Post-injection normal closure of fractures as a mechanism for induced seismicity

Understanding the controlling mechanisms underlying injection-induced seismicity is important for optimizing reservoir productivity and addressing seismicity-related concerns related to hydraulic stimulation in Enhanced Geothermal Systems. Hydraulic stimulation enhances permeability through elevated pressures, which cause normal deformations, and the shear slip of pre-existing fractures. Previous experiments indicate that fracture deformation in the normal direction reverses as the pressure decreases, e.g., at the end of stimulation. We hypothesize that this normal closure of fractures enhances pressure propagation away from the injection region and significantly increases the potential for post-injection seismicity. To test this hypothesis, hydraulic stimulation is modeled by numerically coupling fracture deformation, pressure diffusion and stress alterations for a synthetic geothermal reservoir in which the flow and mechanics are strongly affected by a complex three-dimensional fracture network. The role of the normal closure of fractures is verified by comparing simulations conducted with and without the normal closure effect

Dynamics of axial separation in long rotating drums

We propose a continuum description for the axial separation of granular materials in a long rotating drum. The model, operating with two local variables, concentration difference and the dynamic angle of repose, describes both initial transient traveling wave dynamics and long-term segregation of the binary mixture. Segregation proceeds through ultra-slow logarithmic coarsening.Comment: 4 pages, 3 Postscript figures; submitted to PR

Velocity Distributions of Granular Gases with Drag and with Long-Range Interactions

We study velocity statistics of electrostatically driven granular gases. For two different experiments: (i) non-magnetic particles in a viscous fluid and (ii) magnetic particles in air, the velocity distribution is non-Maxwellian, and its high-energy tail is exponential, P(v) ~ exp(-|v|). This behavior is consistent with kinetic theory of driven dissipative particles. For particles immersed in a fluid, viscous damping is responsible for the exponential tail, while for magnetic particles, long-range interactions cause the exponential tail. We conclude that velocity statistics of dissipative gases are sensitive to the fluid environment and to the form of the particle interaction.Comment: 4 pages, 3 figure

Knots and Random Walks in Vibrated Granular Chains

We study experimentally statistical properties of the opening times of knots in vertically vibrated granular chains. Our measurements are in good qualitative and quantitative agreement with a theoretical model involving three random walks interacting via hard core exclusion in one spatial dimension. In particular, the knot survival probability follows a universal scaling function which is independent of the chain length, with a corresponding diffusive characteristic time scale. Both the large-exit-time and the small-exit-time tails of the distribution are suppressed exponentially, and the corresponding decay coefficients are in excellent agreement with the theoretical values.Comment: 4 pages, 5 figure

Estimating good discrete partitions from observed data: symbolic false nearest neighbors

A symbolic analysis of observed time series data requires making a discrete partition of a continuous state space containing observations of the dynamics. A particular kind of partition, called ``generating'', preserves all dynamical information of a deterministic map in the symbolic representation, but such partitions are not obvious beyond one dimension, and existing methods to find them require significant knowledge of the dynamical evolution operator or the spectrum of unstable periodic orbits. We introduce a statistic and algorithm to refine empirical partitions for symbolic state reconstruction. This method optimizes an essential property of a generating partition: avoiding topological degeneracies. It requires only the observed time series and is sensible even in the presence of noise when no truly generating partition is possible. Because of its resemblance to a geometrical statistic frequently used for reconstructing valid time-delay embeddings, we call the algorithm ``symbolic false nearest neighbors''

Nearest pattern interaction and global pattern formation

We studied the effect of nearest pattern interaction on a globally pattern formation in a 2-dimensional space, where patterns are to grow initially from a noise in the presence of periodic supply of energy. Although our approach is general, we found that this study is relevant in particular to the pattern formation on a periodically vibrated granular layer, as it gives a unified perspective of the experimentally observed pattern dynamics such as oscillon and stripe formations, skew-varicose and crossroll instabilities, and also a kink formation and decoration

Demonstration of the Complementarity of One- and Two-Photon Interference

The visibilities of second-order (single-photon) and fourth-order (two-photon) interference have been observed in a Young's double-slit experiment using light generated by spontaneous parametric down-conversion and a photon-counting intensified CCD camera. Coherence and entanglement underlie one-and two-photon interference, respectively. As the effective source size is increased, coherence is diminished while entanglement is enhanced, so that the visibility of single-photon interference decreases while that of two-photon interference increases. This is the first experimental demonstration of the complementarity between single- and two-photon interference (coherence and entanglement) in the spatial domain.Comment: 21 pages, 7 figure

A Model for Force Fluctuations in Bead Packs

We study theoretically the complex network of forces that is responsible for the static structure and properties of granular materials. We present detailed calculations for a model in which the fluctuations in the force distribution arise because of variations in the contact angles and the constraints imposed by the force balance on each bead of the pile. We compare our results for force distribution function for this model, including exact results for certain contact angle probability distributions, with numerical simulations of force distributions in random sphere packings. This model reproduces many aspects of the force distribution observed both in experiment and in numerical simulations of sphere packings

Inelastic Collapse of Three Particles

A system of three particles undergoing inelastic collisions in arbitrary spatial dimensions is studied with the aim of establishing the domain of ``inelastic collapse''---an infinite number of collisions which take place in a finite time. Analytic and simulation results show that for a sufficiently small restitution coefficient, $0\leq r<7-4\sqrt{3}\approx 0.072$, collapse can occur. In one dimension, such a collapse is stable against small perturbations within this entire range. In higher dimensions, the collapse can be stable against small variations of initial conditions, within a smaller $r$ range, $0\leq r<9-4\sqrt{5}\approx 0.056$.Comment: 6 pages, figures on request, accepted by PR

Entanglement, Mixedness, and Spin-Flip Symmetry in Multiple-Qubit Systems

A relationship between a recently introduced multipartite entanglement measure, state mixedness, and spin-flip symmetry is established for any finite number of qubits. It is also shown that, within those classes of states invariant under the spin-flip transformation, there is a complementarity relation between multipartite entanglement and mixedness. A number of example classes of multiple-qubit systems are studied in light of this relationship.Comment: To appear in Physical Review A; submitted 14 May 200