Compaction dynamics in ductile granular media

Ductile compaction is common in many natural systems, but the temporal evolution of such systems is rarely studied. We observe surprising oscillations in the weight measured at the bottom of a self-compacting ensemble of ductile grains. The oscillations develop during the first ten hours of the experiment, and usually persist through the length of an experiment (one week). The weight oscillations are connected to the grain--wall contacts, and are directly correlated with the observed strain evolution and the dynamics of grain--wall contacts during the compaction. Here, we present the experimental results and characteristic time constants of the system, and discuss possible reasons for the measured weight oscillations.Comment: 11 pages, 14 figure

Fracture Surfaces as Multiscaling Graphs

Fracture paths in quasi-two-dimenisonal (2D) media (e.g thin layers of materials, paper) are analyzed as self-affine graphs $h(x)$ of height $h$ as a function of length $x$. We show that these are multiscaling, in the sense that $n^{th}$ order moments of the height fluctuations across any distance $\ell$ scale with a characteristic exponent that depends nonlinearly on the order of the moment. Having demonstrated this, one rules out a widely held conjecture that fracture in 2D belongs to the universality class of directed polymers in random media. In fact, 2D fracture does not belong to any of the known kinetic roughening models. The presence of multiscaling offers a stringent test for any theoretical model; we show that a recently introduced model of quasi-static fracture passes this test.Comment: 4 pages, 5 figure

Invasion Percolation Between two Sites

We investigate the process of invasion percolation between two sites (injection and extraction sites) separated by a distance r in two-dimensional lattices of size L. Our results for the non-trapping invasion percolation model indicate that the statistics of the mass of invaded clusters is significantly dependent on the local occupation probability (pressure) Pe at the extraction site. For Pe=0, we show that the mass distribution of invaded clusters P(M) follows a power-law P(M) ~ M^{-\alpha} for intermediate values of the mass M, with an exponent \alpha=1.39. When the local pressure is set to Pe=Pc, where Pc corresponds to the site percolation threshold of the lattice topology, the distribution P(M) still displays a scaling region, but with an exponent \alpha=1.02. This last behavior is consistent with previous results for the cluster statistics in standard percolation. In spite of these discrepancies, the results of our simulations indicate that the fractal dimension of the invaded cluster does not depends significantly on the local pressure Pe and it is consistent with the fractal dimension values reported for standard invasion percolation. Finally, we perform extensive numerical simulations to determine the effect of the lattice borders on the statistics of the invaded clusters and also to characterize the self-organized critical behavior of the invasion percolation process.Comment: 7 pages, 11 figures, submited for PR

Knock-Limited Performance of Triptane and 28-R Fuel Blends as Affected by Changes in Compression Ratio and in Engine Operating Variables

A knock-limited performance investigation was conducted on blends of triptane and 28-P fuel with a 12-cylinder, V-type, liquid-cooled aircraft engine of 1710-cubic-inch displacement at three compression ratios: 6.65, 7.93, and 9.68. At each compression ratio, the effect of changes in temperature of the inlet air to the auxiliary-stage supercharger and in fuel-air ratio were investigated at engine speeds of 2280 and. 3000 rpm. The results show that knock-limited engine performance, as improved by the use of triptane, allowed operation at both take-off and cruising power at a compression ratio of 9.68. At an inlet-air temperature of 60 deg F, an engine speed of 3000 rpm ; and a fuel-air ratio of 0,095 (approximately take-off conditions), a knock-limited engine output of 1500 brake horsepower was possible with 100-percent 28-R fuel at a compression ratio of 6.65; 20-percent triptane was required for the same power output at a compression ratio of 7.93, and 75 percent at a compression ratio of 9.68 allowed an output of 1480 brake horsepower. Knock-limited power output was more sensitive to changes in fuel-air ratio as the engine speed was increased from 2280 to 3000 rpm, as the compression ratio is raised from 6.65 to 9.68, or as the inlet-air temperature is raised from 0 deg to 120 deg F

Shape deformations and angular momentum transfer in trapped Bose-Einstein condensates

Angular momentum can be transferred to a trapped Bose-Einstein condensate by distorting its shape with an external rotating field, provided the rotational frequency is larger than a critical frequency fixed by the energy and angular momentum of the excited states of the system. By using the Gross-Pitaevskii equation and sum rules, we explore the dependence of such a critical frequency on the multipolarity of the excitations and the asymmetry of the confining potential. We also discuss its possible relevance for vortex nucleation in rotating traps.Comment: 4 pages revtex, 2 figures include

Dynamic instability of a rotating Bose-Einstein condensate

We consider a Bose-Einstein condensate subject to a rotating harmonic potential, in connection with recent experiments leading to the formation of vortices. We use the classical hydrodynamic approximation to the non-linear Schr\"odinger equation to determine almost analytically the evolution of the condensate. We predict that this evolution can exhibit dynamical instabilities, for the stirring procedure previously demonstrated at ENS and for a new stirring procedure that we put forward. These instabilities take place within the range of stirring frequency and amplitude for which vortices are produced experimentally. They provide therefore an initiating mechanism for vortex nucleation.Comment: 4 pages, 3 figures, last version including comparison with experiment

Testing equivalence of pure quantum states and graph states under SLOCC

A set of necessary and sufficient conditions are derived for the equivalence of an arbitrary pure state and a graph state on n qubits under stochastic local operations and classical communication (SLOCC), using the stabilizer formalism. Because all stabilizer states are equivalent to a graph state by local unitary transformations, these conditions constitute a classical algorithm for the determination of SLOCC-equivalence of pure states and stabilizer states. This algorithm provides a distinct advantage over the direct solution of the SLOCC-equivalence condition for an unknown invertible local operator S, as it usually allows for easy detection of states that are not SLOCC-equivalent to graph states.Comment: 9 pages, to appear in International Journal of Quantum Information; Minor typos corrected, updated references

Discrepancies in Determinations of the Ginzburg-Landau Parameter

Long-standing discrepancies within determinations of the Ginzburg-Landau parameter $\kappa$ from supercritical field measurements on superconducting microspheres are reexamined. The discrepancy in tin is shown to result from differing methods of analyses, whereas the discrepancy in indium is a consequence of significantly differing experimental results. The reanalyses however confirms the lower $\kappa$ determinations to within experimental uncertainties.Comment: submitted to Phys. Rev.