8,349 research outputs found
New Global Minima for Thomson's Problem of Charges on a Sphere
Using numerical arguments we find that for = 306 a tetrahedral
configuration () and for N=542 a dihedral configuration () are likely
the global energy minimum for Thomson's problem of minimizing the energy of
unit charges on the surface of a unit conducting sphere. These would be the
largest by far, outside of the icosadeltahedral series, for which a global
minimum for Thomson's problem is known. We also note that the current
theoretical understanding of Thomson's problem does not rule out a symmetric
configuration as the global minima for N=306 and 542. We explicitly find that
analogues of the tetrahedral and dihedral configurations for larger than
306 and 542, respectively, are not global minima, thus helping to confirm the
theory of Dodgson and Moore (Phys. Rev. B 55, 3816 (1997)) that as grows
dislocation defects can lower the lattice strain of symmetric configurations
and concomitantly the energy. As well, making explicit previous work by
ourselves and others, for we give a full accounting of
icosadeltahedral configuration which are not global minima and those which
appear to be, and discuss how this listing and our results for the tetahedral
and dihedral configurations may be used to refine theoretical understanding of
Thomson's problem.Comment: 1- Manuscript revised. 2- A new global minimum found for a dihedral
(D_5) configuration found for N=54
A Novel Symmetric Four Dimensional Polytope Found Using Optimization Strategies Inspired by Thomson's Problem of Charges on a Sphere
Inspired by, and using methods of optimization derived from classical three
dimensional electrostatics, we note a novel beautiful symmetric four
dimensional polytope we have found with 80 vertices. We also describe how the
method used to find this symmetric polytope, and related methods can
potentially be used to find good examples for the kissing and packing problems
in D dimensions
Influence of Dislocations in Thomson's Problem
We investigate Thomson's problem of charges on a sphere as an example of a
system with complex interactions. Assuming certain symmetries we can work with
a larger number of charges than before. We found that, when the number of
charges is large enough, the lowest energy states are not those with the
highest symmetry. As predicted previously by Dodgson and Moore, the complex
patterns in these states involve dislocation defects which screen the strains
of the twelve disclinations required to satisfy Euler's theorem.Comment: 9 pages, 4 figures in gif format. Original PS files can be obtained
in http://fermi.fcu.um.es/thomso
Numerical study of relaxation in electron glasses
We perform a numerical simulation of energy relaxation in three-dimensional
electron glasses in the strongly localized regime at finite temperatures. We
consider systems with no interactions, with long-range Coulomb interactions and
with short-range interactions, obtaining a power law relaxation with an
exponent of 0.15, which is independent of the parameters of the problem and of
the type of interaction. At very long times, we always find an exponential
regime whose characteristic time strongly depends on temperature, system size,
interaction type and localization radius. We extrapolate the longest relaxation
time to macroscopic sizes and, for interacting samples, obtain values much
larger than the measuring time. We finally study the number of electrons
participating in the relaxation processes of very low energy configurations.Comment: 6 eps figures. To be published in Phys. Rev.
Symmetries in Fluctuations Far from Equilibrium
Fluctuations arise universally in Nature as a reflection of the discrete
microscopic world at the macroscopic level. Despite their apparent noisy
origin, fluctuations encode fundamental aspects of the physics of the system at
hand, crucial to understand irreversibility and nonequilibrium behavior. In
order to sustain a given fluctuation, a system traverses a precise optimal path
in phase space. Here we show that by demanding invariance of optimal paths
under symmetry transformations, new and general fluctuation relations valid
arbitrarily far from equilibrium are unveiled. This opens an unexplored route
toward a deeper understanding of nonequilibrium physics by bringing symmetry
principles to the realm of fluctuations. We illustrate this concept studying
symmetries of the current distribution out of equilibrium. In particular we
derive an isometric fluctuation relation which links in a strikingly simple
manner the probabilities of any pair of isometric current fluctuations. This
relation, which results from the time-reversibility of the dynamics, includes
as a particular instance the Gallavotti-Cohen fluctuation theorem in this
context but adds a completely new perspective on the high level of symmetry
imposed by time-reversibility on the statistics of nonequilibrium fluctuations.
The new symmetry implies remarkable hierarchies of equations for the current
cumulants and the nonlinear response coefficients, going far beyond Onsager's
reciprocity relations and Green-Kubo formulae. We confirm the validity of the
new symmetry relation in extensive numerical simulations, and suggest that the
idea of symmetry in fluctuations as invariance of optimal paths has
far-reaching consequences in diverse fields.Comment: 8 pages, 4 figure
Discovery of a wide companion near the deuterium burning mass limit in the Upper Scorpius association
We present the discovery of a companion near the deuterium burning mass limit
located at a very wide distance, at an angular separation of 4.6+/-0.1 arcsec
(projected distance of ~ 670 AU) from UScoCTIO108, a brown dwarf of the very
young Upper Scorpius association. Optical and near-infrared photometry and
spectroscopy confirm the cool nature of both objects, with spectral types of M7
and M9.5, respectively, and that they are bona fide members of the association,
showing low gravity and features of youth. Their masses, estimated from the
comparison of their bolometric luminosities and theoretical models for the age
range of the association, are 60+/-20 and 14^{+2}_{-8} MJup, respectively. The
existence of this object around a brown dwarf at this wide orbit suggests that
the companion is unlikely to have formed in a disk based on current planet
formation models. Because this system is rather weakly bound, they did not
probably form through dynamical ejection of stellar embryos.Comment: 10 pages, including 4 figures and 2 table
Interstitial Fractionalization and Spherical Crystallography
Finding the ground states of identical particles packed on spheres has
relevance for stabilizing emulsions and a venerable history in the literature
of theoretical physics and mathematics. Theory and experiment have confirmed
that defects such as disclinations and dislocations are an intrinsic part of
the ground state. Here we discuss the remarkable behavior of vacancies and
interstitials in spherical crystals. The strain fields of isolated
disclinations forced in by the spherical topology literally rip interstitials
and vacancies apart, typically into dislocation fragments that combine with the
disclinations to create small grain boundary scars. The fractionation is often
into three charge-neutral dislocations, although dislocation pairs can be
created as well. We use a powerful, freely available computer program to
explore interstitial fractionalization in some detail, for a variety of power
law pair potentials. We investigate the dependence on initial conditions and
the final state energies, and compare the position dependence of interstitial
energies with the predictions of continuum elastic theory on the sphere. The
theory predicts that, before fragmentation, interstitials are repelled from
5-fold disclinations and vacancies are attracted. We also use vacancies and
interstitials to study low energy states in the vicinity of "magic numbers"
that accommodate regular icosadeltahedral tessellations.Comment: 21 pages, 9 figure
VLT X-shooter spectroscopy of the nearest brown dwarf binary
The aim of the project is to characterise both components of the nearest
brown dwarf sytem to the Sun, WISE J104915.57-531906.1 (=Luhman16AB) at optical
and near-infrared wavelengths. We obtained high signal-to-noise
intermediate-resolution (R~6000-11000) optical (600-1000 nm) and near-infrared
(1000-2480nm) spectra of each component of Luhman16AB, the closest brown dwarf
binary to the Sun, with the X-Shooter instrument on the Very Large Telescope.
We classify the primary and secondary of the Luhman16 system as L6-L7.5 and
T0+/-1, respectively, in agreement with previous measurements published in the
literature. We present measurements of the lithium pseudo-equivalent widths,
which appears of similar strength on both components (8.2+/-1.0 Angstroms and
8.4+/-1.5 Angstroms for the L and T components, respectively). The presence of
lithium (Lithium 7) in both components imply masses below 0.06 Msun while
comparison with models suggests lower limits of 0.04 Msun. The detection of
lithium in the T component is the first of its kind. Similarly, we assess the
strength of other alkali lines (e.g. pseudo-equivalent widths of 6-7 Angstroms
for RbI and 4-7 Angstroms for CsI) present in the optical and near-infrared
regions and compare with estimates for L and T dwarfs. We also derive effective
temperatures and luminosities of each component of the binary: -4.66+/-0.08 dex
and 1305(+180)(-135) for the L dwarf and -4.68+/-0.13 dex and 1320(+185)(-135)
for the T dwarf, respectively. Using our radial velocity determinations, the
binary does not appear to belong to any of the well-known moving group. Our
preliminary theoretical analysis of the optical and J-band spectra indicates
that the L- and T-type spectra can be reproduced with a single temperature and
gravity but different relative chemical abundances which impact strongly the
spectral energy distribution of L/T transition objects.Comment: 12 pages, 9 figure, 3 tables, accepted to A&
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