Slow dynamics in a single bead with mechanical conditioning and transient heating.

The contact stiffness of an aluminum bead confined between two slabs diminishes upon mechanical conditioning, and then recovers as log(t) after the conditioning ceases. Here that structure is evaluated for its response to transient heating and cooling, with and without accompanying conditioning vibrations. It is found that, under heating or cooling alone, stiffness changes are mostly consistent with temperature-dependent material moduli; there is little or no slow dynamics. Hybrid tests in which vibration conditioning is followed by heating or cooling lead to recoveries that begin as log(t) and then become more complex. On subtracting the known response to heating or cooling alone we discern the influence of higher or lower temperatures on slow dynamic recovery from vibrations. It is found that heating accelerates the initial log(t) recovery, but by an amount more than predicted by an Arrhenius model of thermally activated barrier penetrations. Transient cooling has no discernible effect, in contrast to the Arrhenius prediction that it slows recovery.

Diffuse energy transport and coda-wave interferometry for resonant transmission between reverberant structures.

Approximate analytic and numerical theories are developed with which to model, and compare with laboratory measurements, the diffuse ultrasonic field transmitted from one elastic body to another through a resonant coupling. Particular focus is on the sensitivity of the transmitted field to perturbations in the natural frequency of the coupling and the manifestation of such perturbations as time delays in the second body. The immediate application is to measurements of slow dynamic elastic nonlinearity. It is found that the developed approximate theories do a good job of predicting the time dependence of the mean square transmitted signal and signal spectra. They also predict the time delays, both their erratic character and means. Analytic dependence of these time shifts on the fractional frequency perturbation df/f is derived.

Slow dynamic elastic recovery in unconsolidated metal structures.

Slow dynamic nonlinearity is widely observed in brittle materials with complex heterogeneous or cracked microstructures. It is seen in rocks, concrete, and cracked glass blocks. Unconsolidated structures show the behavior as well: aggregates of glass beads under pressure and a single glass bead confined between two glass plates. A defining feature is the loss of stiffness after a mechanical conditioning, followed by a logarithmic-in-time recovery. Materials observed to exhibit slow dynamics are sufficiently different in microstructure, chemical composition, and scale (ranging from the laboratory to the seismological) to suggest some kind of universality. There lacks a full theoretical understanding of the universality in general and the log(time) recovery in particular. One suspicion has been that the phenomenon is associated with glassy grain boundaries and microcracking. Seminal studies were focused on sandstones and other natural rocks, but in recent years other experimental venues have been introduced with which to inform theory. Here, we present measurements on some simple metallic systems: an unconsolidated aggregate of aluminum beads under a confining pressure, an aluminum bead confined between two aluminum plates, and a steel bead confined between steel plates. Ultrasonic waves are used as probes of the systems, and changes are assessed with coda wave interferometry. Three different methods of low-frequency conditioning are applied; all reveal slow dynamic nonlinearities. Results imply that glassy microstructures and cracking do not play essential roles, as they would appear to be absent in our systems.

Slow dynamic nonlinearity in unconsolidated glass bead packs.

Slow dynamic nonlinearity describes a poorly understood, creeplike phenomena that occurs in brittle composite materials such as rocks and cement. It is characterized by a drop in stiffness induced by a mechanical conditioning, followed by a log(time) recovery. A consensus theoretical understanding of the behavior has not been developed. Here we introduce an alternative experimental venue with which to inform theory. Unconsolidated glass bead packs are studied rather than rocks or cement because the structure and internal contacts of bead packs are less complex and better understood. Slow dynamics has been observed in such systems previously. However, the measurements to date tend to be irregular. Particular care is used here in the experimental design to overcome the difficulties inherent in bead pack studies. This includes the design of the bead pack support, the use of low-frequency conditioning, and the use of ultrasonic waves as a probe with coda wave interferometry to assess changes. Slow dynamics is observed in our system after three different methods for low-frequency conditioning, one of which has not been reported in the literature previously.

Slow dynamics in a single glass bead.

Slow dynamic nonlinearity is ubiquitous amongst brittle materials, such as rocks and concrete, with cracked microstructures. A defining feature of the behavior is the logarithmic-in-time recovery of stiffness after a mechanical conditioning. Materials observed to exhibit slow dynamics are sufficiently different in microstructure, chemical composition, and scale (ranging from the laboratory to the seismological) to suggest some kind of universality. A consensus of theoretical understanding of the universality in general and the log(time) recovery in particular is lacking. Seminal studies were focused on sandstones and other natural rocks, but in recent years other experimental venues have been introduced with which to inform theory. One such system is unconsolidated glass bead packs. However, bead packs still contain many contact points. The force distribution amongst the contacts is unknown. Here, we present slow dynamics measurements on a yet simpler system-a single glass bead confined between two large glass plates. The system is designed with a view towards rapid control of the contact zone environment. Ultrasonic waves are used as a probe of the system, and changes are assessed with coda wave interferometry. Three different methods of low-frequency conditioning are applied; all lead to slow dynamic recoveries. Results imply that force chains do not play an essential role in granular media slow dynamics, as they are absent in our system.

Temporally weighting a time varying noise field to improve Green function retrieval.

The authors consider the retrieval of Green functions G from the correlations of non-stationary non-fully diffuse noise incident on an array of sensors. Multiple schemes are proposed for optimizing the time-varying weights with which correlations may be stacked. Using noise records created by direct numerical simulation of waves in a two-dimensional multiply scattering medium, cases are shown in which conventional stacking does a poor job and for which the proposed schemes substantially improve the recovered G, rendering it more causal and/or more symmetric, and more similar to the actual G. It is found that the schemes choose weights such that the effective incident intensity distribution is closer to isotropic.

Avalanches and scaling collapse in the large-N Kuramoto model.

We study avalanches in the Kuramoto model, defined as excursions of the order parameter due to ephemeral episodes of synchronization. We present scaling collapses of the avalanche sizes, durations, heights, and temporal profiles, extracting scaling exponents, exponent relations, and scaling functions that are shown to be consistent with the scaling behavior of the power spectrum, a quantity independent of our particular definition of an avalanche. A comprehensive scaling picture of the noise in the subcritical finite-N Kuramoto model is developed, linking this undriven system to a larger class of driven avalanching systems.

Fluctuations in the cross-correlation for fields lacking full diffusivity: The statistics of spurious features.

Inasmuch as ambient noise fields are often not fully diffuse the question arises as to how, or whether, noise cross-correlations converge to Green's function in practice. Well-known theoretical estimates suggest that the quality of convergence scales with the square root of the product of integration time and bandwidth. However, correlations from natural environments often show random features too large to be consistent with fluctuations from insufficient integration time. Here it is argued that empirical seismic correlations suffer in practice from spurious arrivals due to scatterers, and not from insufficient integration time. Estimates are sought for differences by considering a related problem consisting of waves from a finite density of point sources. The resulting cross-correlations are analyzed for their mean and variance. The mean is, as expected, Green's function with amplitude dependent on noise strength. The variance is found to have support for all times up to its maximum at the main arrival. The signal-to-noise ratio there scales with the square root of source density. Numerical simulations support the theoretical estimates. The result permits estimates of spurious arrivals' impact on identification of cross-correlations with Green's function and indicates that spurious arrivals may affect estimates of amplitudes, complicating efforts to infer attenuation.

On band gap predictions for multiresonant metamaterials on plates.

Recently wide frequency band gaps were observed in an experimental realization of a multiresonant metamaterial for Lamb waves propagating in thin plates. The band gaps rose from hybridization between the flexural plate (A0 Lamb waves) and longitudinal resonances in rods attached perpendicularly. Shortly thereafter a theory based on considering a one-dimensional periodic array of rods and the scattering matrix for a single rod successfully described the observations. This letter presents an alternative simpler theory, arguably accurate at high rod density, that treats the full two-dimensional array of rods and makes no assumption of periodicity. This theory also fits the measurements.

Avalanche Statistics Identify Intrinsic Stellar Processes near Criticality in KIC 8462852.

The star KIC8462852 (Tabby's star) has shown anomalous drops in light flux. We perform a statistical analysis of the more numerous smaller dimming events by using methods found useful for avalanches in ferromagnetism and plastic flow. Scaling exponents for avalanche statistics and temporal profiles of the flux during the dimming events are close to mean field predictions. Scaling collapses suggest that this star may be near a nonequilibrium critical point. The large events are interpreted as avalanches marked by modified dynamics, limited by the system size, and not within the scaling regime.

Effect of dispersion on the convergence rate for Green's function retrieval.

Much information about wave propagation in a variety of structures has been obtained from Green's function retrieval by noise correlation. Here it is examined how dispersion affects Green's function retrieval and, in particular, its signal-to-noise ratio (SNR). On recalling how the inherent spread of a signal due to band limitation is augmented by spread due to dispersion and propagation distance, and how both affect amplitude, it is argued that SNR in highly dispersive media can be substantially lowered by strong dispersion. It is argued that this is most relevant for gravity waves over large propagation distances in the ocean or atmosphere. In particular, it is discussed that dispersion could explain recent retrieval failure from surface gravity wave noise in the ocean. Methods are considered to ameliorate the poor SNR due to dispersion. Numerical simulation is used to substantiate the analytic results.

Comment on "Relative variance of the mean squared pressure in multimode media: rehabilitating former approaches" [J. Acoust. Soc. Am. 136, 2621-2629 (2014)].

Models for the statistics of responses in finite reverberant structures, and in particular, for the variance of the mean square pressure in reverberation rooms, have been studied for decades. It is therefore surprising that a recent communication has claimed that the literature has gotten the simplest of such calculations very wrong. Monsef, Cozza, Rodrigues, Cellard, and Durocher [(2014). J. Acoust. Soc. Am. 136, 2621-2629] have derived a modal-based expression for the relative variance that differs significantly from expressions that have been accepted since 1969. This Comment points out that the Monsef formula is clearly incorrect, and then for the interested reader, points out the subtle place where they made their mistake.

Retrieval of Green's function in the radiative transfer regime.

The field-field correlation function of an imperfectly diffuse acoustic field is shown to equal the (time derivative of) Green's function times the specific intensity of the noise at the position of the pseudo-source directed toward the pseudo-receiver. The identity is established in a high frequency limit in which stations are separated by distances large compared to a wavelength and in which equal-time correlations vary smoothly in space. The specific intensity is governed by a radiative transport equation. This observation permits interpretation of correlation amplitudes and promises to facilitate the retrieval of attenuation, site amplification factors, and scattering strengths from noise correlations.

On the Larsen effect to monitor small fast changes in materials.

At sufficient gain an ultrasonic feedback circuit rings with a "Larsen" tone that depends on the acoustic properties of the solid body to which it is attached. Because the frequency of this tone may be measured virtually continuously and with high precision, it is potentially capable of responding to fast small changes in materials. Here a tentative theory for Larsen dynamics is introduced and compared with laboratory measurements. Larsen monitoring is then applied to observation of the curing process of a cement paste sample and to studies of "slow dynamics" in which mesoscale nonlinear materials subjected to modest loads experience a drop in modulus but then recover in a characteristic manner like log(t). The present technique, using as it does higher frequencies and the Larsen effect and brief transient loads, extends investigations of slow dynamics to earlier times. For the materials and loads investigated, it is found that log(t) behavior fails at the shortest times, recovery being faster over the first several milliseconds.

Scattering fidelity in elastodynamics. II. Further experimental results.

The agreement of past measurements of elastodynamic scattering fidelity with predictions based on random matrix theory, even in bodies with ostensibly regular ray dynamics, has motivated further measurements with a precision capable of detecting fine deviations. Two aluminum blocks are studied, one rectangular, one irregular. As previously, it is found that fidelity decays more slowly in the irregular object. It is further shown that the time dependence of that decay corresponds well with predictions based on random matrix theory and the Gaussian orthogonal ensemble and that predictions based on Poissonian model statistics do not correspond. In some cases deviations from theory are seen that are consistent with partially broken reflection symmetries and inhomogeneous dissipation.

Anderson localization of ultrasound in plates: further experimental results.

Diffuse wave transport is studied in a thick plate with densely machined-in multiple scatterers. As anticipated by theory, energy at short wavelengths diffuses across the structure. Energy localizes at longer wavelengths for which lambda2pi is comparable to the mean free path.

Wigner distribution of a transducer beam pattern within a multiple scattering formalism for heterogeneous solids.

Diffuse ultrasonic backscatter measurements have been especially useful for extracting microstructural information and for detecting flaws in materials. Accurate interpretation of experimental data requires robust scattering models. Quantitative ultrasonic scattering models include components of transducer beam patterns as well as microstructural scattering information. Here, the Wigner distribution is used in conjunction with the stochastic wave equation to model this scattering problem. The Wigner distribution represents a distribution in space and time of spectral energy density as a function of wave vector and frequency. The scattered response is derived within the context of the Wigner distribution of the beam pattern of a Gaussian transducer. The source and receiver distributions are included in the analysis in a rigorous fashion. The resulting scattered response is then simplified in the single-scattering limit typical of many diffuse backscatter experiments. Such experiments, usually done using a modified pulse-echo technique, utilize the variance of the signals in space as the primary measure of microstructure. The derivation presented forms a rigorous foundation for the multiple scattering process associated with ultrasonic experiments in heterogeneous media. These results are anticipated to be relevant to ultrasonic nondestructive evaluation of polycrystalline and other heterogeneous solids.

Unitarization of the classical statistical s matrix for systems with localization.

It has recently been observed that a large reverberant cavity admits a classically motivated random s matrix that is not unitary but that can be made so in a minimally invasive manner. A random process with an envelope approximately exp(-t/TH) representing reflection from a structure having no internal time scales other than Heisenberg time T_{H} was shown to lead to a unitary S matrix exhibiting mesoscopic behaviors not present in the classically inspired original . These included enhanced backscatter, quantum echo, power law tails, and level repulsion. Here the procedure is extended to two systems having, in addition to Heisenberg times, internal time scales corresponding to conduction and diffusion. The repaired S matrices for coupled rooms and one-dimensional random structures with multiple scattering are found to correspond to Wigner K matrices with signatures of localization.

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.

Wave-vector resonance in a nonlinear multiwavespeed chaotic billiard.

Nonlinear coupling between eigenmodes of a system leads to spectral energy redistribution. For multiwavespeed chaotic billiards, the average coupling strength can exhibit sharp discontinuities as a function of frequency related to wave-vector coincidences between constituent waves of different wavespeeds. The phenomenon is investigated numerically for an ensemble of two-dimensional square two-wavespeed billiards with rough boundaries and quadratic nonlinearity representative of elastodynamic waves. Results of direct numerical simulations are compared with theoretical predictions.