Smoothing of sandpile surfaces after intermittent and continuous avalanches: three models in search of an experiment

We present and analyse in this paper three models of coupled continuum equations all united by a common theme: the intuitive notion that sandpile surfaces are left smoother by the propagation of avalanches across them. Two of these concern smoothing at the `bare' interface, appropriate to intermittent avalanche flow, while one of them models smoothing at the effective surface defined by a cloud of flowing grains across the `bare' interface, which is appropriate to the regime where avalanches flow continuously across the sandpile.Comment: 17 pages and 26 figures. Submitted to Physical Review

Glassy dynamics in granular compaction

Two models are presented to study the influence of slow dynamics on granular compaction. It is found in both cases that high values of packing fraction are achieved only by the slow relaxation of cooperative structures. Ongoing work to study the full implications of these results is discussed.Comment: 12 pages, 9 figures; accepted in J. Phys: Condensed Matter, proceedings of the Trieste workshop on 'Unifying concepts in glass physics

Laboratory experiments on cohesive soil bed fluidization by water waves

Part I. Relationships between the rate of bed fluidization and the rate of wave energy dissipation, by Jingzhi Feng and Ashish J. Mehta and Part II. In-situ rheometry for determining the dynamic response of bed, by David J.A. Williams and P. Rhodri Williams. A series of preliminary laboratory flume experiments were carried out to examine the time-dependent behavior of a cohesive soil bed subjected to progressive, monochromatic waves. The bed was an aqueous, 50/50 (by weight) mixture of a kaolinite and an attapulgite placed in a plexiglass trench. The nominal bed thickness was 16 cm with density ranging from 1170 to 1380 kg/m 3, and water above was 16 to 20 cm deep. Waves of design height ranging from 2 to 8 cm and a nominal frequency of 1 Hz were run for durations up to 2970 min. Part I of this report describes experiments meant to examine the rate at which the bed became fluidized, and its relation to the rate of wave energy dissipation. Part II gives results on in-situ rheometry used to track the associated changes in bed rigidity. Temporal and spatial changes of the effective stress were measured during the course of wave action, and from these changes the bed fluidization rate was calculated. A wave-mud interaction model developed in a companion study was employed to calculate the rate of wave energy dissipation. The dependence of the rate of fluidization on the rate of energy dissipation was then explored. Fluidization, which seemingly proceeded down from the bed surface, occurred as a result of the loss of structural integrity of the soil matrix through a buildup of the excess pore pressure and the associated loss of effective stress. The rate of fluidization was typically greater at the beginning of wave action and apparently approached zero with time. This trend coincided with the approach of the rate of energy dissipation to a constant value. In general it was also observed that, for a given wave frequency, the larger the wave height the faster the rate of fluidization and thicker the fluid mud layer formed. On the other hand, increasing the time of bed consolidation prior to wave action decreased the fluidization rate due to greater bed rigidity. Upon cessation of wave action structural recovery followed. Dynamic rigidity was measured by specially designed, in situ shearometers placed in the bed at appropriate elevations to determine the time-dependence of the storage and loss moduli, G' and G", of the viscoelastic clay mixture under 1 Hz waves. As the inter-particle bonds of the space-filling, bed material matrix weakened, the shear propagation velocity decreased measurably. Consequently, G' decreased and G" increased as a transition from dynamically more elastic to more viscous response occurred. These preliminary experiments have demonstrated the validity of the particular rheometric technique used, and the critical need for synchronous, in-situ measurements of pore pressures and moduli characterizing bed rheology in studies on mud fluidization. This study was supported by WES contract DACW39-90-K-0010. (This document contains 151 pages.

Finite-difference distributions for the Ginibre ensemble

The Ginibre ensemble of complex random matrices is studied. The complex valued random variable of second difference of complex energy levels is defined. For the N=3 dimensional ensemble are calculated distributions of second difference, of real and imaginary parts of second difference, as well as of its radius and of its argument (angle). For the generic N-dimensional Ginibre ensemble an exact analytical formula for second difference's distribution is derived. The comparison with real valued random variable of second difference of adjacent real valued energy levels for Gaussian orthogonal, unitary, and symplectic, ensemble of random matrices as well as for Poisson ensemble is provided.Comment: 8 pages, a number of small changes in the tex

Fine asymptotic behavior in eigenvalues of random normal matrices: Ellipse Case

We consider the random normal matrices with quadratic external potentials where the associated orthogonal polynomials are Hermite polynomials and the limiting support (called droplet) of the eigenvalues is an ellipse. We calculate the density of the eigenvalues near the boundary of the droplet up to the second subleading corrections and express the subleading corrections in terms of the curvature of the droplet boundary. From this result we additionally get the expected number of eigenvalues outside the droplet. We also obtain the asymptotics of the kernel and found that, in the bulk, the correction term is exponentially small. This leads to the vanishing of certain Cauchy transform of the orthogonal polynomial in the bulk of the droplet up to an exponentially small error.Comment: 39 pages, 5 figures. Extended version: Theorem 1.2, Theorem 1.4, Section 6 and Section 7.3 are ne

The Energetic Costs of Cellular Computation

Cells often perform computations in response to environmental cues. A simple example is the classic problem, first considered by Berg and Purcell, of determining the concentration of a chemical ligand in the surrounding media. On general theoretical grounds (Landuer's Principle), it is expected that such computations require cells to consume energy. Here, we explicitly calculate the energetic costs of computing ligand concentration for a simple two-component cellular network that implements a noisy version of the Berg-Purcell strategy. We show that learning about external concentrations necessitates the breaking of detailed balance and consumption of energy, with greater learning requiring more energy. Our calculations suggest that the energetic costs of cellular computation may be an important constraint on networks designed to function in resource poor environments such as the spore germination networks of bacteria.Comment: 9 Pages (including Appendix); 4 Figures; v3 corrects even more typo

Shaking a Box of Sand

We present a simple model of a vibrated box of sand, and discuss its dynamics in terms of two parameters reflecting static and dynamic disorder respectively. The fluidised, intermediate and frozen (`glassy') dynamical regimes are extensively probed by analysing the response of the packing fraction to steady, as well as cyclic, shaking, and indicators of the onset of a `glass transition' are analysed. In the `glassy' regime, our model is exactly solvable, and allows for the qualitative description of ageing phenomena in terms of two characteristic lengths; predictions are also made about the influence of grain shape anisotropy on ageing behaviour.Comment: Revised version. To appear in Europhysics Letter

Jacobi Crossover Ensembles of Random Matrices and Statistics of Transmission Eigenvalues

We study the transition in conductance properties of chaotic mesoscopic cavities as time-reversal symmetry is broken. We consider the Brownian motion model for transmission eigenvalues for both types of transitions, viz., orthogonal-unitary and symplectic-unitary crossovers depending on the presence or absence of spin-rotation symmetry of the electron. In both cases the crossover is governed by a Brownian motion parameter {\tau}, which measures the extent of time-reversal symmetry breaking. It is shown that the results obtained correspond to the Jacobi crossover ensembles of random matrices. We derive the level density and the correlation functions of higher orders for the transmission eigenvalues. We also obtain the exact expressions for the average conductance, average shot-noise power and variance of conductance, as functions of {\tau}, for arbitrary number of modes (channels) in the two leads connected to the cavity. Moreover, we give the asymptotic result for the variance of shot-noise power for both the crossovers, the exact results being too long. In the {\tau} \rightarrow 0 and {\tau} \rightarrow \infty limits the known results for the orthogonal (or symplectic) and unitary ensembles are reproduced. In the weak time-reversal symmetry breaking regime our results are shown to be in agreement with the semiclassical predictions.Comment: 24 pages, 5 figure