Nonlinear acoustic spectroscopy of carbonate rocks

The paper presents the results of experimental research into the nonlinear acoustic properties of carbonate rocks depending on saturation. The linear acoustic properties of the same sample depending on saturation were presented earlier in Physical Acoustics. The previously obtained data point to the isotropy of the material, which makes it possible to restrict analysis to only two vibration modes. Responses for finite deformations were measured for the longitudinal and shear modes of an isotropic sample, which made it possible to analyze the nonlinear properties of macroscopic deformations with a change in volume and pure displacement. A heretofore unknown feature of the response was revealed for finite deformation values; it is related to the occurrence of a jumplike transition from classical nonlinearity to a hysteresis type of nonlinearity. As well, the deformation amplitude corresponding to the transition depends on fluid saturation. We studied the slow relaxation that occurs after long-term excitation of a sample with a deformation amplitude on the order of 10^?6. Data are presented on relaxation for deformation from pure displacement and deformation with a change in volume, which made it possible to isolate features related to the type of deformation and to compare the obtained data with the earlier published theoretical model. These data are compared with the results of other research groups.     

Nonlinear and nonequilibrium dynamics in geomaterials

The transition from linear to nonlinear dynamical elasticity in rocks is of considerable interest in seismic wave propagation as well as in understanding the basic dynamical processes in consolidated granular materials. We have carried out a careful experimental investigation of this transition for Berea and Fontainebleau sandstones. Below a well-characterized strain, the materials behave linearly, transitioning beyond that point to a nonlinear behavior which can be accurately captured by a simple macroscopic dynamical model. At even higher strains, effects due to a driven nonequilibrium state, and relaxation from it, complicate the characterization of the nonlinear behavior.     

Nonlinear X-ray spectroscopy

Two-photon fluorescence at X-ray frequencies is considered. The material parameters relevant to this nonlinear process are found to be the linear absorption coefficients and oscillator strengths. The two-photon fluorescent decay of a K-shell hole in Cu is predicted to be easily observable with available techniques.     

Nonlinear comb spectroscopy

A numerical solution for the polarization of two-level atoms that interact with a polyharmonic field was obtained. An analytical solution for the particular case of a symmetrical position of carrier frequency relative to transition frequency is possible. The results showed that nonlinear effects occur in a polarization spectrum at the small amplitudes of comb components and small frequency distances between them. Consequently, it is necessary to take into account nonlinear effects in comb spectroscopy.     

Nonlinear spectroscopy of antiferromagnetics

ijk and on their phase. One of the hexagonal manganites, YMnO₃ is chosen to demonstrate in detail the experimental methods for obtaining this information. The interference of different contributions is utilized to study domain topography. Received: 26 October 1998     

Nonlinear acoustic propagation and focusing

Two model equations of nonlinear acoustics are considered. The implications of a point transformation between forms of the generalised Burgers equation (GBE) is discussed. New exact and asymptotic solutions are obtained. The dissipative Zabolotskaya-Khokhlov (DZK) equation describing acoustic wave propagation with allowance for transverse amplitude variation is studied. By considering a transformation onto the GBE, solutions exhibiting caustic behaviour are presented. A mechanism for the control of such singularities is presented along with a comparison with shock formation time.Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 9EW, England. Published in Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 36, No. 8, pp. 783–787, August, 1993.     

Nonlinear acoustic methods of crack diagnostics

This paper is a brief overeview of experimental studies of nonlinear acoustic phenomena due to the presence of cracks in solids. The possibilities for using these phenomena in crack diagnostics are discussed. To explain the observed effects, we present the physical models of a single crack and a fractured medium.Institute of Applied Physics Russian Academy of Sciences, Nizhny Novgorod. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 38, Nos. 3–4, pp. 169–187, March–April, 1995.     

Vibrational spectroscopy of structural defects in oligothiophenes

Vibrational spectra of oligothiophenes with structural defects are calculated within the density-functional-theory methodology. The effects of the defective αβ linkages on the infrared (IR) and Raman spectra are characterized from calculations of all isomers up to the hexamer. The signatures of αβ linked monomers can be found in IR spectra from broken symmetry arguments which result in absorptions localized in the defective region. The positions of the absorption peaks in the Raman spectra seem to be unaffected by the presence of such defects; however, strong reductions in the intensities are observed because of the shortening of the conjugation length.     

Nonlinear phase dispersion spectroscopy

Nonlinear phase dispersion spectroscopy is introduced as a means to retrieve wideband, high spectral resolution profiles of the wavelength-dependent real part of the refractive index. The method is based on detecting dispersion effects imparted to a light field with low coherence transmitted through a thin sample and detected interferometrically in the spectral domain. The same sampled signal is also processed to yield quantitative phase maps and spectral information regarding the total attenuation coefficient using spectral-domain phase microscopy and spectroscopic optical coherence tomography (SOCT), respectively. Proof-of-concept experiments using fluorescent and nonfluorescent polystyrene beads and another using a red blood cell demonstrate the ability of the method to quantify various absorptive/dispersive features. The increased sensitivity of this method, novel to our knowledge, is compared to intensity-based spectroscopy (e.g., SOCT), and potential applications are discussed.     

Nonlinear acoustic techniques for landmine detection

Measurements of the top surface vibration of a buried (inert) VS 2.2 anti-tank plastic landmine reveal significant resonances in the frequency range between 80 and 650 Hz. Resonances from measurements of the normal component of the acoustically induced soil surface particle velocity (due to sufficient acoustic-to-seismic coupling) have been used in detection schemes. Since the interface between the top plate and the soil responds nonlinearly to pressure fluctuations, characteristics of landmines, the soil, and the interface are rich in nonlinear physics and allow for a method of buried landmine detection not previously exploited. Tuning curve experiments (revealing "softening" and a back-bone curve linear in particle velocity amplitude versus frequency) help characterize the nonlinear resonant behavior of the soil-landmine oscillator. The results appear to exhibit the characteristics of nonlinear mesoscopic elastic behavior, which is explored. When two primary waves f1 and f2 drive the soil over the mine near resonance, a rich spectrum of nonlinearly generated tones is measured with a geophone on the surface over the buried landmine in agreement with Donskoy [SPIE Proc. 3392, 221-217 (1998); 3710, 239-246 (1999)]. In profiling, particular nonlinear tonals can improve the contrast ratio compared to using either primary tone in the spectrum.     

Laser spectroscopy 4. Nonlinear high resolution spectroscopy

This paper in the series gives a brief outline of the main ideas, methods and types of nonlinear laser spectrometer used for atomic and molecular spectroscopy without Doppler broadening. This is the most developed area of laser spectroscopy and has recently been the subject of several papers^1,2 to which readers are reffered for more detailed information.     

Nonlinear standing waves in 2-D acoustic resonators

This paper deals with 2-D simulation of finite-amplitude standing waves behavior in rectangular acoustic resonators. Set of three partial differential equations in third approximation formulated in conservative form is derived from fundamental equations of gas dynamics. These equations form a closed set for two components of acoustic velocity vector and density, the equations account for external driving force, gas dynamic nonlinearities and thermoviscous dissipation. Pressure is obtained from solution of the set by means of an analytical formula. The equations are formulated in the Cartesian coordinate system. The model equations set is solved numerically in time domain using a central semi-discrete difference scheme developed for integration of sets of convection-diffusion equations with two or more spatial coordinates. Numerical results show various patterns of acoustic field in resonators driven using vibrating piston with spatial distribution of velocity. Excitation of lateral shock-wave mode is observed when resonant conditions are fulfilled for longitudinal as well as for transversal direction along the resonator cavity.     

Nonlinear dispersion relation of geodesic acoustic modes

The energy input and frequency shift of geodesic acoustic modes (GAMs) due to turbulence in tokamak edge plasmas are investigated in numerical two-fluid turbulence studies. Surprisingly, the turbulent GAM dispersion relation is qualitatively equivalent to the linear GAM dispersion but can have drastically enhanced group velocities. In up-down asymmetric geometry the energy input due to turbulent transport may favor the excitation of GAMs with one particular sign of the radial phase velocity relative to the magnetic drifts and may lead to pulsed GAM activity.     

Nonlinear oscillation and acoustic scattering of bubbles

The scattered acoustic pressure and scattered cross section of bubbles is studied using the scattered theory of bubbles. The nonlinear oscillations of bubbles and the scattering acoustic fields of a spherical bubble cluster are numerically simulated based on the bubble dynamic and fluid dynamic. The influences of the interaction between bubbles on scattering acoustic field of bubbles are researched. The results of numerical simulation show that the oscillation phases of bubbles are delayed to a certain extent at different positions in the bubble cluster, but the radii of bubbles during oscillation do not differ too much at different positions. Furthermore, directivity of the acoustic scattering of bubbles is obvious. The scattered acoustic pressures of bubbles are different at the different positions inside and outside of the bubble cluster. The scattering acoustic fields of a spherical bubble cluster depend on the driving pressure amplitude, driving frequency, the equilibrium radii of bubbles, bubble number and the radius of the spherical bubble cluster. These theoretical predictions provide a further understanding of physics behind ultrasonic technique and should be useful for guiding ultrasonic application.     

Nonlinear acoustic wave generation in a three-phase seabed

Generation of an acoustic wave by two pump sound waves is studied in a three-phase marine sediment, which consists of a solid frame and the pore water with air bubbles in it. To avoid shock-wave formation, the interaction is considered in the frequency range where there is a significant sound velocity dispersion. Nonlinear equations are obtained to describe the interaction of acoustic waves in the presence of air bubbles. An expression for the amplitude of the generated wave is obtained and numerical analysis of its dependence on distance and resonance frequency of bubbles is performed.     

Nonlinear acoustic transparency phenomena in strained paramagnetic crystals

Nonlinear dynamics of longitudinal acoustic pulses propagating in a strained paramagnetic cubic crystal at low temperature is analyzed. The direction of constant uniform strain is parallel to one of the fourth-order symmetry axes. Effective-spin 1 ions are considered as paramagnetic impurities with the strongest spin-lattice interaction. In this medium, normally degenerate magnetic sublevels are dynamically shifted by the quadrupole Stark effect, and the frequencies of the transitions induced by an acoustic pulse change accordingly. The self-consistent system of equations derived in this study without using the slowly varying envelope approximation describes pulse propagation at an arbitrary angle to the direction of the static strain. Exponentially and rationally decaying monopolar and breather-like solutions to the system are obtained. An analysis of the solutions reveals an asymmetry of the pulse polarity depending on the type of strain (extension or compression) and the pulse propagation direction. In particular, it is shown that acoustic transparency associated with monopolar strain pulses exhibits threshold behavior. The sign of the time area (zeroth harmonic) of breather-like strain pulses is such that the transition frequency averaged over an oscillation period dynamically decreases. This behavior determines the efficiency of generation of high-order harmonics of acoustic pulses in strained paramagnetic crystals.