Interaction of re-radiated Rayleigh waves with fatigue cracks

The usefulness of ultrasonic re-radiated Rayleigh waves for the detection of small surface-connected fatigue cracks in titanium alloy has been demonstrated. The variation in the frequency spectrum of re-radiated Rayleigh waves in the presence of a fatigue crack has been observed, and the sensitivity of this acoustic propagation mode in a scanning operation has been studied.     

Tunneling of evanescent waves into propagating waves

The tunneling of evanescent waves into propagating waves is related to the convolution of the high spatial frequencies of the source with those of the detectors. Such an approach is demonstrated by treating the evanescent waves which are diffracted from very narrow apertures in a plane screen (with dimensions much smaller than the wavelength) and are converted to propagating waves by tip detectors. The mechanism responsible for the conversion of evanescent waves into propagating waves is explained and a general formula for the conversion of evanescent waves into propagating waves is derived. PACS 42.25.Fx; 42.30.Kq; 42.25.Bs     

Frictional shear cracks

We discuss crack propagation along the interface between two dissimilar materials. The crack edge separates two states of the interface, “stick” and “slip.” In the slip region, we assume that the shear stress is proportional to the sliding velocity; i.e., the linear viscous friction law is valid. In this picture, the static friction appears as the tile Griffith threshold for crack propagation. We calculate the crack velocity as a function of the applied shear stress and find that the main dissipation comes from the macroscopic region and is mainly due to the friction at the interface. The relevance of our results to recent experiments, Baumberger et al., Phys. Rev. Lett. 88, 075509 (2002), is discussed.     

Transmission enhancement by conversion of evanescent waves into propagating waves

The convolution between spatial modes of two different parts of an optical system can convert evanescent waves into propagating waves. This principle is applied to different optical systems for analyzing various effects in transmission enhancements experiments. We discuss here the differences between the present principle which is related to broadening of resonances and the near-field optical microscopy based on a tunneling effect by a tip detector. The present analysis is applied in particular to two systems: a) transmission enhancement in one slit by coupling the transmitted radiation with transversal Fabry–Pérot electromagnetic (EM) modes, and b) transmission enhancement by coupling between a metallic film with arrays of holes and surface plasmons (SP). The present approach gives more information on transmission enhancement phenomena than that obtained by conventional treatments and can also solve certain disagreements between different theories. The differences between the present process of converting evanescent waves into propagating waves, and that related to the new development of getting a super-resolution by an hyperlens are discussed. PACS 41.20.Jb; 73.20.Mf; 42.79.Dj     

Intersonic shear cracks and fault ruptures

Recent experimental observations of intersonic shear rupture events that occur in a variety of material systems have rekindled interest in the intersonic failure phenomenon. Since the early 1990s, engineers and scientists working in all length scales, from the atomistic, the structural, all the way up to the scale of the earth's deformation processes, have undertaken joint efforts to study this unexplored area of fracture mechanics. The analysis in the present article emphasizes the cooperative and complementary manner in which experimental observations and analytical and numerical developments have proceeded. The article first reviews early contributions to the theoretical literature of dynamic subsonic and intersonic fracture and highlights the significant differences between tensile and shear cracks. The article then uses direct laboratory observations as a framework for discussing the physics of intersonic shear rupture occurring in constitutively homogeneous (isotropic and anisotropic) as well as in inhomogeneous systems, all containing preferable crack paths or faults. Experiments, models, and field evidence at a variety of length scales (from the atomistic, the continuum, and up to the scale of geological ruptures) are used to discuss processes such as (1) shock wave formation, (2) large-scale frictional contact and sliding at the rupture faces, and (3) maximum attainable rupture speeds and rupture speed stability. Particular emphasis is given to geophysical field evidence and to the exploration of the possibility of intersonic fault rupture during shallow crustal earthquake events.     

Interaction of acoustic waves with cracks: Elastic and inelastic nonlinearity mechanisms on different time scales

The interrelated elastic and inelastic fast and slow effects of acoustic wave interaction with cracks are discussed from a unified point of view. Special attention is given to the dissipative manifestations of the presence of cracks and to the effects of the symmetrically time-reversible slow dynamics observed for acoustically activated cracks. These effects can be more pronounced than the conventionally discussed nonlinear elastic effects (such as higher harmonic generation). Taking into account the main geometric features of cracks, a thermoelastic mechanism is proposed to consistently interpret the experimental data. Consequences of the results of these studies for seismics are discussed, and the possibilities of using the observed effects for nonlinear acoustic diagnostics of cracks are discussed.     

Statistics of waves propagating in a random medium

We present a review of part of the results obtained by the authors for the statistics of coherent radiation propagating in a random medium both in the framework of diagrammatic techniques and random matrix theory. Distribution functions for the total transmission coefficient and the angular transmission coefficient for the diffusive transport and the crossover between the diffusive and ballistic regimes are obtained.The authors acknowledge the financial support of the Israeli Academy of Sciences and of the Schottenstein Center.     

Excitation of propagating magnetization waves by microstrip antennas

We discuss the self-consistent theory of excitation of dipole-exchange magnetization waves by microstrip antennas in a metal-dielectric-ferrite-dielectric-metal stratified structure, magnetized under an arbitrary angle to the surface. Spin-wave Green's functions are derived, describing the response of the spin-system to a spatially inhomogeneous varying magnetic field. The radiative resistance of microstrip antenna is calculated. In this case the distribution of surface current density in the antenna is found on the basis of the analytic solution of a singular integral equation. The nature of the effect of metallic screens and redistributed surface current densities in the antenna on the frequency dependence of the resistive radiation is investigated. Approximate relations are obtained, convenient for practical calculations of radiative resistance of microstrip antennas both in a free and in a screened ferromagnetic film. The theoretical calculations are verified by data of experiments carried out on monocrystalline films of iron-yttrium garnet.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 24–53, November, 1988.     

Noninvasive generation and measurement of propagating waves in arterial walls

Arterial wall stiffness can be associated with various diseases. Arteriosclerosis involves the buildup of plaques within artery walls that stiffen the arteries. The stiffness of an artery can be assessed by measurement of the pulse wave velocity (PWV). Usually, PWV is estimated using the foot-to-foot method. However, the foot of the pressure wave is not very clear due to reflected waves. Also, the blood pressure wave generated by the heart is normally a low frequency wave, hence the time resolution is low. PWV is an average indicator of artery stiffness between the two measuring positions, and therefore cannot easily identify local stiffness. In this paper a force on the arterial wall is generated noninvasively by the radiation force of ultrasound. Techniques for measuring the propagating wave due to this localized force are studied. The excitation force can be either a very short pulse or a modulated cw signal of a few hundred hertz. The temporal resolution of this method, which is in the range of microseconds, is much higher than the conventional pressure PWV method, and therefore allows the wave velocity to be measured accurately over short distances of a few millimeters.     

Coexistence of confinement and propagating waves: a quantum paradox

The example of a multi-channel system which possesses both bound (not quasi-bound!) and scattering states at the same energy value E is demonstrated. As another multi-channel peculiarity having no one-channel analogues we found a class of absolutely transparent interaction matrices without bound states.     

Eigenmodes for electromagnetic waves propagating in a toroidalcavity

A solution has been attempted by means of the Helmholtz equation for an electromagnetic wave propagating in an empty torus in a system of toroidal coordinates. The electromagnetic fields are expressed in terms of the Hertz vector to obtain a scalar Helmholtz equation. The latter has been solved by making use of an inverse aspect ratio expansion of the solution. Unlike most previous workers, the authors have obtained their solutions in terms of hypergeometric functions whose static limit is the toroidal harmonics. The cylindrical solutions in terms of Bessel functions can also be recovered by taking the appropriate large aspect ratio limit. The eigenmodes, with arbitrary toroidal and poloidal mode numbers, have been obtained by applying the boundary conditions on the metallic walls of infinite conductivity, and they cannot be distinguished as TE or TM modes. Eigenfrequencies for various toroidal and poloidal mode numbers are plotted against the inverse aspect ratio. First-order approximations to the fields in the toroidal cavity have also been derived     

Optically guided beam splitter for propagating matter waves

We study experimentally and theoretically a beam splitter setup for guided atomic matter waves. The matter wave is a guided atom laser that can be tuned from quasimonomode to a regime where many transverse modes are populated, and propagates in a horizontal dipole beam until it crosses another horizontal beam at 45°. We show that depending on the parameters of this X configuration, the atoms can all end up in one of the two beams (the system behaves as a perfect guide switch), or be split between the four available channels (the system behaves as a beam splitter). The splitting regime results from a chaotic scattering dynamics. The existence of these different regimes turns out to be robust against small variations of the parameters of the system. From numerical studies, we also propose a scheme that provides a robust and controlled beam splitter in two channels only.     

Obliquely propagating magnetosonic waves in multicomponent quantum magnetoplasma

Linear properties of obliquely propagating magnetosonic waves (both fast and slow) in multicomponent (electron-positron-ion (e-p-i) and dust-electron-ion (d-e-i)) quantum magnetoplasma are studied. It is found that the quantum Bohm potential term significantly changes the propagation of fast and slow magnetosonic waves in both e-p-i and d-e-i quantum plasmas. The variation of the dispersion characteristics with the increase/decrease of positron concentration in e-p-i and dust concentration in d-e-i quantum magnetoplasma is explored. Finally, the effect of angle θ (that the ambient magnetic field makes with the x-axis) on the dispersion properties of magnetosonic waves in multicomponent quantum magnetoplasma is investigated. The relevance of the present investigation to the dense astrophysical environments and microelectronic devices is also pointed out.     

Inwards propagating waves in a limit cycle medium

The existence of a novel inwards propagating wave motion is demonstrated in a limit-cycle medium both for the FitzHugh-Nagumo and for modified Chernyak-Starobin-Cohen reaction-diffusion systems. The waves (pulses) are seen to be moving "backwards," that is, towards the point where the triggering pulse was initiated, instead of the regular propagation away from the origin. The feasibility of the phenomenon and some of its features are analyzed.     

Fracture mechanics of propagating 3-D fatigue cracks with parametric dislocations

Abstract

Propagation of 3-D fatigue cracks is analyzed using a discrete dislocation representation of the crack opening displacement. Three dimensional cracks are represented with Volterra dislocation loops in equilibrium with the applied external load. The stress intensity factor (SIF) is calculated using the Peach–Koehler (PK) force acting on the crack tip dislocation loop. Loading mode decomposition of the SIF is achieved by selection of Burgers vector components to correspond to each fracture mode in the PK force calculations. The interaction between 3-D cracks and free surfaces is taken into account through application of the superposition principle. A boundary integral solution of an elasticity problem in a finite domain is superposed onto the elastic field solution of the discrete dislocation method in an infinite medium. The numerical accuracy of the SIF is ascertained by comparison with known analytical solution of a 3-D crack problem in pure mode I, and for mixed-mode loading. Finally, fatigue crack growth simulations are performed with the Paris law, showing that 3-D cracks do not propagate in a self-similar shape, but they re-configure as a result of their interaction with external boundaries. A specific numerical example of fatigue crack growth is presented to demonstrate the utility of the developed method for studies of 3-D crack growth during fatigue.     

Temporal broadening of pulsed waves propagating through turbulent media

Pulse signals, propagating through a turbulent medium such as the ionosphere, can be distorted by dispersion and scattering from both the background medium and irregularities embedded in. Thus, the mean square pulse width is changed, and temporal broadening is introduced. We carry out a study on the temporal broadening with theoretical analyses and numerical simulations by using an analytical solution of two-frequency mutual coherence function obtained recently by iteration. As a case of study, pulse broadening is investigated in detail in trans-ionospheric propagation. Results show that most contributions are mainly from the dispersion of the background ionosphere and scattering effects of electron density irregularities in most cases.