8,860 research outputs found
Generalized two-body self-consistent theory of random linear dielectric composites: an effective-medium approach to clustering in highly-disordered media
Effects of two-body dipolar interactions on the effective
permittivity/conductivity of a binary, symmetric, random dielectric composite
are investigated in a self-consistent framework. By arbitrarily splitting the
singularity of the Green tensor of the electric field, we introduce an
additional degree of freedom into the problem, in the form of an unknown
"inner" depolarization constant. Two coupled self-consistent equations
determine the latter and the permittivity in terms of the dielectric contrast
and the volume fractions. One of them generalizes the usual Coherent Potential
condition to many-body interactions between single-phase clusters of
polarizable matter elements, while the other one determines the effective
medium in which clusters are embedded. The latter is in general different from
the overall permittivity. The proposed approach allows for many-body
corrections to the Bruggeman-Landauer (BL) scheme to be handled in a
multiple-scattering framework. Four parameters are used to adjust the degree of
self-consistency and to characterize clusters in a schematic geometrical way.
Given these parameters, the resulting theory is "exact" to second order in the
volume fractions. For suitable parameter values, reasonable to excellent
agreement is found between theory and simulations of random-resistor networks
and pixelwise-disordered arrays in two and tree dimensions, over the whole
range of volume fractions. Comparisons with simulation data are made using an
"effective" scalar depolarization constant that constitutes a very sensitive
indicator of deviations from the BL theory.Comment: 14 pages, 7 figure
The effective number of relevant parties : how voting power improves Laakso-Taageperaâs index
This paper proposes a new method to evaluate the number of rel- evant parties in an assembly. The most widespread indicator of frag- mentation used in comparative politics is the âEïŹective Number of Par- tiesâ(ENP), designed by Laakso and Taagepera (1979). Taking both the number of parties and their relative weights into account, the ENP is arguably a good parsimonious operationalization of the number of ârelevantâ parties. This index however produces misleading results in single-party ma jority situations as it still indicates that more than one party is relevant in terms of government formation. We propose to modify the ENP formula by replacing proportions of seats by voting power measures. This improved index behaves more in line with Sar- toriâs deïŹnition of relevance, without requiring additional information in its construction.Voting power indices; EïŹective Number of Parties; Party system fragmentation; Relevance; Coalition Formation
Reconstructing the free-energy landscape of Met-enkephalin using dihedral Principal Component Analysis and Well-tempered Metadynamics
Well-Tempered Metadynamics (WTmetaD) is an efficient method to enhance the
reconstruction of the free-energy surface of proteins. WTmetaD guarantees a
faster convergence in the long time limit in comparison with the standard
metadynamics. It still suffers however from the same limitation, i.e. the non
trivial choice of pertinent collective variables (CVs). To circumvent this
problem, we couple WTmetaD with a set of CVs generated from a dihedral
Principal Component Analysis (dPCA) on the Ramachadran dihedral angles
describing the backbone structure of the protein. The dPCA provides a generic
method to extract relevant CVs built from internal coordinates. We illustrate
the robustness of this method in the case of the small and very diffusive
Metenkephalin pentapeptide, and highlight a criterion to limit the number of
CVs necessary to biased the metadynamics simulation. The free-energy landscape
(FEL) of Met-enkephalin built on CVs generated from dPCA is found rugged
compared with the FEL built on CVs extracted from PCA of the Cartesian
coordinates of the atoms.Comment: 17 pages, 9 figures (4 in color
Fourier-based schemes with modified Green operator for computing the electrical response of heterogeneous media with accurate local fields
A modified Green operator is proposed as an improvement of Fourier-based
numerical schemes commonly used for computing the electrical or thermal
response of heterogeneous media. Contrary to other methods, the number of
iterations necessary to achieve convergence tends to a finite value when the
contrast of properties between the phases becomes infinite. Furthermore, it is
shown that the method produces much more accurate local fields inside
highly-conducting and quasi-insulating phases, as well as in the vicinity of
the phases interfaces. These good properties stem from the discretization of
Green's function, which is consistent with the pixel grid while retaining the
local nature of the operator that acts on the polarization field. Finally, a
fast implementation of the "direct scheme" of Moulinec et al. (1994) that
allows for parcimonious memory use is proposed.Comment: v2: `postprint' document (a few remaining typos in the published
version herein corrected in red; results unchanged
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