PubMed Health⌕ Search

Biomedical subjects

Richard L Weaver

Publications and source records attributed to Richard L Weaver.

12 recordsLinked to original sources
PubMed2006

Transport and localization amongst coupled substructures.

The dynamics of the transport of the mean-square diffuse wave amplitude among coupled substructures is examined. Applications include coupled quantum dots, reverberation rooms, and chaotic billiards. A self-consistent theory is found to predict classical diffusive behavior at strong coupling, but to predict localization when coupling times are comparable to or greater than Heisenberg times. Predictions are compared to an exact result, to the Vollhardt-Wolfle self-consistent theory for multiply scattering continua, and to direct numerical simulations.

Journal Article↗
PubMed2006

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.

Journal Article↗
PubMed2005

Fluctuations in diffuse field-field correlations and the emergence of the Green's function in open systems.

Recent intense interest in diffuse field correlation functions, with applications to passive imaging in underwater acoustics and seismology, has raised questions about the degree with which a retrieved waveform can be expected to conform to the Green's function, and in particular the degree with which a ray arrival may be discerned. On considering a simple scalar wave model consisting of fields with distributed random sources, the difffuse field-field correlation function R is defined as a sum of correlation integrals, one for each of the many distinct distributed sources. It is then shown that this ensemble of fields has a correlation function with expectation (R) equal to the Green's function. This model also lends itself to calculations of the variance of R, and thus to estimates of the degree to which an R calculated using finite amounts of data will conform to the Green's function. The model predicts that such conformation is strongest at low frequencies. Ray arrivals are detectable if sufficient data have been collected, but the amount of data needed scales in three dimensions with the square of the source-receiver separation, and the square of the frequency. Applications to seismology are discussed.

Journal Article↗
PubMed2005

Toward a theory of wave energy transport in large irregular structures.

An ansatz is proposed by which the energy transport behavior observed at early times in a direct numerical simulation (DNS) of a large irregular structure may be extrapolated to arbitrary times. In the slow-transport limit, this ansatz leads to a diffusion-like equation, similar to that of time-domain statistical energy analysis (SEA), but it does not require substructuring. The model is successfully used to extract diffusion parameters from simulated data of unambiguously diffusive character. The model is then successfully used to extract diffusion parameters from data obtained in a DNS of a simple undamped two-room structure of a kind typically analyzed by SEA or room acoustics.

Journal Article↗
PubMed2004

Generalized Berry conjecture and mode correlations in chaotic plates.

We consider a modification of the Berry conjecture for eigenmode statistics in wave-bearing systems. The eigenmode correlator is conjectured to be proportional to the imaginary part of the Green's function. The generalization is applicable not only to scalar waves in the interior of homogeneous isotropic systems where the correlator is a Bessel function, but to arbitrary points of heterogeneous systems as well. In view of recent experimental measurements, expressions for the intensity correlator in chaotic plates are derived.

Journal Article↗
PubMed2004

Variance of transmitted power in multichannel dissipative ergodic structures invariant under time reversal.

We use random matrix theory (RMT) to study the first two moments of the wave power transmitted in time-reversal invariant systems having ergodic motion. Dissipation is modeled by a number of loss channels of variable coupling strength. To make a connection with ultrasonic experiments on ergodic elastodynamic billiards, the channels injecting and collecting the waves are assumed to be negligibly coupled to the medium and to contribute essentially no dissipation. Within the RMT model we calculate the quantities of interest exactly, employing the supersymmetry technique. This approach is found to be more accurate than another method based on simplifying naive assumptions for the statistics of the eigenfrequencies and the eigenfunctions. The results of the supersymmetric method are confirmed by Monte Carlo numerical simulation and are used to reveal a possible source of the disagreement between the predictions of the naive theory and ultrasonic measurements.

Journal Article↗
PubMed2003

Nonexponential dissipation in a lossy elastodynamic billiard: comparison with Porter-Thomas and random matrix predictions.

We study the dissipation of diffuse ultrasonic energy in a reverberant body coupled to a waveguide, an analog for a mesoscopic electron in a quantum dot. A simple model predicts a Porter-Thomas distribution of level widths and corresponding nonexponential dissipation, a behavior largely confirmed by measurements. For the case of fully open channels, however, measurements deviate from this model to a statistically significant degree. A random matrix supersymmetric calculation is found to accurately model the observed behaviors at all coupling strengths.

Journal Article↗
PubMed2003

Statistics of transmitted power in multichannel dissipative ergodic structures.

We use the random matrix theory (RMT) to study the probability distribution function and moments of the wave power transmitted inside systems with ergodic wave motion. The results describe either open multichannel systems or their closed counterparts with local-in-space internal dissipation. We concentrate on the regime of broken time-reversal invariance and employ two different analytical approaches: the exact supersymmetry method and a simpler technique that uses RMT eigenstatistics for closed nondissipative systems as an input. The results of the supersymmetric method were confirmed by numerical simulation. The simpler method is found to be adequate for closed systems with uniform dissipation, or in the limit of a large number of weak local dampers.

Journal Article↗
PubMed2003

Coda-wave interferometry in finite solids: recovery of P-to-S conversion rates in an elastodynamic billiard.

We study the temperature dependence of diffuse reverberant ultrasound in elastic bodies. Transient wave forms are found to undergo an almost pure dilation of 0.0277% per degree, related to the temperature dependence of wave speeds. The wave forms also suffer a distortion that, we argue, depends on the rate of conversion between the dilatational (P) and shear (S) waves. Distortion is found to scale in a manner consistent with theoretical arguments but also appears to be a function of the degree of ray chaos in the body, indicating that the mixing rates are slower in more regular bodies.

Journal Article↗
PubMed2003

Elastic wave thermal fluctuations, ultrasonic waveforms by correlation of thermal phonons.

It is widely recognized that acoustic degrees of freedom coupled to a thermal bath have amplitudes which fluctuate with a mean square proportional to temperature; this is the basis for the Debye theory of the heat capacity of insulating solids. It is shown here that these elastic wave thermal phonons have correlation functions identical to the system's ultrasonic Green's function, and furthermore that thermal noise in ultrasonic detectors should have correlation functions equivalent to conventional waveforms obtained by active transmission and reception. This suggests the possibility of doing ultrasonics without a source. Theory for the identity is presented, and several room temperature laboratory confirmations are conducted in the frequency range 0.1-1.0 MHz. The thermal nature of the origin of these correlations is established by comparing their strength with theoretical expectations. Applications are discussed.

Models, Theoretical↗