Heap Formation in Granular Media

Using molecular dynamics (MD) simulations, we find the formation of heaps in a system of granular particles contained in a box with oscillating bottom and fixed sidewalls. The simulation includes the effect of static friction, which is found to be crucial in maintaining a stable heap. We also find another mechanism for heap formation in systems under constant vertical shear. In both systems, heaps are formed due to a net downward shear by the sidewalls. We discuss the origin of net downward shear for the vibration induced heap.Comment: 11 pages, 4 figures available upon request, Plain TeX, HLRZ-101/9

Angle of Repose and Angle of Marginal Stability: Molecular Dyanmics of Granular Particles

We present an implementation of realistic static friction in molecular dynamics (MD) simulations of granular particles. In our model, to break contacts between two particles, one has to apply a finite amount of force, determined by the Coulomb criterion. Using a two dimensional model, we show that piles generated by avalanches have a {\it finite} angle of repose $\theta_R$ (finite slopes). Furthermore, these piles are stable under tilting by an angle smaller than a non-zero tilting angle $\theta_T$, showing that $\theta_R$ is different from the angle of marginal stability $\theta_{MS}$, which is the maximum angle of stable piles. These measured angles are compared to a theoretical approximation. We also measure $\theta_{MS}$ by continuously adding particles on the top of a stable pile.Comment: 14 pages, Plain Te

Scalar conservation laws with nonconstant coefficients with application to particle size segregation in granular flow

Granular materials will segregate by particle size when subjected to shear, as occurs, for example, in avalanches. The evolution of a bidisperse mixture of particles can be modeled by a nonlinear first order partial differential equation, provided the shear (or velocity) is a known function of position. While avalanche-driven shear is approximately uniform in depth, boundary-driven shear typically creates a shear band with a nonlinear velocity profile. In this paper, we measure a velocity profile from experimental data and solve initial value problems that mimic the segregation observed in the experiment, thereby verifying the value of the continuum model. To simplify the analysis, we consider only one-dimensional configurations, in which a layer of small particles is placed above a layer of large particles within an annular shear cell and is sheared for arbitrarily long times. We fit the measured velocity profile to both an exponential function of depth and a piecewise linear function which separates the shear band from the rest of the material. Each solution of the initial value problem is non-standard, involving curved characteristics in the exponential case, and a material interface with a jump in characteristic speed in the piecewise linear case

Pumping two dilute gas Bose-Einstein condensates with Raman light scattering

We propose an optical method for increasing the number of atoms in a pair of dilute gas Bose-Einstein condensates. The method uses laser-driven Raman transitions which scatter atoms between the condensate and non-condensate atom fractions. For a range of condensate phase differences there is destructive quantum interference of the amplitudes for scattering atoms out of the condensates. Because the total atom scattering rate into the condensates is unaffected the condensates grow. This mechanism is analogous to that responsible for optical lasing without inversion. Growth using macroscopic quantum interference may find application as a pump for an atom laser.Comment: 4 pages, no figure

Existence of a maximum balanced matching in the hypercube

We prove, that for the maximum possible edges can be chosen simultaneously from each parallel class of the n-cube in such a way that no two edges have a common vertex. © 2013 Copyright Grace Scientific Publishing, LLC

Stabilized high-power laser system for the gravitational wave detector advanced LIGO

An ultra-stable, high-power cw Nd:YAG laser system, developed for the ground-based gravitational wave detector Advanced LIGO (Laser Interferometer Gravitational-Wave Observatory), was comprehensively characterized. Laser power, frequency, beam pointing and beam quality were simultaneously stabilized using different active and passive schemes. The output beam, the performance of the stabilization, and the cross-coupling between different stabilization feedback control loops were characterized and found to fulfill most design requirements. The employed stabilization schemes and the achieved performance are of relevance to many high-precision optical experiments

Classification of irreducible quasifinite modules over map Virasoro algebras

We give a complete classification of the irreducible quasifinite modules for algebras of the form Vir \otimes A, where Vir is the Virasoro algebra and A is a Noetherian commutative associative unital algebra over the complex numbers. It is shown that all such modules are tensor products of generalized evaluation modules. We also give an explicit sufficient condition for a Verma module of Vir \otimes A to be reducible. In the case that A is an infinite-dimensional integral domain, this condition is also necessary.Comment: 25 pages. v2: Minor changes, published versio

A constitutive law for dense granular flows

A continuum description of granular flows would be of considerable help in predicting natural geophysical hazards or in designing industrial processes. However, the constitutive equations for dry granular flows, which govern how the material moves under shear, are still a matter of debate. One difficulty is that grains can behave like a solid (in a sand pile), a liquid (when poured from a silo) or a gas (when strongly agitated). For the two extreme regimes, constitutive equations have been proposed based on kinetic theory for collisional rapid flows, and soil mechanics for slow plastic flows. However, the intermediate dense regime, where the granular material flows like a liquid, still lacks a unified view and has motivated many studies over the past decade. The main characteristics of granular liquids are: a yield criterion (a critical shear stress below which flow is not possible) and a complex dependence on shear rate when flowing. In this sense, granular matter shares similarities with classical visco-plastic fluids such as Bingham fluids. Here we propose a new constitutive relation for dense granular flows, inspired by this analogy and recent numerical and experimental work. We then test our three-dimensional (3D) model through experiments on granular flows on a pile between rough sidewalls, in which a complex 3D flow pattern develops. We show that, without any fitting parameter, the model gives quantitative predictions for the flow shape and velocity profiles. Our results support the idea that a simple visco-plastic approach can quantitatively capture granular flow properties, and could serve as a basic tool for modelling more complex flows in geophysical or industrial applications.Comment: http://www.nature.com/nature/journal/v441/n7094/abs/nature04801.htm

A Hydrodynamic model for a dynamical jammed-to-flowing transition in gravity driven granular media

Granular material on an inclined plane will flow like a fluid if the angle $\theta$ the plane makes with the horizontal is large enough. We employ a modification of a hydrodynamic model introduced previously to describe Couette flow experiments to describe chute flow down a plane. In this geometry, our model predicts a jammed-to-flowing transition as $\theta$ is increased even though it does not include solid friction, which might seem necessary to stabilize a state without flow. The transition is driven by coupling between mean and fluctuating velocity. In agreement with experiments and simulations, it predicts flow for layers with a thickness H larger than a critical value $H_{\rm stop}(\theta)$ and absence of flow for $H<H_{\rm stop}(\theta)$

Stabilized lasers for advanced gravitational wave detectors

Second generation gravitational wave detectors require high power lasers with more than 100 W of output power and with very low temporal and spatial fluctuations. To achieve the demanding stability levels required, low noise techniques and adequate control actuators have to be part of the high power laser design. In addition feedback control and passive noise filtering is used to reduce the fluctuations in the so-called prestabilized laser system (PSL). In this paper, we discuss the design of a 200 W PSL which is under development for the Advanced LIGO gravitational wave detector and will present the first results. The PSL noise requirements for advanced gravitational wave detectors will be discussed in general and the stabilization scheme proposed for the Advanced LIGO PSL will be described