12,964 research outputs found
Dynamic Edge Caching with Popularity Drifting
Caching at the network edge devices such as wireless caching stations (WCS)
is a key technology in the 5G network. The spatial-temporal diversity of
content popularity requires different content to be cached in different WCSs
and periodically updated to adapt to temporal changes. In this paper, we study
how the popularity drifting speed affects the number of required broadcast
transmissions by the MBS and then design coded transmission schemes by
leveraging the broadcast advantage under the index coding framework. The key
idea is that files already cached in WCSs, which although may be currently
unpopular, can serve as side information to facilitate coded broadcast
transmission for cache updating. Our algorithm extends existing index
coding-based schemes from a single-request scenario to a multiple-request
scenario via a "dynamic coloring" approach. Simulation results indicate that a
significant bandwidth saving can be achieved by adopting our scheme
Linear instability of Poiseuille flows with highly non-ideal fluids
The objective of this work is to investigate linear modal and algebraic
instability in Poiseuille flows with fluids close to their vapour-liquid
critical point. Close to this critical point, the ideal gas assumption does not
hold and large non-ideal fluid behaviours occur. As a representative non-ideal
fluid, we consider supercritical carbon dioxide (CO) at pressure of 80 bar,
which is above its critical pressure of 73.9 bar. The Poiseuille flow is
characterized by the Reynolds number
(), the product of Prandtl
() and Eckert number
(), and the wall temperature that in
addition to pressure determines the thermodynamic reference condition. For low
Eckert numbers, the flow is essentially isothermal and no difference with the
well-known stability behaviour of incompressible flows is observed. However, if
the Eckert number increases, the viscous heating causes gradients of
thermodynamic and transport properties, and non-ideal gas effects become
significant. Three regimes of the laminar base flow can be considered,
subcritical (temperature in the channel is entirely below its pseudo-critical
value), transcritical, and supercritical temperature regime. If compared to the
linear stability of an ideal gas Poiseuille flow, we show that the base flow is
more unstable in the subcritical regime, inviscid unstable in the transcritical
regime, while significantly more stable in the supercritical regime. Following
the corresponding states principle, we expect that qualitatively similar
results will be obtained for other fluids at equivalent thermodynamic states.Comment: 34 pages, 22 figure
On the Continuity of Stochastic Exit Time Control Problems
We determine a weaker sufficient condition than that of Theorem 5.2.1 in
Fleming and Soner (2006) for the continuity of the value functions of
stochastic exit time control problems.Comment: The proof of Lemma 3.1 is slightly modified, and Remark 4.1 is
rephrased for better presentations. In addition, some typos are corrected
Preduals of quadratic Campanato spaces associated to operators with heat kernel bounds
Let be a nonnegative, self-adjoint operator on with
the Gaussian upper bound on its heat kernel. As a generalization of the square
Campanato space , in \cite{DXY}
the quadratic Campanato space is
defined by a variant of the maximal function associated with the semigroup
. On the basis of \cite{DX} and \cite{YY} this paper
addresses the preduality of through
an induced atom (or molecular) decomposition. Even in the case the
discovered predual result is new and natural.Comment: 19 page
- β¦