75,074 research outputs found
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
The Nub of an Automorphism of a Totally Disconnected, Locally Compact Group
To any automorphism, , of a totally disconnected, locally compact
group, , there is associated a compact, -stable subgroup of ,
here called the \emph{nub} of , on which the action of is
topologically transitive. Topologically transitive actions of automorphisms of
compact groups have been studied extensively in topological dynamics and
results obtained transfer, via the nub, to the study of automorphisms of
general locally compact groups.
A new proof that the contraction group of is dense in the nub is
given, but it is seen that the two-sided contraction group need not be dense.
It is also shown that each pair , with compact and
topologically transitive, is an inverse limit of pairs that have `finite depth'
and that analogues of the Schreier Refinement and Jordan-H\"older Theorems hold
for pairs with finite depth
Killarney Clary\u27s \u3cem\u3eWho Whispered Near Me\u3c/em\u3e and Edward Barrett\u27s \u3cem\u3eCommon Preludes\u3c/em\u3e
Wealth, income, earnings and the statistical mechanics of flow systems
This paper looks at empirical data from economics regarding wealth, earnings and income, alongside a
flow model for an economy based on the general Lotka-Volterra models of Levy & Solomon. The data and modelling suggest that a simple economic system might provide a tractable model for giving an exact statistical mechanical solution for an 'out of equilibrium' flow model. This might also include an exact mathematical definition of a 'dissipative structure' derived from maximum entropy
considerations. This paper is primarily a qualitative discussion of how such a mathematical proof might be achieved
Why Money Trickles Up - Wealth & Income Distributions
This paper combines ideas from classical economics and modern finance with
the general Lotka-Volterra models of Levy & Solomon to provide straightforward
explanations of wealth and income distributions. Using a simple and realistic
economic formulation, the distributions of both wealth and income are fully
explained. Both the power tail and the log-normal like body are fully captured.
It is of note that the full distribution, including the power law tail, is
created via the use of absolutely identical agents. It is further demonstrated
that a simple scheme of compulsory saving could eliminate poverty at little
cost to the taxpayer.Comment: 45 pages of text, 36 figure
Trauma and Affective Spill
A review of Bryoni Trezise, Performing Feeling in Cultures of Memory(Palgrave Macmillan, 2014)
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