spectral analysis of a nonlinear oscillator driven by random and periodic forces. I. Linearized theory

We have combined the techniques of statistical and harmonic linearization to develop a linearized approximation theory for the calculation of the second-order statistics (i.e., autocorrelation functions and spectral densities) of nonlinear systems driven by both random and periodic forces. For the special case of a Duffing oscillator (a damped anharmonic oscillator with a cubic nonlinearity) driven by Gaussian white noise and by a sinusoidal force, explicit expressions for the renormalized (linearized) frequency, the autocorrelation function, and the spectral density of the oscillator displacement in terms of all the system parameters have been derived. We have determined the region of the parameter space in which the applied periodic force has a significant influence on the second-order statistics of the oscillator.This research was supported by the Office of Naval Research, by the National Science Foundation under grant No. CHE78-21460 and by a grant from Charles and Reneé Taubman.     

二维随机介质中的能量分布和频谱特性

研究了二维随机介质中能量的空间分布和一些特定区域的频谱特性.结果显示介质中能量呈局域化分布,其分布与介质中颗粒的随机分布有关,还与激发光的波长有密切的关系,介质中能量聚集的区域和介质的准封闭区域有一定关系但并非一一对应.所考察的各准封闭区域的频谱均随时间变化,在同一激发光的激励下各准封闭区域的频谱均不相同,而同一区域在不同的激发光的激励下频谱也不相同.当激发波长与准封闭区域的结构参数偏差较大时,频谱中谱峰会出现此消彼涨的模式竞争现象,而且能量衰减得较快;而当激发波长与该结构参数较接近时,相应的频谱中存在一 关键词： 激光物理 有限时域差分法 局域化 频谱特性     

Elastic properties of a magnetic fluid with an air cavity retained by levitation forces

The paper describes the process of an air cavity rising in a magnetic fluid filling a tube with a bottom, transport, and retention of the cavity by magnetic levitation forces. The elastic and dissipative properties of a vibratory system with an inertial element that is a column of a magnetic fluid over an air cavity are considered. The possibility of using a transported air cavity as a movable reflector for a sound wave is evaluated.     

Free energy and some sample path properties of a random walk with random potential

We study the asymptotic behavior of the free energy for a model (defined by Sinai) of one-dimensional random walk with random potential. In particular, we obtain a central limit theorem and a strong law of large numbers for this free energy. We use some results on the free energy to study some sample path properties of this random walk which are related respectively to its recurrence and localization. Some exponents describing the recurrence and localization are found.     

The effect of random errors on a large statistical energy analysis model

The framework of analysis known as Statistical Energy Analysis has many important applications particularly in systems where detailed information is not available. As a result of the approximations made, to simplify the calculations, random error can be introduced into the SEA model. For large systems this gives rise to uncertainty in the energy levels. It is shown that the effect of these errors on the model depends on the “shape” of the model. A compact model dominated by short paths is less affected than a model controlled by long paths. In either case the ratio of the average error in the resultant energy level to the average error in the coupling loss factor decreases as the errors increase. This means that large models may be used with confidence even when based on data that is known to be approximate.     

Fluctuation-induced forces between inclusions in a fluid membrane under tension

We develop an exact method to calculate thermal Casimir forces between inclusions of arbitrary shapes and separation, embedded in a fluid membrane whose fluctuations are governed by the combined action of surface tension, bending modulus, and Gaussian rigidity. Each object's shape and mechanical properties enter only through a characteristic matrix, a static analog of the scattering matrix. We calculate the Casimir interaction between two elastic disks embedded in a membrane. In particular, we find that at short separations the interaction is strong and independent of surface tension.