二维渗流相关长度ξ(p)的幂估计(英文)

相关长度ξ(p)是渗流理论中最重要的一个量。本文对它给出了一个幂估计     

STABILITY NUMBER IN SUBCLASSES OF P5-FREE GRAPHS

Two new hereditary classes of P5-free graphs where the stability number can be found in polynomial time are proposed. They generalize several known results.     

Elastic wave thermal fluctuations,ultrasonic waveforms by correlation of thermal phonons

It is widely recognized that acoustic degrees of freedom coupled to a thermal bath have amplitudes which fluctuate with a mean square proportional to temperature; this is the basis for the Debye theory of the heat capacity of insulating solids. It is shown here that these elastic wave thermal phonons have correlation functions identical to the system's ultrasonic Green's function, and furthermore that thermal noise in ultrasonic detectors should have correlation functions equivalent to conventional waveforms obtained by active transmission and reception. This suggests the possibility of doing ultrasonics without a source. Theory for the identity is presented, and several room temperature laboratory confirmations are conducted in the frequency range 0.1-1.0 MHz. The thermal nature of the origin of these correlations is established by comparing their strength with theoretical expectations. Applications are discussed.     

Shape effect of elongated grains on ultrasonic attenuation in polycrystalline materials

Longitudinal and transverse wave attenuation coefficients are obtained in a simple integral form for ultrasonic waves in cubic polycrystalline materials with elongated grains. Dependences of attenuation on frequency and grain shape are described in detail. The explicit analytical solutions for ellipsoidal grains in the Rayleigh and stochastic frequency limits are given for a wave propagating in an arbitrary direction relative to ellipsoid axes. The attenuation exhibits classic frequency dependence in those frequency limits. However, the dependence on the grain shape in the stochastic limits is unexpected: it is independent of the cross-section of the ellipsoidal grains and depends only on the grain dimension in the propagation direction. In the Rayleigh region attenuation is proportional to effective volume of the ellipsoidal grain and is independent of its shape. A complex behavior of attenuation on the grain shape/size and frequency is exhibited in the transition region. The results obtained reduce to the classic dependences of attenuation on parameters for polycrystals with equiaxed grains.     

Entrainment and stimulated emission of ultrasonic piezoelectric auto-oscillators

Theoretical modeling and laboratory tests are conducted for nonlinear auto-oscillating piezoelectric ultrasonic devices coupled to reverberant elastic bodies. The devices are shown to exhibit behavior familiar from the theory of coupled auto-oscillators. In particular, these spontaneously emitting devices adjust their limit-cycle frequency to the spectrum of the body. It is further shown that the auto-oscillations can be entrained by an applied field; an incident wave at a frequency close to the frequency of the natural limit cycle entrains the oscillator. Special attention is paid to the phase of entrainment. Depending on details, the phase is such that the oscillator can be in a state of stimulated emission: the incident field amplifies the ultrasonic power emitted by the oscillator. These behaviors are essential to eventual design of an ultrasonic system that would consist of a number of such devices all synchronized to their mutual field, a system that would be an analog to a laser. A prototype uaser is constructed.     

Complex modal statistics in a reverberant dissipative body

The statistics of the ultrasonic resonance peaks of a finite elastic body are investigated. The distribution of peak phases, and the normalized variance of peak amplitudes, are shown to be consistent with a hypothesis that the modes themselves are complex Gaussian random numbers. A value q = 0.33 for the ratio of the standard deviations of the imaginary and real parts of the modes is found to fit the data, and to bring recent theory of power variances into better accord with measurements.     

Enhanced backscattering and modal echo of reverberant elastic waves

We report experimental evidence for coherent backscattering of waves in a three-dimensional elastic body. Ultrasonic spectral energy density consequent to a transient excitation is measured as a function of time and of distance from the source. In accord with the predictions of random matrix theory, an enhancement is found near the source by a weak localization factor of 2 at early times, but a factor of 3 at late times. The effect appears to be independent of absorption.     

Temperature dependence of diffuse field phase

Diffuse fields, which have scattered from microstructure or reflected from walls so much as to prohibit conventional analyses, are usually examined by means of the time evolution of their ultrasonic spectral energy density. The phase information is usually discarded as resisting analysis. The phase, while unpredictable is, however, robust; according to theory it remains constant if source and receiver are not disturbed. Nevertheless, in practice we do observe slow drifts of phase over time scales of minutes. Here we examine the hypothesis that the phase drifts are due to temperature fluctuations. Temperature changes on cooling from 40 degrees C to room temperature were monitored and compared with changes in diffuse field phase. It was found that the reverberant ultrasonic field in a 7 cm aluminum block evolves with temperature in a manner that is in accord with published data on the temperature dependence of the ultrasonic velocities. Our 1 MHz transient source gives rise to a complex waveform that is observed to undergo an almost pure dilation. The precision with which this shift can be measured approaches 20 ns. This is remarkable when compared with the 100 ms travel time of the signal. Thus the temperature dependence of elastic wave speed is measured with a precision limited by the precision of one's thermometer. The signal is also found to suffer some distortion which, it is suggested, is related to the different rates of change of longitudinal and shear speeds. The corresponding prediction for the degree of distortion is found to be in accord with measurements.     

On the emergence of the Green's function in the correlations of a diffuse field: pulse-echo using thermal phonons

It is shown that a diffuse field is not devoid of phase information, but has a correlation function equal to the Green's function. More specifically, the cross-correlation between diffuse signals in two transducers is very nearly equal to the direct response of one transducer to an impulse applied to the other. This is true whether the diffuse field is one that was created by a distant source, or (if the detectors are sufficiently sensitive) created by thermal fluctuations in the specimen. Here we outline and review proofs, and laboratory demonstrations, from three recent archival publications.     

循环流化床气固曳力模型

气固曳力是稠密气固两相流动,尤其是垂直流动中的主要作用力,相应的模型也是数值模拟中准确描述气固两相运动的关键.为了解决现有经验或半经验模型的普适性问题,合理描述流动中经常发生的颗粒团聚现象及其对气固曳力的影响,从理论分析入手,运用最小能量的概念,将传统的CFD方法与宏观的系统分析方法相结合,建立了一个新的计及颗粒团聚效应的气固曳力理论模型.与现有模型相比,新模型不仅具有相同的函数变化关系,可合理地描述气固两相相互作用的物理过程,而且避免了以往经验系数不准确导致的各种误差,为稠密气固两相流动的数值描述提供了重要依据.