1,120 research outputs found
Effective Dielectric Tensor for Electromagnetic Wave Propagation in Random Media
We derive exact strong-contrast expansions for the effective dielectric
tensor \epeff of electromagnetic waves propagating in a two-phase composite
random medium with isotropic components explicitly in terms of certain
integrals over the -point correlation functions of the medium. Our focus is
the long-wavelength regime, i.e., when the wavelength is much larger than the
scale of inhomogeneities in the medium. Lower-order truncations of these
expansions lead to approximations for the effective dielectric constant that
depend upon whether the medium is below or above the percolation threshold. In
particular, we apply two- and three-point approximations for \epeff to a
variety of different three-dimensional model microstructures, including
dispersions of hard spheres, hard oriented spheroids and fully penetrable
spheres as well as Debye random media, the random checkerboard, and
power-law-correlated materials. We demonstrate the importance of employing
-point correlation functions of order higher than two for high
dielectric-phase-contrast ratio. We show that disorder in the microstructure
results in an imaginary component of the effective dielectric tensor that is
directly related to the {\it coarseness} of the composite, i.e., local
volume-fraction fluctuations for infinitely large windows. The source of this
imaginary component is the attenuation of the coherent homogenized wave due to
scattering. We also remark on whether there is such attenuation in the case of
a two-phase medium with a quasiperiodic structure.Comment: 40 pages, 13 figure
Decision-Making for Long Memory Data in Technical-Economic Design, Fractals and Decision Area Bubbles
Fatty Acid Methyl Esters as Biosolvents of Epoxy Resins: A Physicochemical Study
The C8 to C18 fatty acid methyl esters (FAME) have been compared as solvents for two epoxy resin pre-polymers, bisphenol A diglycidyl ether (DGEBA) and triglycidyl paminophenol ether (TGPA). It was found that the solubilization limits vary according to the ester and that methyl caprylate is the best solvent of both resins. To explain these solubility performances, physical and chemical properties of FAME were studied, such as the Hansen parameters, viscosity, binary diffusion coefficient and vaporization enthalpy. Determination of the physicochemical parameters of FAME was carried out by laboratory experimentations and by calculation from bibliographic data. The Hansen parameters of FAME and epoxy resins pre-polymers were theoretically and experimentally determined. The FAME chain length showed a long dependence on the binary diffusion parameters and kinematic viscosity, which are mass and momentum transport properties. Moreover, the vaporization enthalpy of these compounds was directly correlated with the solubilization limits
The Composite Fermion Hierarchy: Condensed States of Composite Fermion Excitations?
A composite Fermion hierarchy theory is constructed in a way related to the
original Haldane picture by applying the composite Fermion (CF) transformation
to quasiparticles of Jain states. It is shown that the Jain theory coincides
with the Haldane hierarchy theory for principal CF fillings. Within the Fermi
liquid approach for few electron systems on the sphere a simple interpretation
of many-quasiparticle spectra is given and provides an explanation of failure
of CF hierarchy picture when applied to the hierarchical state.Comment: 6 pages, Revtex, 4 figures in PostScript, submitted to Phys. Rev.
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Transport properties of heterogeneous materials derived from Gaussian random fields: Bounds and Simulation
We investigate the effective conductivity () of a class of
amorphous media defined by the level-cut of a Gaussian random field. The three
point solid-solid correlation function is derived and utilised in the
evaluation of the Beran-Milton bounds. Simulations are used to calculate
for a variety of fields and volume fractions at several different
conductivity contrasts. Relatively large differences in are observed
between the Gaussian media and the identical overlapping sphere model used
previously as a `model' amorphous medium. In contrast shows little
variability between different Gaussian media.Comment: 15 pages, 14 figure
Modeling long-range memory with stationary Markovian processes
In this paper we give explicit examples of power-law correlated stationary
Markovian processes y(t) where the stationary pdf shows tails which are
gaussian or exponential. These processes are obtained by simply performing a
coordinate transformation of a specific power-law correlated additive process
x(t), already known in the literature, whose pdf shows power-law tails 1/x^a.
We give analytical and numerical evidence that although the new processes (i)
are Markovian and (ii) have gaussian or exponential tails their autocorrelation
function still shows a power-law decay =1/T^b where b grows with a
with a law which is compatible with b=a/2-c, where c is a numerical constant.
When a<2(1+c) the process y(t), although Markovian, is long-range correlated.
Our results help in clarifying that even in the context of Markovian processes
long-range dependencies are not necessarily associated to the occurrence of
extreme events. Moreover, our results can be relevant in the modeling of
complex systems with long memory. In fact, we provide simple processes
associated to Langevin equations thus showing that long-memory effects can be
modeled in the context of continuous time stationary Markovian processes.Comment: 5 figure
Type-Decomposition of a Pseudo-Effect Algebra
The theory of direct decomposition of a centrally orthocomplete effect
algebra into direct summands of various types utilizes the notion of a
type-determining (TD) set. A pseudo-effect algebra (PEA) is a (possibly)
noncommutative version of an effect algebra. In this article we develop the
basic theory of centrally orthocomplete PEAs, generalize the notion of a TD set
to PEAs, and show that TD sets induce decompositions of centrally orthocomplete
PEAs into direct summands.Comment: 18 page
Analytical Benchmark Problems for Multifidelity Optimization Methods
The paper presents a collection of analytical benchmark problems specifically
selected to provide a set of stress tests for the assessment of multifidelity
optimization methods. In addition, the paper discusses a comprehensive ensemble
of metrics and criteria recommended for the rigorous and meaningful assessment
of the performance of multifidelity strategies and algorithms
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