The rheology of dense, polydisperse granular fluids under shear

The solution of the Enskog equation for the one-body velocity distribution of a moderately dense, arbitrary mixture of inelastic hard spheres undergoing planar shear flow is described. A generalization of the Grad moment method, implemented by means of a novel generating function technique, is used so as to avoid any assumptions concerning the size of the shear rate. The result is illustrated by using it to calculate the pressure, normal stresses and shear viscosity of a model polydisperse granular fluid in which grain size, mass and coefficient of restitution varies amoungst the grains. The results are compared to a numerical solution of the Enskog equation as well as molecular dynamics simulations. Most bulk properties are well described by the Enskog theory and it is shown that the generalized moment method is more accurate than the simple (Grad) moment method. However, the description of the distribution of temperatures in the mixture predicted by Enskog theory does not compare well to simulation, even at relatively modest densities.Comment: 8 postscript figures Replaced with new version correcting an error in the SME calculations and misc. small corrections. Second replacement with final correction of SME calculation

The Sender-Excited Secret Key Agreement Model: Capacity, Reliability and Secrecy Exponents

We consider the secret key generation problem when sources are randomly excited by the sender and there is a noiseless public discussion channel. Our setting is thus similar to recent works on channels with action-dependent states where the channel state may be influenced by some of the parties involved. We derive single-letter expressions for the secret key capacity through a type of source emulation analysis. We also derive lower bounds on the achievable reliability and secrecy exponents, i.e., the exponential rates of decay of the probability of decoding error and of the information leakage. These exponents allow us to determine a set of strongly-achievable secret key rates. For degraded eavesdroppers the maximum strongly-achievable rate equals the secret key capacity; our exponents can also be specialized to previously known results. In deriving our strong achievability results we introduce a coding scheme that combines wiretap coding (to excite the channel) and key extraction (to distill keys from residual randomness). The secret key capacity is naturally seen to be a combination of both source- and channel-type randomness. Through examples we illustrate a fundamental interplay between the portion of the secret key rate due to each type of randomness. We also illustrate inherent tradeoffs between the achievable reliability and secrecy exponents. Our new scheme also naturally accommodates rate limits on the public discussion. We show that under rate constraints we are able to achieve larger rates than those that can be attained through a pure source emulation strategy.Comment: 18 pages, 8 figures; Submitted to the IEEE Transactions on Information Theory; Revised in Oct 201

The infrared conductivity of Nax_xCoO2_2: evidence of gapped states

We present infrared ab-plane conductivity data for the layered cobaltate Na$_x$CoO$_2$ at three different doping levels ($x=0.25, 0.50$, and 0.75). The Drude weight increases monotonically with hole doping, $1-x$. At the lowest hole doping level $x$=0.75 the system resembles the normal state of underdoped cuprate superconductors with a scattering rate that varies linearly with frequency and temperature and there is an onset of scattering by a bosonic mode at 600 \cm. Two higher hole doped samples ($x=0.50$ and 0.25) show two different-size gaps (110 \cm and 200 \cm, respectively) in the optical conductivities at low temperatures and become insulators. The spectral weights lost in the gap region of 0.50 and 0.25 samples are shifted to prominent peaks at 200 \cm and 800 \cm, respectively. We propose that the two gapped states of the two higher hole doped samples ($x$=0.50 and 0.25) are pinned charge ordered states.Comment: 4 pages, 3 figure

Exact Multiplicities in the Three-Anyon Spectrum

Using the symmetry properties of the three-anyon spectrum, we obtain exactly the multiplicities of states with given energy and angular momentum. The results are shown to be in agreement with the proper quantum mechanical and semiclassical considerations, and the unexplained points are indicated.Comment: 16 pages plus 3 postscript figures, Kiev Institute for Theoretical Physics preprint ITP-93-32