20,770 research outputs found
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
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