Technique for determining the channel expansion rate at the stage of electrical breakdown using a grounded intercepting ring

A method is described that allows one to study the conductivity dynamics of a channel produced by explosion of a wire at the stage of electrical breakdown. Experimental data have been presented for the expansion rate of the conductivity channel in extended (up to 1.9 m long) arbitrarily shaped gapes that were produced by an exploding copper wire 90 µm in diameter. The initial stored energy and applied voltage were, respectively, 2.7–3.7 kJ and 8–10 kV. It has been shown that the expansion rate of the conductivity channel coincides with the propagation rate of a shock wave and is inversely proportional to the square root of its radius and propagation time. The radius of the shock wave is a linear function of the square root of its propagation rate. Experimental data are in satisfactory agreement with the calculated results obtained by Lin [18] in terms of the model of an intense shock wave. It has been shown that the diameter of the conductivity channel depends on the position of the trailing edge of the shock wave.     

Perturbation theory for QED bound states

A new method is presented for deriving a systematic perturbative expansion for QED bound states, which does not rely upon solving any new or old equation. The starting point is a given nonperturbative zeroth order Green's function, obtained by a suitable “relativistic dressing” of the nonrelativistic Green's function for the Schrödinger equation with Coulomb potential, which embodies the Coulombic bound states and is known. The comparison with the complete Green's function as given by standard perturbative QED gives a perturbative kernel which is then used for the expansion of the QED Green's function in terms of the given non-perturbative zeroth order Green's function.     

负梯度水文环境下海山对声传播的影响

利用一次南海海山环境下的声传播实验数据,研究了负梯度水文环境下海底山对声传播的影响。针对实验数据中的传播损失异常,从射线声学角度给出了合理的解释,表明海底山的存在引起传播损失在距离上剧烈波动。在距离接收阵较近的7.6 km处,声源位于海山斜坡上,斜坡的反射使接收传播损失减小约8 dB,体现出斜坡增强特征。当声源位于海山后,海底山的遮蔽作用使23.8 km处的传播损失增加超过20 dB,不同位置处海山遮蔽效应的差异使传播损失随距离起伏。利用抛物模型对实验环境下的声传播进行了定量仿真,仿真传播损失同实验结果符合,验证了实验数据中海底山的反射和遮蔽作用。此外,对实验环境下海山的遮蔽损失进行分析,发现在不同声源位置处,海山遮蔽损失在特定频带上同频率对数具有线性关系。      

深远海线性内波条件下声场时间相关性的空间分布

深海声场特定的干涉结构导致其时间相关性的空间起伏,研究这种空间特性可以为水声信号的探测与处理提供重要参考。利用抛物方程声场仿真模型,联合Monte-Carlo数值方法计算分析了深远海线性内波条件下声场时间相关性的空间分布特性。与现有的研究相比,给出了时间相关性的距离和深度起伏特征。结果表明,当接收达到一定距离,声场时间相关性的空间分布具有与声场干涉条纹类似的结构,声场干涉越强,时间相关性越好。此外,声源频率和声速标准差的变化会引起时间相关性空间分布规律的改变,且会聚区传播模式下的改变强于深海声道传播模式。      

Stochastic differential equation analysis for sound scattering by random internal waves in the ocean

The scattering of a weakly divergent narrow sound beam by random inhomogeneities of a fluctuating ocean is considered in the coupled-mode approximation. The random index of sound refraction is described using the Garrett-Munk internal wave spectrum. The problem is solved using the stochastic differential equations for the first-and second-order statistical moments of the acoustic field. The equations are formulated according to the cumulant expansion method. The existence of weakly divergent narrow sound beams in long-range sound propagation was one of the last discoveries of L.M. Brekhovskikh, to which he attached much importance. The concentration of sound into narrow beams away from the axis of the underwater sound channel was first observed experimentally and then explained by Brekhovskikh and his former students Goncharov, Kurtepov, and Petukhov. In the present paper, the scattered field intensity of a sound beam is calculated for different frequencies and source depths. Analytical expressions are obtained for the coefficients of the differential equation. The intermode energy transfer that accompanies the long-range propagation of a weakly divergent sound beam is analyzed. A comparison with the conventionally used Monte Carlo simulation in the parabolic equation approximation is performed.     

The extended Fourier pseudospectral time-domain method for atmospheric sound propagation

An extended Fourier pseudospectral time-domain (PSTD) method is presented to model atmospheric sound propagation by solving the linearized Euler equations. In this method, evaluation of spatial derivatives is based on an eigenfunction expansion. Evaluation on a spatial grid requires only two spatial points per wavelength. Time iteration is done using a low-storage optimized six-stage Runge-Kutta method. This method is applied to two-dimensional non-moving media models, one with screens and one for an urban canyon, with generally high accuracy in both amplitude and phase. For a moving atmosphere, accurate results have been obtained in models with both a uniform and a logarithmic wind velocity profile over a rigid ground surface and in the presence of a screen. The method has also been validated for three-dimensional sound propagation over a screen. For that application, the developed method is in the order of 100 times faster than the second-order-accurate FDTD solution to the linearized Euler equations. The method is found to be well suited for atmospheric sound propagation simulations where effects of complex meteorology and straight rigid boundary surfaces are to be investigated.     

Long-range sound propagation in the northeastern Atlantic

Experimental data on the long-range propagation of explosion-generated signals are analyzed. The experiments were performed in the northeastern Atlantic under the conditions of a two-axis underwater sound channel. The sound field in the upper channel was governed by the vertical redistribution of the ray structure and sound energy under the influence of a smooth increase in the depth of the channel’s axis along the propagation path. The explosions were produced in the upper sound channel at a depth of 200 m, which was constant along the path. The time structure of the sound field is analyzed for the upper channel (a reception depth of 200 m) and for deeper layers lying somewhat below the boundary between the upper and lower sound channels (a reception depth of 1200 m). The deviation of the decay law obtained for the sound field level in the upper channel from the cylindrical law is used to estimate the attenuation coefficient. The low-frequency (several hundreds of hertz) attenuation coefficients experimentally determined with allowance for the sound field redistribution agree well with the calculated sound absorption in seawater. The attenuation coefficients determined by the differential method also agree well with the absorption calculated by the formulas proposed earlier. The analysis of the time structure of the sound field near the boundary between the upper and lower channels reveals a permanent insonification of this horizon by weak water-path signals propagating with the velocity typical of the signals traveling in the upper channel.     

Renormalized expansions for functional integrals: Generalized coherent potential approach to lattice models

An expansion for generating functionals (partition sums) of models expressed as lattice functional integrals with local (on-site) interactions is presented. This expansion renormalizes the standard perturbative expansion in such a way that certain its terms are summed up non-perturbatively. A non-self-consistent and a self-consistent versions of the expansion are formulated and criteria for an estimation of validity of approximations resulting from the both expansions are given. The simplest approximation being the first term of this expansion is applied to two lattice models: classicalN-component spin model and the model of non-interacting electrons in a disordered crystal. In the former model the critical temperature is calculated within 10% accuracy and in the latter, the coherent potential approximation is obtained.     

Long-range sound propagation in the Mediterranean Sea

The data of several experiments on the long-range propagation of explosion-generated and tonal sound signals are analyzed. The experiments are performed by the Acoustics Institute in the Mediterranean Sea with a fully developed sound channel. A substantial difference is observed for the propagation conditions in the western and eastern parts of the sea. This difference concerns the vertical sound speed profiles, the time structures of the sound field in the underwater sound channel, the duration of the explosion-generated signal, and the positions of the convergence zones. The experiment is compared with calculations. The observed difference in the experimental and calculated positions of the first convergence zone is explained by the imperfection of the relation used to recalculate the salinity, water temperature, and hydrostatic pressure to the sound speed. In spite of substantial difference in the propagation conditions on two 600-km paths, the experimental low-frequency attenuation coefficients on these paths (and on some shorter ones) agree well with each other for the frequency band of several kilohertz. The data are also close to those published for another 600-km path. All the paths mentioned run in different parts of the Mediterranean Sea. The frequency dependence of sound attenuation (absorption) can be well described by the relation that accounts for the absorption caused by the boron present in the sea water.     

浅海不确定声场的随机多项式展开法研究

为获得求解浅海不确定声场的普适模型,建立了随机多项式展开法与Helmholtz方程的非嵌入式耦合模型,其间运用概率配点法求解多项式系数。针对仅当海水深度不确定时的Pekeris波导、声速剖面和海深均不确定时的Pekeris波导以及下限深度不确定温跃层等几种情形,计算了传播损失概率密度分布。结果表明所建模型对声场计算模型普适性强,计算精度和计算效率高,可用于研究含多个不确定环境参数、声速剖面复杂的浅海环境中声传播的不确定性。      

The Virial Expansion of a Dilute Bose Gas in Two Dimensions

In terms of the s-wave phase shift of the two-body scattering at thermal wavelength, a systematic perturbative expansion of the Virial coefficients is developed for a two-dimensional dilute system of bosons in its gaseous phase at low temperature. The thermodynamic functions are calculated to the second order of the expansion parameter. The observability of the universal low energy limit of the two dimensional phase shift with a quasi-two dimensional atomic gas in an anisotropic trap is discussed.     

Landau theory of magnetic phase diagrams and first order magnetisation processes

The Landau free energy expansion up to sixth order in the magnetisation has been used to study ferro- and paramagnetic phases in zero and finite applied magnetic fields. Magnetic phase diagrams are determined in terms of Landau coefficient ratios which indicate first order and metamagnetic phase transitions. In addition the critical magnetic field and specific magnetisations corresponding to first order magnetisation processes are calculated in terms of these coefficients. A method of evaluating Landau coefficients is also demonstrated.     

Long-range sound propagation in the central part of the Barents Sea

The data of the experiments on long-range propagation of explosion-generated and tonal sound signals, which had been performed in different years in the central part of the Barents Sea in summertime conditions, are used to analyze the space structure of the sound field intensity, to estimate the attenuation coefficient due to the sound energy loss in the bottom sediments, and to determine the frequency dependence of this coefficient. A comparison of the data on the long-range propagation of explosion-generated signals is performed between two experiments carried out on the same 230-km-long path crossing the Central Basin of the Barents Sea, several years in succession. The two experiments differ in the propagation conditions: in the first experiment, a near-bottom sound channel extends along the entire path, and in the second experiment, the path crosses a frontal zone characterized by fairly complex variations of the sound speed field. Calculations are carried out to show that the specific behavior of the frequency dependence of attenuation can be explained by the powerlaw frequency dependence (with an exponent of 1.4) of the sound absorption in the water-saturated upper layer of the bottom sediments. It is also shown that the difference in the decay laws obtained for the sound field levels in the two experiments is caused by the difference in the corresponding hydrological conditions.     

Optimized constraints for the linearized geoacoustic inverse problem

A geoacoustic inversion scheme to estimate the depth-dependent sound speed characteristics of the shallow-water waveguide is presented. The approach is based on the linearized perturbative technique developed by Rajan et al. [J. Acoust. Soc. Am. 82, 998-1017 (1987)]. This method is applied by assuming a background starting model for the environment that includes both the water column and the seabed. Typically, the water column properties are assumed to be known and held fixed in the inversion. Successful application of the perturbative inverse technique lies in handling issues of stability and uniqueness associated with solving a discrete ill-posed problem. Conventionally, such problems are regularized, a procedure which results in a smooth solution. Past applications of this inverse technique have been restricted to cases for which the water column sound speed profile was known and sound speed in the seabed could be approximated by a smooth profile. In this work, constraints that are better suited to specific aspects of the geoacoustic inverse problem are applied. These techniques expand on the original application of the perturbative inverse technique by including the water column sound speed profile in the solution and by allowing for discontinuities in the seabed sound speed profile.     

Transverse-longitudinal coherence function of a sound field for line-of-sight propagation in a turbulent atmosphere

Using the narrow-angle and Markov approximations, a formula for the transverse-longitudinal coherence function of a sound field propagating in a turbulent atmosphere with temperature and wind velocity fluctuations is derived. This function, which applies to observation points that are arbitrarily located in space, generalizes the transverse coherence function (coherence when the observation points are in a plane perpendicular to the sound propagation path), which has been studied extensively. The new result is expressed in terms of the transverse coherence function and the extinction coefficient of the mean sound field. The transverse-longitudinal coherence function of a plane sound wave is then calculated and studied in detail for the Gaussian and von Kármán spectra of temperature and wind velocity fluctuations. It is shown, for relatively small propagation distances, that the magnitude of the coherence function decreases in the longitudinal direction but remains almost constant in the transverse direction. On the other hand, for moderate and large propagation distances, the magnitude of the coherence decreases faster in the transverse direction than in the longitudinal. For some parameters of the problem, the coherence function has relatively large local maxima and minima as the transverse and longitudinal coordinates are varied. With small modifications, many results obtained in the paper can be applied to studies of electromagnetic wave propagation in a turbulent atmosphere.     

Time-domain impedance formulation for transmission line matrix modelling of outdoor sound propagation

Outdoor sound propagation modelling has attracted considerable attention in the past and has lead to many analytical and numerical models. More recently, the increase of computational power has led to consider time-domain methods that enable to consider transient phenomena. Among these models, the transmission line matrix (TLM) method has been proposed, but the sound absorption at boundaries appears to be a somewhat underdeveloped aspect of this approach. In this paper, a specific implementation of impedance boundary condition is proposed. The method is based on the approximation of the impedance as a sum of linear systems, which allows the formulation of an equivalent impedance model in the time-domain. The proposed implementation is applied for two common impedance models of porous material. Numerical simulations have been carried out in the case of sound propagation over a flat ground with and without an impedance discontinuity, and for several values of specific airflow resistivity. TLM numerical predictions expressed in terms of excess attenuation relative to free field show a good agreement with analytical solutions.     

无碰撞等离子体的相干重整化理论

本文提出对Власов-Poisson方程进行微扰处理的一种重整化方案。利用图形展开方法证明了该理论到任意阶微扰的可重整化性质。给出了重整化传播量的一般形式。分析了相干项和绝对非相干项的物理意义。给出了重整化介电函数的正确表示,并对它的意义做了讨论。通过和以往重整化理论的比较,指出这种重整化方案是一种真正的完全重整化。 关键词：     

On the calculation of the transmission line parameters for long tubes using the method of multiple scales

The present paper deals with the classical problem of linear sound propagation in tubes with isothermal walls. The perturbation technique of the method of multiple scales in combination with matched asymptotic expansions is applied to derive the first-order solutions and, in addition, the second-order solutions representing the correction due to boundary layer attenuation. The propagation length is assumed to be so large that in order to obtain asymptotic solutions which extend over the whole spatial range the first-order corrections to the classical attenuation rates of the different modes come into play as well. Starting with the case of the characteristic wavelength being large compared to the characteristic dimension of the duct, the analysis is then extended to the case where both of these quantities are of the same order of magnitude. Furthermore, the transmission line parameters and the transfer functions relating the sound pressures at the ends of the duct to the axial velocities are calculated.     

Improved calculations of quark distributions in hadrons: the case of the pion

The earlier introduced method of calculation of quark distributions in hadrons, based on QCD sum rules, is improved. The imaginary part of the virtual photon forward scattering amplitude on some hadronic current is considered in the case, when initial and final virtualities of the current , and are different, . The operator product expansion (OPE) in , is performed. The sum rule for quark distribution is obtained using double dispersion representation of the amplitude on one side in terms of calculated in QCD OPE and on the other side in terms of physical states contributions. Double Borel transformation in , is applied to the sum rule, killing background non-diagonal transition terms which deteriorated the accuracy in previous calculations. The case of the valence quark distribution in the pion is considered, which was impossible to treat by the previous method. OPE up to dimension 6 operators is performed and leading order perturbative corrections are accounted. Valence u-quark distribution in was found at intermediate x, , and normalization point . These results may be used as input for evolution equations. Received: 14 July 1999 / Published online: 6 March 2000