Experimental analysis of the Strato-rotational Instability in a cylindrical Couette flow

This study is devoted to the experimental analysis of the Strato-rotational Instability (SRI). This instability affects the classical cylindrical Couette flow when the fluid is stably stratified in the axial direction. In agreement with recent theoretical and numerical analyses, we describe for the first time in detail the destabilization of the stratified flow below the Rayleigh line (i.e. the stability threshold without stratification). We confirm that the unstable modes of the SRI are non axisymmetric, oscillatory, and take place as soon as the azimuthal linear velocity decreases along the radial direction. This new instability is relevant for accretion disks.Comment: 4 pages, 4 figures. PRL in press 200

When is electromagnetic spectrum fungible?

Fungibility is a common assumption for market-based spectrum management. In this paper, we explore the dimensions of practical fungibility of frequency bands from the point of view of the spectrum buyer who intends to use it. The exploration shows that fungibility is a complex, multidimensional concept that cannot casually be assumed. We develop two ideas for quantifying fungibility-(i) of a fungibility space in which the 'distance' between two slices of spectrum provides score of fungibility and (ii) a probabilistic score of fungibility. © 2012 IEEE

Existence of nodal solutions for Dirac equations with singular nonlinearities

We prove, by a shooting method, the existence of infinitely many solutions of the form $\psi(x^0,x) = e^{-i\Omega x^0}\chi(x)$ of the nonlinear Dirac equation {equation*} i\underset{\mu=0}{\overset{3}{\sum}} \gamma^\mu \partial_\mu \psi- m\psi - F(\bar{\psi}\psi)\psi = 0 {equation*} where $\Omega>m>0,$ $\chi$ is compactly supported and \[F(x) = \{{array}{ll} p|x|^{p-1} & \text{if} |x|>0 0 & \text{if} x=0 {array}.] with $p\in(0,1),$ under some restrictions on the parameters $p$ and $\Omega.$ We study also the behavior of the solutions as $p$ tends to zero to establish the link between these equations and the M.I.T. bag model ones

Avalanches in mean-field models and the Barkhausen noise in spin-glasses

We obtain a general formula for the distribution of sizes of "static avalanches", or shocks, in generic mean-field glasses with replica-symmetry-breaking saddle points. For the Sherrington-Kirkpatrick (SK) spin-glass it yields the density rho(S) of the sizes of magnetization jumps S along the equilibrium magnetization curve at zero temperature. Continuous replica-symmetry breaking allows for a power-law behavior rho(S) ~ 1/(S)^tau with exponent tau=1 for SK, related to the criticality (marginal stability) of the spin-glass phase. All scales of the ultrametric phase space are implicated in jump events. Similar results are obtained for the sizes S of static jumps of pinned elastic systems, or of shocks in Burgers turbulence in large dimension. In all cases with a one-step solution, rho(S) ~ S exp(-A S^2). A simple interpretation relating droplets to shocks, and a scaling theory for the equilibrium analog of Barkhausen noise in finite-dimensional spin glasses are discussed.Comment: 6 pages, 1 figur

Freezing Transition in Decaying Burgers Turbulence and Random Matrix Dualities

We reveal a phase transition with decreasing viscosity $\nu$ at \nu=\nu_c>0 in one-dimensional decaying Burgers turbulence with a power-law correlated random profile of Gaussian-distributed initial velocities \sim|x-x'|^{-2}. The low-viscosity phase exhibits non-Gaussian one-point probability density of velocities, continuously dependent on \nu, reflecting a spontaneous one step replica symmetry breaking (RSB) in the associated statistical mechanics problem. We obtain the low orders cumulants analytically. Our results, which are checked numerically, are based on combining insights in the mechanism of the freezing transition in random logarithmic potentials with an extension of duality relations discovered recently in Random Matrix Theory. They are essentially non mean-field in nature as also demonstrated by the shock size distribution computed numerically and different from the short range correlated Kida model, itself well described by a mean field one step RSB ansatz. We also provide some insights for the finite viscosity behaviour of velocities in the latter model.Comment: Published version, essentially restructured & misprints corrected. 6 pages, 5 figure

Tradable Permits Under Threat to Manage Nonpoint Source Pollution

In this article we treat the problem of nonpoint source pollution as a problem of moral hazard in group. To solve this kind of problem we consider a group performance based tax coupled to tradable permits market. The tax is activated if the group fails to meet the ambient standard. So the role of the tax is to provide an incitation to ensure that the agents provide the abatement level necessary to achieve the standard. The role of the tradable permits market is to distribute effectively this abatement level through the price of the permits which rises with the exchange of the permits.nonpoint source pollution, ambient tax, tradable permits market, Environmental Economics and Policy,

A New Phase of Tethered Membranes: Tubules

We show that fluctuating tethered membranes with {\it any} intrinsic anisotropy unavoidably exhibit a new phase between the previously predicted ``flat'' and ``crumpled'' phases, in high spatial dimensions $d$ where the crumpled phase exists. In this new "tubule" phase, the membrane is crumpled in one direction but extended nearly straight in the other. Its average thickness is $R_G\sim L^{\nu_t}$ with $L$ the intrinsic size of the membrane. This phase is more likely to persist down to $d=3$ than the crumpled phase. In Flory theory, the universal exponent $\nu_t=3/4$, which we conjecture is an exact result. We study the elasticity and fluctuations of the tubule state, and the transitions into it.Comment: 4 pages, self-unpacking uuencoded compressed postscript file with figures already inside text; unpacking instructions are at the top of file. To appear in Phys. Rev. Lett. November (1995

Shock statistics in higher-dimensional Burgers turbulence

We conjecture the exact shock statistics in the inviscid decaying Burgers equation in D>1 dimensions, with a special class of correlated initial velocities, which reduce to Brownian for D=1. The prediction is based on a field-theory argument, and receives support from our numerical calculations. We find that, along any given direction, shocks sizes and locations are uncorrelated.Comment: 4 pages, 8 figure