A note on Stokes' problem in dense granular media using the μ(I)\mu(I)--rheology

The classical Stokes' problem describing the fluid motion due to a steadily moving infinite wall is revisited in the context of dense granular flows of mono-dispersed beads using the recently proposed $\mu(I)$--rheology. In Newtonian fluids, molecular diffusion brings about a self-similar velocity profile and the boundary layer in which the fluid motion takes place increases indefinitely with time $t$ as $\sqrt{\nu t}$, where $\nu$ is the kinematic viscosity. For a dense granular visco-plastic liquid, it is shown that the local shear stress, when properly rescaled, exhibits self-similar behaviour at short-time scales and it then rapidly evolves towards a steady-state solution. The resulting shear layer increases in thickness as $\sqrt{\nu_g t}$ analogous to a Newtonian fluid where $\nu_g$ is an equivalent granular kinematic viscosity depending not only on the intrinsic properties of the granular media such as grain diameter $d$, density $\rho$ and friction coefficients but also on the applied pressure $p_w$ at the moving wall and the solid fraction $\phi$ (constant). In addition, the $\mu(I)$--rheology indicates that this growth continues until reaching the steady-state boundary layer thickness $\delta_s = \beta_w (p_w/\phi \rho g )$, independent of the grain size, at about a finite time proportional to $\beta_w^2 (p_w/\rho g d)^{3/2} \sqrt{d/g}$, where $g$ is the acceleration due to gravity and $\beta_w = (\tau_w - \tau_s)/\tau_s$ is the relative surplus of the steady-state wall shear-stress $\tau_w$ over the critical wall shear stress $\tau_s$ (yield stress) that is needed to bring the granular media into motion... (see article for a complete abstract).Comment: in press (Journal of Fluid Mechanics

Weak helix submanifolds of euclidean spaces

It is shown that there exist nonstrong weak 2-helix surfaces of R

Entanglement entropy and quantum field theory: a non-technical introduction

In these proceedings we give a pedagogical and non-technical introduction to the Quantum Field Theory approach to entanglement entropy. Particular attention is devoted to the one space dimensional case, with a linear dispersion relation, that, at a quantum critical point, can be effectively described by a two-dimensional Conformal Field Theory.Comment: 10 Pages, 2 figures. Talk given at the conference "Entanglement in Physical and information sciences", Centro Ennio de Giorgi, Pisa, December 200

An integrable modification of the critical Chalker-Coddington network model

We consider the Chalker-Coddington network model for the Integer Quantum Hall Effect, and examine the possibility of solving it exactly. In the supersymmetric path integral framework, we introduce a truncation procedure, leading to a series of well-defined two-dimensional loop models, with two loop flavours. In the phase diagram of the first-order truncated model, we identify four integrable branches related to the dilute Birman-Wenzl-Murakami braid-monoid algebra, and parameterised by the loop fugacity $n$. In the continuum limit, two of these branches (1,2) are described by a pair of decoupled copies of a Coulomb-Gas theory, whereas the other two branches (3,4) couple the two loop flavours, and relate to an $SU(2)_r \times SU(2)_r / SU(2)_{2r}$ Wess-Zumino-Witten (WZW) coset model for the particular values $n= -2\cos[\pi/(r+2)]$ where $r$ is a positive integer. The truncated Chalker-Coddington model is the $n=0$ point of branch 4. By numerical diagonalisation, we find that its universality class is neither an analytic continuation of the WZW coset, nor the universality class of the original Chalker-Coddington model. It constitutes rather an integrable, critical approximation to the latter.Comment: 34 pages, 18 figures, 3 appendice

Field trials and test results of portable DVB-T systems with transmit delay diversity

This paper describes work carried out by Brunel University and Broadreach Systems (UK) to quantify the advantages that can be achieved if Transmit Diversity is applied to systems employing the DVB standard. The techniques investigated can be applied to standard receiver equipment without modification. An extensive and carefully planned field trial was performed during the winter of 2007/2008 in Uxbridge (UK) to validate predictions from theoretical modeling and laboratory simulations. The transmissions were performed in the 730 MHz frequency band with a DVB-T transmitter and a mean power of 18.4dBW. Transmit delay diversity has been observed to deliver significant reception improvement in automotive and indoor- non line of sight situations

Curvature Matrix Models for Dynamical Triangulations and the Itzykson-DiFrancesco Formula

We study the large-N limit of a class of matrix models for dually weighted triangulated random surfaces using character expansion techniques. We show that for various choices of the weights of vertices of the dynamical triangulation the model can be solved by resumming the Itzykson-Di Francesco formula over congruence classes of Young tableau weights modulo three. From this we show that the large-N limit implies a non-trivial correspondence with models of random surfaces weighted with only even coordination number vertices. We examine the critical behaviour and evaluation of observables and discuss their interrelationships in all models. We obtain explicit solutions of the model for simple choices of vertex weightings and use them to show how the matrix model reproduces features of the random surface sum. We also discuss some general properties of the large-N character expansion approach as well as potential physical applications of our results.Comment: 37 pages LaTeX; Some clarifying comments added, last Section rewritte

The Large N Harmonic Oscillator as a String Theory

We propose a duality between the large-N gauged harmonic oscillator and a novel string theory in two dimensions.Comment: 31 pages, 2 figures; v2: fixed typo

Prostaglandin PGE2 at very low concentrations suppresses collagen cleavage in cultured human osteoarthritic articular cartilage: this involves a decrease in expression of proinflammatory genes, collagenases and COL10A1, a gene linked to chondrocyte hypertrophy

Suppression of type II collagen (COL2A1) cleavage by transforming growth factor (TGF)-β2 in cultured human osteoarthritic cartilage has been shown to be associated with decreased expression of collagenases, cytokines, genes associated with chondrocyte hypertrophy, and upregulation of prostaglandin (PG)E2 production. This results in a normalization of chondrocyte phenotypic expression. Here we tested the hypothesis that PGE2 is associated with the suppressive effects of TGF-β2 in osteoarthritic (OA) cartilage and is itself capable of downregulating collagen cleavage and hypertrophy in human OA articular cartilage. Full-depth explants of human OA knee articular cartilage from arthroplasty were cultured with a wide range of concentrations of exogenous PGE2 (1 pg/ml to 10 ng/ml). COL2A1 cleavage was measured by ELISA. Proteoglycan content was determined by a colorimetric assay. Gene expression studies were performed with real-time PCR. In explants from patients with OA, collagenase-mediated COL2A1 cleavage was frequently downregulated at 10 pg/ml (in the range 1 pg/ml to 10 ng/ml) by PGE2 as well as by 5 ng/ml TGF-β2. In control OA cultures (no additions) there was an inverse relationship between PGE2 concentration (range 0 to 70 pg/ml) and collagen cleavage. None of these concentrations of added PGE2 inhibited the degradation of proteoglycan (aggrecan). Real-time PCR analysis of articular cartilage from five patients with OA revealed that PGE2 at 10 pg/ml suppressed the expression of matrix metalloproteinase (MMP)-13 and to a smaller extent MMP-1, as well as the proinflammatory cytokines IL-1β and TNF-α and type X collagen (COL10A1), the last of these being a marker of chondrocyte hypertrophy. These studies show that PGE2 at concentrations much lower than those generated in inflammation is often chondroprotective in that it is frequently capable of selectively suppressing the excessive collagenase-mediated COL2A1 cleavage found in OA cartilage. The results also show that chondrocyte hypertrophy in OA articular cartilage is functionally linked to this increased cleavage and is often suppressed by these low concentrations of added PGE2. Together these initial observations reveal the importance of very low concentrations of PGE2 in maintaining a more normal chondrocyte phenotype

The O(n) model on the annulus

We use Coulomb gas methods to propose an explicit form for the scaling limit of the partition function of the critical O(n) model on an annulus, with free boundary conditions, as a function of its modulus. This correctly takes into account the magnetic charge asymmetry and the decoupling of the null states. It agrees with an earlier conjecture based on Bethe ansatz and quantum group symmetry, and with all known results for special values of n. It gives new formulae for percolation (the probability that a cluster connects the two opposite boundaries) and for self-avoiding loops (the partition function for a single loop wrapping non-trivially around the annulus.) The limit n->0 also gives explicit examples of partition functions in logarithmic conformal field theory.Comment: 20 pp. v.2: important references added to earlier work, minor typos correcte