Interstitial Fluid Effects in Hopper Flows of Granular Material

In recent years a number of theoretical, experimental and computational research programs (Refs. [5], [8] and [3] for example) have substantially increased our fundamental understanding of the mechanics of flowing granular material. However most of these studies have concentrated on the simplest type of flow namely that of uniform size particles in the absence of any interstitial fluid effects or other complicating factors. The purpose of the present paper is to investigate the effects of interstitial fluid. In his classic study of granular flows Bagnold (1954) observed from his Couette flow studies that viscous effects of the interstitial fluid became significant when a number (which is now termed the Bagnold number, Ba) defined as [equation] becomes less than about 450. Here [delta] is the velocity gradient or shear rate. (We have chosen to omit from the definition of Ba a volume fraction parameter which is usually of order unity and is therefore not important qualitively). In the Couette flow experiments the appropriate shear rate, [delta], is clearly defined; in other flows (such as the very practical flow in a hopper) the corresponding condition (or shear rate) in not known. The purpose here is to investigate the effects of the interstitial fluid in the primarily extensional flows which occur in the flow of a granular material in a hopper

Shock Wave Measurements in Cloud Cavitation

One of the most destructive (and noisy) forms of cavitation is that referred to as "cloud cavitation" because it involves a large collection of bubbles which behave as a coherent whole. The present paper presents the results of an experimental study of the processes of collapse of a cavitation bubble cloud, specifically that generated by an oscillating hydrofoil in a water tunnel. Measurements of the far-field noise show that this is comprised of substantial pulses radiated from the cloud at the moment of collapse. Also, transducers within the cavitation zone encounter very large pressure pulses (or shock waves) with amplitudes of the order of tens of atmospheres and typical durations of the order of tenths of a millisecond. These shock waves appear to be responsible for the enhanced noise and damage potential which results from that phenomenon

Pressure Pulses Generated by Cloud Cavitation

This paper describes an experimental investigation of the large unsteady and impulsive pressures which are experienced on the suction surface of both an oscillating and static hydrofoil as a result of cloud cavitation. The present experiments used piezo-electric transducers to measure unsteady pressures at four locations along the chord of the foil and at two locations along the walls of the tunnel test section. These transducers measured very large positive pressure pulses with amplitudes of the order of tens of atmospheres and with durations of the order of tenths of milliseconds. Two distinct types of pressure pulse were identified. "Local" pulses occurred at a single transducer location and were randomly distributed in position and time; several local impulses could be recorded by each transducer during an oscillation cycle. On the other hand, "global" impulses were registered by all the transducers almost simultaneously. Correlation of the transducer output with high speed movies of the cavitation revealed that they were produced by a large scale collapse of the bubble cloud. The location of the global impulses relative to the foil oscillation was quite repeatable and produced substantial far-field noise. The high speed movies also showed that the local impulses were caused both by crescent-shaped regions of low void fraction and by small bubbly structures. These regions appeared to be bounded by bubbly shock waves which were associated with the large pressure pulses. The paper also quantifies the effect of reduced frequency, cavitation number and tunnel velocity on the strength of the pressure pulses by presenting the acoustic impulse for a range of flow conditions. The reduced frequency is an important parameter in the determination of the total impulse level and the local and global pulse distribution. Large impulses are present on the foil surface even at cavitation numbers which do not result in large levels of acoustic radiation or global impulse. The total impulse increases with increasing tunnel velocity

Quantum Walks of SU(2)_k Anyons on a Ladder

We study the effects of braiding interactions on single anyon dynamics using a quantum walk model on a quasi-1-dimensional ladder filled with stationary anyons. The model includes loss of information of the coin and nonlocal fusion degrees of freedom on every second time step, such that the entanglement between the position states and the exponentially growing auxiliary degrees of freedom is lost. The computational complexity of numerical calculations reduces drastically from the fully coherent anyonic quantum walk model, allowing for relatively long simulations for anyons which are spin-1/2 irreps of SU(2)_k Chern-Simons theory. We find that for Abelian anyons, the walk retains the ballistic spreading velocity just like particles with trivial braiding statistics. For non-Abelian anyons, the numerical results indicate that the spreading velocity is linearly dependent on the number of time steps. By approximating the Kraus generators of the time evolution map by circulant matrices, it is shown that the spatial probability distribution for the k=2 walk, corresponding to Ising model anyons, is equal to the classical unbiased random walk distribution.Comment: 12 pages, 4 figure

Observations of Shock Waves in Cloud Cavitation

This paper describes an investigation of the dynamics and acoustics of cloud cavitation, the structures which are often formed by the periodic breakup and collapse of a sheet or vortex cavity. This form of cavitation frequently causes severe noise and damage, though the precise mechanism responsible for the enhancement of these adverse effects is not fully understood. In this paper, we investigate the large impulsive surface pressures generated by this type of cavitation and correlate these with the images from high-speed motion pictures. This reveals that several types of propagating structures (shock waves) are formed in a collapsing cloud and dictate the dynamics and acoustics of collapse. One type of shock wave structure is associated with the coherent collapse of a well-defined and separate cloud when it is convected into a region of higher pressure. This type of global structure causes the largest impulsive pressures and radiated noise. But two other types of structure, termed 'crescent-shaped regions' and 'leading-edge structures' occur during the less-coherent collapse of clouds. These local events are smaller and therefore produce less radiated noise but the interior pressure pulse magnitudes are almost as large as those produced by the global events. The ubiquity and severity of these propagating shock wave structures provides a new perspective on the mechanisms reponsible for noise and damage in cavitating flows involving clouds of bubbles. It would appear that shock wave dynamics rather than the collapse dynamics of single bubbles determine the damage and noise in many cavitating flows

Cloud cavitation on an oscillating hydrofoil

Cloud cavitation, often formed by the breakdown of a sheet or vortex cavity, is believed to be responsible for much of the noise and erosion damage that occurs under cavitating conditions. For this paper, cloud cavitation was produced through the periodic forcing of the flow by an oscillating hydrofoil. The present work examines the acoustic signal generated by the collapse of cloud cavitation, and compares the results to those obtained by studies of single travelling bubble cavitation. In addition, preliminary studies involving the use of air injection on the suction surface of the hydrofoil explore its mitigating effects on the cavitation noise

Simulating typical entanglement with many-body Hamiltonian dynamics

We study the time evolution of the amount of entanglement generated by one dimensional spin-1/2 Ising-type Hamiltonians composed of many-body interactions. We investigate sets of states randomly selected during the time evolution generated by several types of time-independent Hamiltonians by analyzing the distributions of the amount of entanglement of the sets. We compare such entanglement distributions with that of typical entanglement, entanglement of a set of states randomly selected from a Hilbert space with respect to the unitarily invariant measure. We show that the entanglement distribution obtained by a time-independent Hamiltonian can simulate the average and standard deviation of the typical entanglement, if the Hamiltonian contains suitable many-body interactions. We also show that the time required to achieve such a distribution is polynomial in the system size for certain types of Hamiltonians.Comment: Revised, 11 pages, 7 figure

Quantum Entangled Dark Solitons Formed by Ultracold Atoms in Optical Lattices

Inspired by experiments on Bose-Einstein condensates in optical lattices, we study the quantum evolution of dark soliton initial conditions in the context of the Bose-Hubbard Hamiltonian. An extensive set of quantum measures is utilized in our analysis, including von Neumann and generalized quantum entropies, quantum depletion, and the pair correlation function. We find that quantum effects cause the soliton to fill in. Moreover, soliton-soliton collisions become inelastic, in strong contrast to the predictions of mean-field theory. These features show that the lifetime and collision properties of dark solitons in optical lattices provide clear signals of quantum effects.Comment: 4 pages, 4 figures; version appearing in PRL, only minor changes from v

Loops and Strings in a Superconducting Lattice Gauge Simulator

We propose an architecture for an analog quantum simulator of electromagnetism in 2+1 dimensions, based on an array of superconducting fluxonium devices. The encoding is in the integer (spin-1 representation of the quantum link model formulation of compact U(1) lattice gauge theory. We show how to engineer Gauss' law via an ancilla mediated gadget construction, and how to tune between the strongly coupled and intermediately coupled regimes. The witnesses to the existence of the predicted confining phase of the model are provided by nonlocal order parameters from Wilson loops and disorder parameters from 't Hooft strings. We show how to construct such operators in this model and how to measure them nondestructively via dispersive coupling of the fluxonium islands to a microwave cavity mode. Numerical evidence is found for the existence of the confined phase in the ground state of the simulation Hamiltonian on a ladder geometry.Comment: 17 pages, 5 figures. Published versio