22,772 research outputs found
Overall Dynamic Constitutive Relations of Micro-structured Elastic Composites
A method for homogenization of a heterogeneous (finite or periodic) elastic
composite is presented. It allows direct, consistent, and accurate evaluation
of the averaged overall frequency-dependent dynamic material constitutive
relations. It is shown that when the spatial variation of the field variables
is restricted by a Bloch-form (Floquet-form) periodicity, then these relations
together with the overall conservation and kinematical equations accurately
yield the displacement or stress modeshapes and, necessarily, the dispersion
relations. It also gives as a matter of course point-wise solution of the
elasto-dynamic field equations, to any desired degree of accuracy. The
resulting overall dynamic constitutive relations however, are general and need
not be restricted by the Bloch-form periodicity. The formulation is based on
micro-mechanical modeling of a representative unit cell of the composite
proposed by Nemat-Nasser and coworkers; see, e.g., [1] and [2].Comment: 23 pages, 6 figures, submitted to JMP
A Characterization of the Shannon Ordering of Communication Channels
The ordering of communication channels was first introduced by Shannon. In
this paper, we aim to find a characterization of the Shannon ordering. We show
that contains if and only if is the skew-composition of with
a convex-product channel. This fact is used to derive a characterization of the
Shannon ordering that is similar to the Blackwell-Sherman-Stein theorem. Two
channels are said to be Shannon-equivalent if each one is contained in the
other. We investigate the topologies that can be constructed on the space of
Shannon-equivalent channels. We introduce the strong topology and the BRM
metric on this space. Finally, we study the continuity of a few channel
parameters and operations under the strong topology.Comment: 23 pages, presented in part at ISIT'17. arXiv admin note: text
overlap with arXiv:1702.0072
Continuity of Channel Parameters and Operations under Various DMC Topologies
We study the continuity of many channel parameters and operations under
various topologies on the space of equivalent discrete memoryless channels
(DMC). We show that mutual information, channel capacity, Bhattacharyya
parameter, probability of error of a fixed code, and optimal probability of
error for a given code rate and blocklength, are continuous under various DMC
topologies. We also show that channel operations such as sums, products,
interpolations, and Ar{\i}kan-style transformations are continuous.Comment: 31 pages. Submitted to IEEE Trans. Inform. Theory and in part to
ISIT201
Bounds on Effective Dynamic Properties of Elastic Composites
We present general, computable, improvable, and rigorous bounds for the total
energy of a finite heterogeneous volume element or a periodically distributed
unit cell of an elastic composite of any known distribution of inhomogeneities
of any geometry and elasticity, undergoing a harmonic motion at a fixed
frequency or supporting a single-frequency Bloch-form elastic wave of a given
wave-vector. These bounds are rigorously valid for \emph{any consistent
boundary conditions} that produce in the finite sample or in the unit cell,
either a common average strain or a common average momentum. No other
restrictions are imposed. We do not assume statistical homogeneity or isotropy.
Our approach is based on the Hashin-Shtrikman (1962) bounds in elastostatics,
which have been shown to provide strict bounds for the overall elastic moduli
commonly defined (or actually measured) using uniform boundary tractions and/or
linear boundary displacements; i.e., boundary data corresponding to the overall
uniform stress and/or uniform strain conditions. Here we present strict bounds
for the dynamic frequency-dependent constitutive parameters of the composite
and give explicit expressions for a direct calculation of these bounds
On the Input-Degradedness and Input-Equivalence Between Channels
A channel is said to be input-degraded from another channel if
can be simulated from by randomization at the input. We provide a
necessary and sufficient condition for a channel to be input-degraded from
another one. We show that any decoder that is good for is also good for
. We provide two characterizations for input-degradedness, one of which is
similar to the Blackwell-Sherman-Stein theorem. We say that two channels are
input-equivalent if they are input-degraded from each other. We study the
topologies that can be constructed on the space of input-equivalent channels,
and we investigate their properties. Moreover, we study the continuity of
several channel parameters and operations under these topologies.Comment: 30 pages. Submitted to IEEE Trans. Inform. Theory and in part to
ISIT2017. arXiv admin note: substantial text overlap with arXiv:1701.0446
Oriented paths in n-chromatic digraphs
In this thesis, we try to treat the problem of oriented paths in n-chromatic
digraphs. We first treat the case of antidirected paths in 5-chromatic
digraphs, where we explain El-Sahili's theorem and provide an elementary and
shorter proof of it. We then treat the case of paths with two blocks in
n-chromatic digraphs with n greater than 4, where we explain the two different
approaches of Addario-Berry et al. and of El-Sahili. We indicate a mistake in
Addario-Berry et al.'s proof and provide a correction for it.Comment: 25 pages, Master thesis in Graph Theory at the Lebanese Universit
- …