Channel flows of granular materials and their rheological implications

While the flow of a dry granular material down an inclined channel may seem at first sight to be a relatively simple flow, the experiments which have been conducted up to now suggest sufficient complexity which may be present in all but the very simplest granular material flows; consequently it is important to our general understanding of granular material rheology that these experimental observations be fully understood. This review of the current knowledge of channel flows will focus on the basic mechanics of these flows and the contributions the observations have made to an understanding of the rheology. In order to make progress in this objective, it is necessary to avoid some of the complications which can occur in practice. Thus we shall focus only on those flows in which the interstitial fluid plays very little role in determining the rheology. In his classic paper, Bagnold (1954) was able to show that the regime in which the rheology was dominated by particle/particle or particle/wall interactions and in which the viscous stresses in the interstitial fluid played a negligible role could be defined by a single, Reynolds-number-like parameter. It transpires that the important component in this parameter is a number which we shall call the Bagnold number, Ba, defined by Ba = p₈d²δ/µF where p₈,µF are the particle density and interstitial fluid viscosity, d is the particle diameter and δ is the principal velocity gradient in the flow. In the shear flows explored by Bagnold δ is the shear rate. Bagnold (1954) found that when Ba was greater than about 450 the rheology was dominated by particle/particle and particle/wall collisions. On the other hand, for Ba < 40, the viscosity of the interstitial fluid played the dominant role. More recently Zeininger and Brennen (1985) showed that the same criteria were applicable to the extensional flows in hoppers provided the extensional velocity gradient was used for δ. This review will focus on the simpler flows at large Ba where the interstitial fluid effects are small. Other important ancillary effects can be caused by electrical charge separation between the particles or between the particles and the boundary walls. Such effects can be essential in some flows such as those in electrostatic copying machines. Most experimenters have observed electrical effects in granular material flows, particularly when metal components of the structure are not properly grounded. The effect of such electrical forces on the rheology of the flow is a largely unexplored area of research. The lack of discussion of these effects in this review should not be interpreted as a dismissal of their importance. Apart from electrical and interstitial fluid effects, this review will also neglect the effects caused by non-uniformities in the size and shape of the particles. Thus, for the most part, we focus on flows of particles of spherical shape and uniform size. It is clear that while an understanding of all of these effects will be necessary in the long term, there remain some important issues which need to be resolved for even the simplest granular material flows

The Operator Product Expansion of the Lowest Higher Spin Current at Finite N

For the N=2 Kazama-Suzuki(KS) model on CP^3, the lowest higher spin current with spins (2, 5/2, 5/2,3) is obtained from the generalized GKO coset construction. By computing the operator product expansion of this current and itself, the next higher spin current with spins (3, 7/2, 7/2, 4) is also derived. This is a realization of the N=2 W_{N+1} algebra with N=3 in the supersymmetric WZW model. By incorporating the self-coupling constant of lowest higher spin current which is known for the general (N,k), we present the complete nonlinear operator product expansion of the lowest higher spin current with spins (2, 5/2, 5/2, 3) in the N=2 KS model on CP^N space. This should coincide with the asymptotic symmetry of the higher spin AdS_3 supergravity at the quantum level. The large (N,k) 't Hooft limit and the corresponding classical nonlinear algebra are also discussed.Comment: 62 pages; the footnotes added, some redundant appendices removed, the presentations in the whole paper improved and to appear in JHE

Meta-Stable Brane Configurations by Adding an Orientifold-Plane to Giveon-Kutasov

In hep-th/0703135, they have found the type IIA intersecting brane configuration where there exist three NS5-branes, D4-branes and anti-D4-branes. By analyzing the gravitational interaction for the D4-branes in the background of the NS5-branes, the phase structures in different regions of the parameter space were studied in the context of classical string theory. In this paper, by adding the orientifold 4-plane and 6-plane to the above brane configuration, we describe the intersecting brane configurations of type IIA string theory corresponding to the meta-stable nonsupersymmetric vacua of these gauge theories.Comment: 21 pp, 6 figures; reduced bytes of figures, DBI action analysis added and to appear in JHE

Recent Neutrino Data and Type III Seesaw with Discrete Symmetry

In light of the recent neutrino experiment results from Daya Bay and RENO Collaborations, we study phenomenology of neutrino mixing angles in the Type III seesaw model with an discrete $A_4 \times Z_2$ symmetry, whose spontaneously breaking scale is much higher than the electroweak scale. At tree level, the tri-bimaximal (TBM) form of the lepton mixing matrix can be obtained from leptonic Yukawa interactions in a natural way. We introduce all possible effective dimension-5 operators, invariant under the Standard Model gauge group and $A_4 \times Z_2$, and explicitly show that they induce a deviation of the lepton mixing from the TBM mixing matrix, which can explain a large mixing angle $\theta_{13}$ together with small deviations of the solar and atmospheric mixing angles from the TBM. Two possible scenarios are investigated, by taking into account either negligible or sizable contributions from the light charged lepton sector to the lepton mixing matrix. Especially it is found in the latter scenario that all the neutrino experimental data, including the recent best-fit value of $\theta_{13} = 8.68^{\circ}$, can be accommodated. The leptonic CP violation characterized by the Jarlskog invariant $J_{CP}$ has a non-vanishing value, indicating a signal of maximal CP violation.Comment: 28 pages, 7 figures and references are adde

Panel Data Models with Multiple Time-Varying Individual Effects

This paper considers a panel data model with time-varying individual effects. The data are assumed to contain a large number of cross-sectional units repeatedly observed over a fixed number of time periods. The model has a feature of the fixed-effects model in that the effects are assumed to be correlated with the regressors. The unobservable individual effects are assumed to have a factor structure. For consistent estimation of the model, it is important to estimate the true number of factors. We propose a generalized methods of moments procedure by which both the number of factors and the regression coefficients can be consistently estimated. Some important identification issues are also discussed. Our simulation results indicate that the proposed methods produce reliable estimates.panel data, time-varying individual effects, factor models

The Large N 't Hooft Limit of Kazama-Suzuki Model

We consider N=2 Kazama-Suzuki model on CP^N=SU(N+1)/SU(N)xU(1). It is known that the N=2 current algebra for the supersymmetric WZW model, at level k, is a nonlinear algebra. The N=2 W_3 algebra corresponding to N=2 was recovered from the generalized GKO coset construction previously. For N=4, we construct one of the higher spin currents, in N=2 W_5 algebra, with spins (2, 5/2, 5/2, 3). The self-coupling constant in the operator product expansion of this current and itself depends on N as well as k explicitly. We also observe a new higher spin primary current of spins (3, 7/2, 7/2, 4). From the behaviors of N=2, 4 cases, we expect the operator product expansion of the lowest higher spin current and itself in N=2 W_{N+1} algebra. By taking the large (N, k) limit on the various operator product expansions in components, we reproduce, at the linear order, the corresponding operator product expansions in N=2 classical W_{\infty}^{cl}[\lambda] algebra which is the asymptotic symmetry of the higher spin AdS_3 supergravity found recently.Comment: 44 pages; the two typos in the first paragraph of page 23 corrected and to appear in JHE

On quantum error-correction by classical feedback in discrete time

We consider the problem of correcting the errors incurred from sending quantum information through a noisy quantum environment by using classical information obtained from a measurement on the environment. For discrete time Markovian evolutions, in the case of fixed measurement on the environment, we give criteria for quantum information to be perfectly corrigible and characterize the related feedback. Then we analyze the case when perfect correction is not possible and, in the qubit case, we find optimal feedback maximizing the channel fidelity.Comment: 11 pages, 1 figure, revtex