Fernando Lund

Ultrasound as a probe of turbulence

Abstract Formulae relating the two-point, space time, vorticity correlation tensor to the intensity of ultrasound scattered by a bounded region of nonvanishing vorticity are given both in two and in three dimensions. The incident wave is supposed to be of low intensity and of frequency high in comparison with typical frequencies of the target flow, which is assumed to be of low Mach number; viscosity is assumed not to affect sound propagation. This result suggests a non-intrusive, direct, way of measuring vorticity correlations. The derivation emphasizes the central role played by vorticity as the basic scattering mechanism of the incident sound.

Strong scattering of short-period seismic waves by the core-mantle boundary and the P-diffracted wave

We interpret the long-tail-in-time (up to 3 minutes) decay of short-period Pdiff as being due to multiple scattering within D″, which, for this purpose, is assumed to be an heterogeneous region with a low velocity zone just next to the core-mantle boundary. A simple multiple scattering theory, generalized for a two-dimensional spherical geometry, provides good agreement with observations for values of the scattering and attenuation coefficients (η) of about 10−3 km−1.

Scattering of dislocated wave fronts by vertical vorticity and the Aharonov-Bohm effect. I. Shallow water.

When a surface wave interacts with a vertical vortex in shallow water the latter induces a dislocation in the incident wave fronts that is analogous to what happens in the Aharonov-Bohm effect for the scattering of electrons by a confined magnetic field. In addition to this global similarity between these two physical systems there is scattering. This paper reports a detailed calculation of this scattering, which is quantitatively different from the electronic case in that a surface wave penetrates the inside of a vortex while electrons do not penetrate a solenoid. This difference, together with an additional difference in the equations that govern both physical systems, lead to a quite different scattering in the case of surface waves, whose main characteristic is a strong asymmetry in the scattering cross section. The assumptions and approximations under which these effects happen are carefully considered, and their applicability to the case of the scattering of acoustic waves by vorticity is noted.

Nonlinear waves in elastic media

Abstract We ask about the possible existence of solitary waves in infinite, homogeneous, isotropic, elastic media. Namely, can a nonlinear localized wave packet propagate without altering its shape in such materials? We consider one- dimensional propagation both of body and surface waves. In the first case we show, under rather general assumptions, that if a wave packet propagates without altering its shape it must, of necessity, be a solution of a linear wave equation and in this sense, (body) solitary waves do not exist. Surface solitary waves may however exist: a model equation is derived in which nonlinear and dispersive effects balance each other to allow for waves-both periodic and solitary-of constant shape. It is conceivable they are of some relevance in seismology.

Insights into the Mechanism of an SN2 Reaction from the Reaction Force and the Reaction Electronic Flux

The mechanism of a simple S(N)2 reaction, viz; OH(-) + CH(3)F = CH(3)OH + F(-) has been studied within the framework of reaction force and reaction electronic flux. We have computationally investigated three different types of reaction mechanisms with two different types of transition states, leading to two different products. The electronic transfer contribution of the reaction electronic flux was found to play a crucial role in this reaction. Natural bond order analysis and dual descriptor provide additional support for elucidating the mechanism of this reaction.

Scattering of an elastic wave by a single dislocation

The scattering amplitude for the scattering of anti-plane shear waves by screw dislocations, and of in-plane shear and acoustic waves by edge dislocations are computed within the framework of elasticity theory. The former case reproduces well-known results obtained on the basis of an electromagnetic analogy. The latter case involves four scattering amplitudes in order to fully take into account mode conversion, and an adequately generalized optical theorem for vector waves is provided. In contrast to what happens for scattering by obstacles, the scattering amplitude increases with wavelength, and, in general, mode conversion in the forward direction does not vanish.

Defect dynamics for the nonlinear Schrödinger equation derived from a variational principle

Abstract The equation of motion for defect solutions to the nonlinear Schrodinger equation is derived from a variational principle, both in two and three dimensions.

Ultrasound as a probe of dislocation density in aluminum

Abstract Dislocations are at the heart of the plastic behavior of crystalline materials yet it is notoriously difficult to perform quantitative, non-intrusive measurements of their single or collective properties. Dislocation density is a critical variable that determines dislocation mobility, strength and ductility. On the one hand, individual dislocations can be probed in detail with transmission electron microscopy. On the other hand, their collective properties must be simulated numerically. Here we show that ultrasound technology can be used to measure dislocation density. This development rests on theory—a generalization of the Granato–Lucke theory for the interaction of elastic waves with dislocations—and resonant ultrasound spectroscopy (RUS) measurements. The chosen material is aluminum, to which different dislocation contents were induced through annealing and cold-rolling processes. The dislocation densities obtained with RUS compare favorably with those inferred from X-ray diffraction, using the modified Williamson–Hall method.

Propagation of elastic waves through polycrystals: the effects of scattering from dislocation arrays

We address the problem of an elastic wave coherently propagating through a two-dimensional polycrystal. The main source of scattering is taken to be the interaction with grain boundaries that are in turn modelled as line distribution of dislocations—a good approximation for low angle grain boundaries. First, the scattering due to a single linear array is worked out in detail in a Born approximation, both for longitudinal and transverse polarization and allowing for mode conversion. Next, the polycrystal is modelled as a continuum medium filled with such lines that are in turn assumed to be randomly distributed. The properties of the coherent wave are worked out in a multiple scattering formalism, with the calculation of a mass operator, the main technical ingredient. Expansion of this operator to second-order in perturbation theory gives expressions for the index of refraction and attenuation length. This work is motivated by two sources of recent experiments: firstly, the experiments of Zhang et al. (Zhang, G., Simpson Jr, W. A., Vitek, J. M., Barnard, D. J., Tweed, L. J. & Foley J. 2004 J. Acoust. Soc. Am. 116, 109–116.) suggesting that current understanding of wave propagation in polycrystalline material fails to interpret experimental results; secondly, the experiments of Zolotoyabko & Shilo who show that dislocations are potentially strong scatterers for elastic waves.

Ultrasound scattering by a swirling jet

Recent analytical work has shown that when an acoustic plane wave propagates through a rotational flow field there is a linear relationship between the Fourier component of the scattered acoustic pressure and the Fourier transform in space and time of the vorticity component that is normal to the plane defined by the wave vectors of the incident and scattered acoustic waves. Hence, ultrasound scattering can be used as a non-intrusive spectral probe of vorticity and potentially as a tool for direct measurements of vorticity distributions. Some aspects of this technique have been tested in a swirling air jet emanating from a 2.54 cm diameter nozzle where the swirl is generated upstream of the jet nozzle by a rotating paddle. For a given exit volume flow rate, swirl numbers up to 0.4 are realized. Radial distributions of the streamwise and tangential velocity components downstream of the jet exit plane are measured using two-component hot-wire anemometry and the corresponding distributions of streamwise vort...