Three-state analytic theory of two-dimensional nuclear magnetic resonance in systems with coupled macro- and micropores.

Two-dimensional (2D) nuclear magnetic resonance (NMR) experiments involve a sequence of longitudinal (T(1)) and transverse (T(2)) measurements. In a previous paper we showed that if each of these 1D measurements can be represented by two exponential decays then there can be an accurate analytic solution for the 2D measurements with no additional information. In this paper we extend the theory to the case where there are three decay channels for the 1D measurements.

Density of states in granular media in the presence of damping.

We consider the density of states of granular media in which each grain-grain contact is damped with a damping force proportional to the relative velocity of the two grains, in addition to the usual spring constant. Under the assumption that the so-called criterion of proportional damping is only weakly violated we are able to deduce the density of states for undamped frequencies from the measured complex-valued frequencies of damped oscillations. We deduce a quantitative estimate of the deviation from the proportional criterion.

Analytic theory of two-dimensional NMR in systems with coupled macro- and micropores.

Two-dimensional (2D) nuclear magnetic resonance (NMR) experiments involve a sequence of longitudinal (T(1)) and transverse (T(2)) measurements. When such experiments are applied to porous media, they are believed to provide new and important information regarding diffusive coupling between distinct pore subpopulations. However, we show in this paper that, in many cases of interest, this is simply not true.

Nonlinear phasing and dephasing of three-wave mixing of acoustic guided waves.

We measure the propagation of guided acoustic waves in a nonlinear three-wave mixing experiment in a water-filled steel pipe. These waves exhibit a predicted phasing-dephasing behavior as a function of propagation distance due to the underlying velocity dispersion between the fundamentals and the nonlinearly generated waves. We extract the dimensionless nonlinear parameter, β, which is weakly frequency dependent.

Normal-mode spectrum of finite-sized granular systems: The effects of fluid viscosity at the grain contacts.

We investigate the effects of adsorbed films on the attenuative properties of loose granular media occupying a finite-sized rigid container that is open at the top. We measure the effective mass, M[over ̃](ω), of loose tungsten particles prepared under two different sets of conditions: (i) We lightly coat tungsten grains with a fixed volume fraction of silicone oil (polydimethylsiloxane, PDMS), where the liquid viscosity is varied for individual realizations, and (ii) in the other set of experiments we vary the humidity. On a theoretical level, we are able to decompose the effective mass into a sum over the contributions from each of the normal modes of the granular medium.

Experiments on stress dependent borehole acoustic waves.

In the laboratory setup, a borehole traverses a dry sandstone formation, which is subjected to a controlled uniaxial stress in the direction perpendicular to the borehole axis. Measurements are made in a single loading-unloading stress cycle from zero to 10 MPa and then back down to zero stress. The applied stress and the presence of the borehole induce anisotropy in the bulk of the material and stress concentration around the borehole, both azimuthally and radially.

Effect of granular media on the vibrational response of a resonant structure: theory and experiment.

The acoustic response of a structure that contains a cavity filled with a loose granular material is analyzed. The inputs to the theory are the effective masses of each subsystem: that of the empty-cavity resonating structure and that of the granular medium within the cavity. This theory accurately predicts the frequencies, widths, and relative amplitudes of the various flexural mode resonances observed with rectangular bars, each having a cavity filled with loose tungsten granules.

Dynamic effective mass of granular media and the attenuation of structure-borne sound.

We report a theoretical and experimental investigation into the fundamental physics of why loose granular media are effective deadeners of structure-borne sound. Here, we demonstrate that a measurement of the effective mass, M(omega), of the granular medium is a sensitive and direct way to answer the question: what is the specific mechanism whereby acoustic energy is transformed into heat? Specifically, we apply this understanding to the case of the flexural resonances of a rectangular bar with a grain-filled cavity within it. The pore space in the granular medium is air of varying humidity.

Aspects of diffusive-relaxation dynamics with a nonuniform, partially absorbing boundary in general porous media.

We consider the Helmholtz problem in the context of the evolution of uniform initial distribution of a physical attribute in general porous media subject to a partially absorbing boundary condition. Its spectral property as a reflection of the boundary geometry has been widely exploited, such as in biological and geophysical applications. We consider the situation where the critical assumptions which enable such applications break down.

Capillary forces in the acoustics of patchy-saturated porous media.

A linearized theory of the acoustics of porous elastic formations, such as rocks, saturated with two different viscous fluids is generalized to take into account a pressure discontinuity across the fluid boundaries. The latter can arise due to the surface tension of the membrane separating the fluids. We show that the frequency-dependent bulk modulus K(omega) for wavelengths longer than the characteristic structural dimensions of the fluid patches has a similar analytic behavior to the case of a vanishing membrane stiffness and depends on the same parameters of the fluid-distribution topology.