Shear wave caustics and the shadows of surface breaking cracks

A refinement to the detection of defects in rods and pipes by means of their ultrasonic shadows is presented. It has been previously shown that in standard non-destructive test configurations ultrasonic waves inside cylindrical test objects form caustics, surfaces of high sound intensity. Here it is demonstrated that when a crack edge crosses a caustic the diffraction of sound around the defect is enhanced, which allows the point at which this intersection occurs to be detected. Because the caustic is a well-defined geometric entity the position of the crack edge is now known. This effect presents a novel method of sizing defects that extend in from the surface. Experiments were performed in water immersion using 5 MHz sound. The test specimens were 76 mm diameter aluminium cylinders into which slots were cut to act as artificial defects.     

Laser polarimetry of polarization-phase statistical moments of the object field of optically anisotropic scattering layers

Issues related to the direct polarization-interference measurements of the second and higher statistical moments of the random object field of a phase-inhomogeneous layer are considered. The relation between the statistical parameters of the surface and volume structure of the object and the statistics of the vector laser field is determined. The results of analytical modeling are compared with direct experimental measurements.     

On the structure of space-time caustics

Caustics formed by timelike and null geodesics in a space-timeM are investigated. Care is taken to distinguish the conjugate points in the tangent space (T-conjugate points) from conjugate points in the manifold (M-conjugate points). It is shown that most nonspacelike conjugate points are regular, i.e. with all neighbouring conjugate points having the same degree of degeneracy. The regular timelikeT-conjugate locus is shown to be a smooth 3-dimensional submanifold of the tangent space. Analogously, the regular nullT-conjugate locus is shown to be a smooth 2-dimensional submanifold of the light cone in the tangent space. The smoothness properties of the null caustic are used to show that if an observer sees focusing in all directions, then there will necessarily be a cusp in the caustic. If, in addition, all the null conjugate points have maximal degree of degeneracy (as in the closed Friedmann-Robertson-Walker universes), then the space-time is closed.     

南中国海海域存在孤立子内波条件下的声场统计特性

利用南中国海浅海海域低频声传播起伏实验中获取的水文数据,结合二维平流模型重构出声传播路径上的动态声速场,使用蒙特卡洛方法研究了有无孤立子内波经过时声传播路径上的声传播损失统计特性,并与实验结果进行了对比分析。仿真和实验结果表明:当孤立子内波经过声传播路径时,声传播损失起伏剧烈;与"下发上收"相比,"下发下收"情况下传播损失的概率分布更加分散。     

Problem of distribution moments in statistical physics

The statistical possibilities of studying intrasystem processes in multielement systems are determined by solving the problem of the moments of distributions specified in mathematical and physical formulations. The characteristic properties of the distributions can be revealed by analyzing the simple and product moments (integer, fractional, and functional) and the relationships between them. The proposed method of complex analysis of experimental data and theoretical calculations is illustrated using the examples of the Maxwellian velocity distribution of molecules, the Planck radiation spectral power distribution, and the size distribution of microscopic particles in a disperse-hardened alloy. State University, Zaporozhye. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 92–97, April, 1997.     

NDT of rods and pipes using shear wave caustics

An important feature of shear wave insonification of circularly cylindrical samples is the caustic formations which occur inside the samples, after internal reflections at the external sample boundaries. Strong echoes are obtained from defects in the outer regions of the samples when they pass through these caustic regions because of the concentration of energy along the caustic. The caustic effectively acts as an acoustic microscope system which probes the surfaces of the defects as they intersect it. The returned pulse-echo data can be utilized to determine the size, shape, and position of the defects. This is illustrated with samples containing artificial and real defects.     

On the Ising model in the presence of magnetic field

We demonstrate that the partition function of the 2-dimensional Ising model in the presence of a magnetic field can be expressed in terms of the distributions of the prime numbers in closed form.     

On the average moments of a polar molecule in a non-uniform electric field

We calculate the orientational average of the total electric dipole and quadrupole moments of a polar molecule in a non-uniform electric field and comment on the results.     

Relating statistical moments and entropy in the stable boundary layer

Fourth order moments and their connection with other statistics, including second order moments, skewness and entropy, in stable boundary layers are investigated with a large eddy simulation model (LES), wind tunnel experiment data (WT) and measurements on a meteorological tower in an urban area (MT). The relationship between skewness and kurtosis has been studied through two formulae, whose coefficients are determined for the three data sets. Shannon entropy is analysed as an index of the turbulent flow organization in order to further understand the possible reason for the failure of the QN hypothesis. To quantify this relationship between Shannon entropy and kurtosis, a power function is proposed.     

On the self-organization of atomic magnetic moments after application of an electric field

An attempt is made to reveal the self-organization of atomic magnetic moments in rare-earth ferrimagnets of the TbFe₂ type, an effect reported on in the works of S.K. Godovikov. A careful experimental study and a critical analysis of the data reported in his publications suggest that there are no grounds to maintain that this phenomenon exists.     

On statistical fluctuations in detector readings in a radiation field

The process of particle passage through a substance is random, hence the readings of a detector recording the radiation are a random variable. Equations are derived in this paper for the probabilistic characteristics of the detector readings and a relationship is established between these characteristics and the mean values for whose computation the ordinary apparatus of transport theory can be used.     

Conserved moments in nonequilibrium field dynamics

We demonstrate with the example of Cahn-Hilliard dynamics that the macroscopic kinetics of first-order phase transitions exhibits an infinite number of constants of motion. Moreover, this result holds in any space dimension for a broad class of nonequilibrium processes whose macroscopic behavior is governed by equations of the form /t = W(), where is an order parameter,W is an arbitrary function of , and is a linear Hermitian operator. We speculate on the implications of this result.     

Splitting of atomic levels in a strong magnetic field in the presence of an intense resonance wave

A system of quasi-energy levels of an atom in an intense constant magnetic field and in the field of an intense resonance electromagnetic wave is obtained when the interaction energy of the atom with the magnetic field and with the wave field exceeds the energy of relativistic interaction in the atom responsible for the fine structure of the levels.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 117–122, December, 1976.     

Real-time measurement of wave components and intensity in a beam in the presence of a near field

A method is described by which the individual flexural wave components in a beam can be measured in real time. Attention is focussed on the case in which two propagating waves and a single near-field wave exist, although the case of two near fields is also considered. Because the presence of the near field is included, the measurements can be taken close to the force, boundary or discontinuity from which the near field arises. Potential applications include intensity measurement, active control and adaptive-passive vibration control.The wave components are measured by digitally filtering and combining the outputs of an array of sensors, with an array of three, equally spaced sensors being considered in detail. The filters are designed in the frequency domain using a wave decomposition approach, and implemented in the time domain as FIR filters. Design, implementation and performance issues are discussed and an experimental implementation described. It is seen that accurate estimates of the amplitudes of the wave components can be obtained using FIR filters of moderate order, and that the method is relatively insensitive to sensor miscalibration and measurement noise.     

On the neutron diffraction in crystals in the field of a sound wave

Diffraction of neutrons in crystals under influence of a sound wave is considered. The probability of scattering of neutrons at the elastic interaction with the crystal is calculated. On the contrary, scattering of neutrons by an acoustical phonon has inelastic character. The possibility to control the Debye-Waller factor is shown.     

On the asymmetry of a random walk in the presence of a field

Any ensemble of random walks with symmetric transition probabilities will have symmetric properties. However, any single realization of such a random walk may be asymmetric. In an earlier paper, Weiss and Weissman developed a measure of asymmetry and applied it to random walks in the absence of a field, showing that the degree of asymmetry (in the diffusion limit) is independent of time and that the most probable degree of asymmetry corresponds to the maximum possible. We show in the present paper how the presence of a symmetric field can change this result, both in making the degree of asymmetry depend on time, and driving the random walk toward a more symmetric state.