7,005 research outputs found
On micro-structural effects in dielectric mixtures
The paper presents numerical simulations performed on dielectric properties
of two-dimensional binary composites on eleven regular space filling
tessellations. First, significant contributions of different parameters, which
play an important role in the electrical properties of the composite, are
introduced both for designing and analyzing material mixtures. Later, influence
of structural differences and intrinsic electrical properties of constituents
on the composite's over all electrical properties are investigated. The
structural differences are resolved by the spectral density representation
approach. The numerical technique, without any {\em a-priori} assumptions, for
extracting the spectral density function is also presented.Comment: 24 pages, 8 figure and 7 tables. It is submitted to IEEE Transactions
on Dielectrics and Electrical Insulatio
Magic number behavior for heat capacities of medium sized classical Lennard-Jones clusters
Monte Carlo methods were used to calculate heat capacities as functions of
temperature for classical atomic clusters of aggregate sizes that were bound by pairwise Lennard-Jones potentials. The parallel
tempering method was used to overcome convergence difficulties due to
quasiergodicity in the solid-liquid phase-change regions. All of the clusters
studied had pronounced peaks in their heat capacity curves, most of which
corresponded to their solid-liquid phase-change regions. The heat capacity peak
height and location exhibited two general trends as functions of cluster size:
for to 36, the peak temperature slowly increased, while the peak
height slowly decreased, disappearing by ; for , a very small
secondary peak at very low temperature emerged and quickly increased in size
and temperature as increased, becoming the dominant peak by .
Superimposed on these general trends were smaller fluctuations in the peak
heights that corresponded to ``magic number'' behavior, with local maxima found
at and 49, and the largest peak found at . These
magic numbers were a subset of the magic numbers found for other cluster
properties, and can be largely understood in terms of the clusters' underlying
geometries. Further insights into the melting behavior of these clusters were
obtained from quench studies and by examining rms bond length fluctuations.Comment: 15 pages, 17 figures (PDF format
Undecidable First-Order Theories of Affine Geometries
Tarski initiated a logic-based approach to formal geometry that studies
first-order structures with a ternary betweenness relation (\beta) and a
quaternary equidistance relation (\equiv). Tarski established, inter alia, that
the first-order (FO) theory of (R^2,\beta,\equiv) is decidable. Aiello and van
Benthem (2002) conjectured that the FO-theory of expansions of (R^2,\beta) with
unary predicates is decidable. We refute this conjecture by showing that for
all n>1, the FO-theory of monadic expansions of (R^2,\beta) is \Pi^1_1-hard and
therefore not even arithmetical. We also define a natural and comprehensive
class C of geometric structures (T,\beta), where T is a subset of R^2, and show
that for each structure (T,\beta) in C, the FO-theory of the class of monadic
expansions of (T,\beta) is undecidable. We then consider classes of expansions
of structures (T,\beta) with restricted unary predicates, for example finite
predicates, and establish a variety of related undecidability results. In
addition to decidability questions, we briefly study the expressivity of
universal MSO and weak universal MSO over expansions of (R^n,\beta). While the
logics are incomparable in general, over expansions of (R^n,\beta), formulae of
weak universal MSO translate into equivalent formulae of universal MSO.
This is an extended version of a publication in the proceedings of the 21st
EACSL Annual Conferences on Computer Science Logic (CSL 2012).Comment: 21 pages, 3 figure
Kadath: a spectral solver for theoretical physics
Kadath is a library that implements spectral methods in a very modular
manner. It is designed to solve a wide class of problems that arise in the
context of theoretical physics. Several types of coordinates are implemented
and additional geometries can be easily encoded. Partial differential equations
of various types are discretized by means of spectral methods. The resulting
system is solved using a Newton-Raphson iteration. Doing so, Kadath is able to
deal with strongly non-linear situations. The algorithms are validated by
applying the library to four different problems of contemporary physics, in the
fields of gauge field theory and general relativityComment: Accepted to Journal of Computational Physic
The combinatorics of binary arrays
This paper gives an account of the combinatorics of binary arrays, mainly concerning their randomness properties. In many cases the problem reduces to the investigation on difference sets.postprin
Skyrmion Gas Manipulation for Probabilistic Computing
The topologically protected magnetic spin configurations known as skyrmions
offer promising applications due to their stability, mobility and localization.
In this work, we emphasize how to leverage the thermally driven dynamics of an
ensemble of such particles to perform computing tasks. We propose a device
employing a skyrmion gas to reshuffle a random signal into an uncorrelated copy
of itself. This is demonstrated by modelling the ensemble dynamics in a
collective coordinate approach where skyrmion-skyrmion and skyrmion-boundary
interactions are accounted for phenomenologically. Our numerical results are
used to develop a proof-of-concept for an energy efficient
() device with a low area imprint ().
Whereas its immediate application to stochastic computing circuit designs will
be made apparent, we argue that its basic functionality, reminiscent of an
integrate-and-fire neuron, qualifies it as a novel bio-inspired building block.Comment: 41 pages, 20 figure
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