From Avalanches to Fluid Flow: A Continuous Picture of Grain Dynamics Down a Heap

Surface flows are excited by steadily adding spherical glass beads to the top of a heap. To simultaneously characterize the fast single-grain dynamics and the much slower collective intermittency of the flow, we extend photon-correlation spectroscopy via fourth-order temporal correlations in the scattered light intensity. We find that microscopic grain dynamics during an avalanche are similar to those in the continuous flow just above the transition. We also find that there is a minimum jamming time, even arbitrarily close to the transition

Properties of bright squeezed vacuum at increasing brightness

A bright squeezed vacuum (BSV) is a nonclassical macroscopic state of light, which is generated through high-gain parametric down-conversion or four-wave mixing. Although the BSV is an important tool in quantum optics and has a lot of applications, its theoretical description is still not complete. In particular, the existing description in terms of Schmidt modes with gain-independent shapes fails to explain the spectral broadening observed in the experiment as the mean number of photons increases. Meanwhile, the semiclassical description accounting for the broadening does not allow us to decouple the intermodal photon-number correlations. In this work, we present a new generalized theoretical approach to describe the spatial properties of a multimode BSV. In the multimode case, one has to take into account the complicated interplay between all involved modes: each plane-wave mode interacts with all other modes, which complicates the problem significantly. The developed approach is based on exchanging the (k, t ) and (ω, z) representations and solving a system of integrodifferential equations. Our approach predicts correctly the dynamics of the Schmidt modes and the broadening of the angular distribution with the increase in the BSV mean photon number due to a stronger pumping. Moreover, the model correctly describes various properties of a widely used experimental configuration with two crystals and an air gap between them, namely, an SU(1,1) interferometer. In particular, it predicts the narrowing of the intensity distribution, the reduction and shift of the side lobes, and the decline in the interference visibility as the mean photon number increases due to stronger pumping. The presented experimental results confirm the validity of the new approach. The model can be easily extended to the case of the frequency spectrum, frequency Schmidt modes, and other experimental configurations

Diffusing-Light Spectroscopies Beyond the Diffusion Limit: The Role of Ballistic Transport and Anisotropic Scattering

Diffuse transmission and diffusing-wave spectroscopy (DWS) can be used to probe the structure and dynamics of opaque materials such as colloids, foams, and sand. A crucial step is to model photon transport as a diffusion process. This approach is acceptable for optically thick samples, far into the limit of strong multiple scattering; however, it becomes increasingly inaccurate for thinner samples for several reasons. Here, we correct for two of these defects. By modeling photon propagation by a telegrapher equation with suitable boundary conditions, we can account for the ballistic transport of photons at finite speed between successive scattering events. By introducing a discontinuity in the photon concentration at the source point, and then averaging over a range of penetration depths, we can account for the fact that photons usually scatter anisotropically into the forward direction, rather than being completely randomized at each event. The accuracy of our approach is tested by comparison both with random walk computer simulations and with experiments on specially designed suspensions of polystyrene spheres. We find that our predictions extend the utility of diffuse transmission to slabs of all thicknesses and of DWS to slabs down to about two transport mean free paths

Diffusion at constant speed in a model phase space

We reconsider the problem of diffusion of particles at constant speed and present a generalization of the Telegrapher process to higher dimensional stochastic media ($d>1$), where the particle can move along $2^d$ directions. We derive the equations for the probability density function using the ``formulae of differentiation'' of Shapiro and Loginov. The model is an advancement over similiar models of photon migration in multiply scattering media in that it results in a true diffusion at constant speed in the limit of large dimensions.Comment: Final corrected version RevTeX, 6 pages, 1 figur

Stressed backbone and elasticity of random central-force systems

We use a new algorithm to find the stress-carrying backbone of ``generic'' site-diluted triangular lattices of up to 10^6 sites. Generic lattices can be made by randomly displacing the sites of a regular lattice. The percolation threshold is Pc=0.6975 +/- 0.0003, the correlation length exponent \nu =1.16 +/- 0.03 and the fractal dimension of the backbone Db=1.78 +/- 0.02. The number of ``critical bonds'' (if you remove them rigidity is lost) on the backbone scales as L^{x}, with x=0.85 +/- 0.05. The Young's modulus is also calculated.Comment: 5 pages, 5 figures, uses epsfi

Sequential quasi-Monte Carlo: Introduction for Non-Experts, Dimension Reduction, Application to Partly Observed Diffusion Processes

SMC (Sequential Monte Carlo) is a class of Monte Carlo algorithms for filtering and related sequential problems. Gerber and Chopin (2015) introduced SQMC (Sequential quasi-Monte Carlo), a QMC version of SMC. This paper has two objectives: (a) to introduce Sequential Monte Carlo to the QMC community, whose members are usually less familiar with state-space models and particle filtering; (b) to extend SQMC to the filtering of continuous-time state-space models, where the latent process is a diffusion. A recurring point in the paper will be the notion of dimension reduction, that is how to implement SQMC in such a way that it provides good performance despite the high dimension of the problem.Comment: To be published in the proceedings of MCMQMC 201

Granular flow down a rough inclined plane: transition between thin and thick piles

The rheology of granular particles in an inclined plane geometry is studied using molecular dynamics simulations. The flow--no-flow boundary is determined for piles of varying heights over a range of inclination angles $\theta$. Three angles determine the phase diagram: $\theta_{r}$, the angle of repose, is the angle at which a flowing system comes to rest; $\theta_{m}$, the maximum angle of stability, is the inclination required to induce flow in a static system; and $\theta_{max}$ is the maximum angle for which stable, steady state flow is observed. In the stable flow region $\theta_{r}<\theta<\theta_{max}$, three flow regimes can be distinguished that depend on how close $\theta$ is to $\theta_{r}$: i) $\theta>>\theta_{r}$: Bagnold rheology, characterized by a mean particle velocity $v_{x}$ in the direction of flow that scales as $v_{x}\propto h^{3/2}$, for a pile of height $h$, ii) $\theta\gtrsim\theta_{r}$: the slow flow regime, characterized by a linear velocity profile with depth, and iii) $\theta\approx\theta_{r}$: avalanche flow characterized by a slow underlying creep motion combined with occasional free surface events and large energy fluctuations. We also probe the physics of the initiation and cessation of flow. The results are compared to several recent experimental studies on chute flows and suggest that differences between measured velocity profiles in these experiments may simply be a consequence of how far the system is from jamming.Comment: 19 pages, 14 figs, submitted to Physics of Fluid