Estimates of frequency-dependent compressibility from a quasistatic double-porosity model

Gassmann's relationship between the drained and undrained bulk modulus of a porous medium is often used to relate the dry bulk modulus to the saturated bulk modulus for elastic waves, because the compressibility of air is considered so high that the dry rock behaves in a drained fashion and the frequency of elastic waves is considered so high that the saturated rock behaves in an undrained fashion. The bulk modulus calculated from ultrasonic velocities, however, often does not match the Gassmann prediction. Mavko and Jizba examined how local flow effects and unequilibrated pore pressures can lead to greater stiffnesses. Their conceptual model consists of a distribution of porosities obtained from the strain-versus-confining-pressure behavior. Stiff pores that close at higher confining pressures are considered to remain undrained (unrelaxed) while soft pores drain even for high-frequency stress changes. If the pore shape distribution is bimodal, then the rock approximately satisfies the assumptions of a double-porosity, poroelastic material. Berryman and Wang [1995] established linear constitutive equations and identified four different time scales of ow behavior: (1) totally drained, (2) soft pores are drained but stiff pores are undrained, (3) soft and stiff pores are locally equilibrated, but undrained beyond the grain scale, and (4) both soft and stiff pores are undrained. The relative magnitudes of the four associated bulk moduli will be examined for all four moduli and illustrated for several sandstones

Target characterization using decomposition of the time-reversal operator: electromagnetic scattering from small ellipsoids

Decomposition of the time-reversal operator for an array, or equivalently the singular value decomposition of the multistatic response matrix, has been used to improve imaging and localization of targets in complicated media. Typically, each singular value is associated with one scatterer even though it has been shown in several cases that a single scatterer can generate several singular values. In earlier papers Chambers and Berryman [1, 2] showed that a small spherical scatterer can generate up to six singular values depending on the array geometry and sphere composition. It was shown that the existence and characteristics of multiple singular values for each scatterer can, in principle, be used to determine certain properties of the scatterers, e.g. conducting or non-conducting material. In this paper, we extend this analysis to non-spherical targets and show how orientation information about the target may be obtained from the spectrum of singular values. The general properties of the decomposition for small non-spherical dielectric (and possibly conductive) targets in an electromagnetic field are derived and detailed results are obtained for the specific cases of non-magnetic and perfectly conducting needles and disks. It is shown that scatterer orientation can be estimated by tracking the singular values of a linear array as it is rotated around its midpoint

Animal Performance, Storage Losses and Feasibility of Ensiling a Mixture of Tub Ground Low Quality Hay and Wet Distillers’ Grains for Growing Cattle

This study was designed to evaluate long term storage options for wet distillers’ grains including storage losses and performance of backgrounding calves. Thirty six tons of wet distillers’ grains were mixed by mixer wagon with 9 tons of tub ground fescue hay in August of 2007. This mixture packed and stored in a bunker silo, covered with plastic and stored until December at the ISU Beef Nutrition Farm. The mixture was fed to growing cattle and compared to the same feeds mixed daily, and also conventional feeds for a 112 day trial. Performance of all treatments exceeded projections, averaging approximately 3 pounds per day. There were no differences in daily gain or feed conversion among treatments, although cattle fed WDG consumed less feed. Sulfur content of the WDG containing diets exceeded .5% of the diet dry matter. Storage losses were 10.9% for the bunker-stored mixture

A Model for the Elasticity of Compressed Emulsions

We present a new model to describe the unusual elastic properties of compressed emulsions. The response of a single droplet under compression is investigated numerically for different Wigner-Seitz cells. The response is softer than harmonic, and depends on the coordination number of the droplet. Using these results, we propose a new effective inter-droplet potential which is used to determine the elastic response of a monodisperse collection of disordered droplets as a function of volume fraction. Our results are in excellent agreement with recent experiments. This suggests that anharmonicity, together with disorder, are responsible for the quasi-linear increase of $G$ and $\Pi$ observed at $\varphi_c$.Comment: RevTeX with psfig-included figures and a galley macr

Numerical model for granular compaction under vertical tapping

A simple numerical model is used to simulate the effect of vertical taps on a packing of monodisperse hard spheres. Our results are in agreement with an experimantal work done in Chicago and with other previous models, especially concerning the dynamics of the compaction, the influence of the excitation strength on the compaction efficiency, and some ageing effects. The principal asset of the model is that it allows a local analysis of the packings. Vertical and transverse density profiles are used as well as size and volume distributions of the pores. An interesting result concerns the appearance of a vertical gradient in the density profiles during compaction. Furthermore, the volume distribution of the pores suggests that the smallest pores, ranging in size between a tetrahedral and an octahedral site, are not strongly affected by the tapping process, in contrast to the largest pores which are more sensitive to the compaction of the packing.Comment: 8 pages, 15 figures (eps), to be published in Phys. Rev. E. Some corrections have been made, especially in paragraph IV

Packing of Compressible Granular Materials

3D Computer simulations and experiments are employed to study random packings of compressible spherical grains under external confining stress. Of particular interest is the rigid ball limit, which we describe as a continuous transition in which the applied stress vanishes as (\phi-\phi_c)^\beta, where \phi is the (solid phase) volume density. This transition coincides with the onset of shear rigidity. The value of \phi_c depends, for example, on whether the grains interact via only normal forces (giving rise to random close packings) or by a combination of normal and friction generated transverse forces (producing random loose packings). In both cases, near the transition, the system's response is controlled by localized force chains. As the stress increases, we characterize the system's evolution in terms of (1) the participation number, (2) the average force distribution, and (3) visualization techniques.Comment: 4 pages, 7 figures, to appear in Phys. Rev. Let

Beta-delayed proton emission in the 100Sn region

Beta-delayed proton emission from nuclides in the neighborhood of 100Sn was studied at the National Superconducting Cyclotron Laboratory. The nuclei were produced by fragmentation of a 120 MeV/nucleon 112Sn primary beam on a Be target. Beam purification was provided by the A1900 Fragment Separator and the Radio Frequency Fragment Separator. The fragments of interest were identified and their decay was studied with the NSCL Beta Counting System (BCS) in conjunction with the Segmented Germanium Array (SeGA). The nuclei 96Cd, 98Ing, 98Inm and 99In were identified as beta-delayed proton emitters, with branching ratios bp = 5.5(40)%, 5.5+3 -2%, 19(2)% and 0.9(4)%, respectively. The bp for 89Ru, 91,92Rh, 93Pd and 95Ag were deduced for the first time with bp = 3+1.9 -1.7%, 1.3(5)%, 1.9(1)%, 7.5(5)% and 2.5(3)%, respectively. The bp = 22(1)% for 101Sn was deduced with higher precision than previously reported. The impact of the newly measured bp values on the composition of the type-I X-ray burst ashes was studied.Comment: 15 pages, 14 Figures, 4 Table

Nonlinear anomalous diffusion equation and fractal dimension: Exact generalized gaussian solution

In this work we incorporate, in a unified way, two anomalous behaviors, the power law and stretched exponential ones, by considering the radial dependence of the $N$-dimensional nonlinear diffusion equation $\partial\rho /\partial{t}={\bf \nabla} \cdot (K{\bf \nabla} \rho^{\nu})-{\bf \nabla}\cdot(\mu{\bf F} \rho)-\alpha \rho ,$ where $K=D r^{-\theta}$, $\nu$, $\theta$, $\mu$ and $D$ are real parameters and $\alpha$ is a time-dependent source. This equation unifies the O'Shaugnessy-Procaccia anomalous diffusion equation on fractals ($\nu =1$) and the spherical anomalous diffusion for porous media ($\theta=0$). An exact spherical symmetric solution of this nonlinear Fokker-Planck equation is obtained, leading to a large class of anomalous behaviors. Stationary solutions for this Fokker-Planck-like equation are also discussed by introducing an effective potential.Comment: Latex, 6 pages. To appear in Phys. Rev.