1,771 research outputs found
Effective way to sum over long range Coulomb potentials in two and three dimensions
I propose a method to calculate logarithmic interaction in two dimensions and
coulomb interaction in three dimensions under periodic boundary conditions.
This paper considers the case of a rectangular cell in two dimensions and an
orthorhombic cell in three dimensions. Unlike the Ewald method, there is no
parameter to be optimized, nor does it involve error functions, thus leading to
the accuracy obtained. This method is similar in approach to that of Sperb [R.
Sperb, Mol. Simulation, 22, 199 (1999).], but the derivation is considerably
simpler and physically appealing. An important aspect of the proposed method is
the faster convergence of the Green function for a particular case as compared
to Sperb's work. The convergence of the sums for the most part of unit cell is
exponential, and hence requires the calculation of only a few dozen terms. In a
very simple way, we also obtain expressions for interaction for systems with
slab geometries. Expressions for the Madelung constant of CsCl and NaCl are
also obtained.Comment: To appear in Phy. Rev.
Absence of Domain Wall Roughening in a Transverse Field Ising Model with Long-Range Interactions
We investigate roughening transitions in the context of transverse-field
Ising models. As a modification of the transverse Ising model with short range
interactions, which has been shown to exhibit domain wall roughening, we have
looked into the possibility of a roughening transition for the case of
long-range interactions, since such a system is physically realized in the
insulator LiHoF4. The combination of strong Ising anisotropy and long-range
forces lead naturally to the formation of domain walls but we find that the
long-range forces destroy the roughening transition.Comment: 7 pages, 5 figures, revtex
Ledoux-Convection in Protoneutron Stars --- a Clue to Supernova Nucleosynthesis?
Two-dimensional hydrodynamical simulations of the deleptonization of a newly
formed neutron star were performed. Driven by negative lepton fraction and
entropy gradients, convection starts near the neutrinosphere about 20-30 ms
after core bounce, but moves deeper into the protoneutron star, and after about
one second the whole protoneutron star is convective. The deleptonization of
the star proceeds much faster than in the corresponding spherically symmetrical
model because the lepton flux and the neutrino luminosities increase by up to a
factor of two. The convection below the neutrinosphere raises the
neutrinospheric temperatures and mean energies of the emitted neutrinos by
10-20%. This can have important implications for the supernova explosion
mechanism and changes the detectable neutrino signal from the Kelvin-Helmholtz
cooling of the protoneutron star. In particular, the enhanced electron neutrino
flux relative to the electron antineutrino flux during the early post-bounce
evolution might solve the overproduction problem of certain elements in the
neutrino-heated ejecta in models of type-II supernova explosions.Comment: 17 pages, LaTeX, 8 postscript figures, uses epsf.sty. To appear in
ApJ 473 (Letters), 1996 December 1
Monitoring infrastructure policy reforms and rural poverty reduction in Ghana : the case of Keta Sea Defence Project
Over the years Ghana has adopted many policy reforms with the aim of reducing poverty. Though official reports indicate reduction in poverty, poverty has become a rural phenomenon. An essential factor identified as crucial for rural poverty reduction is infrastructure. Though the government of Ghana has acknowledged the potential contribution of infrastructure to poverty reduction, and continues to increase annual expenditure on infrastructure provision, the government is worried about the failure of many infrastructure projects to reduce poverty. Since policies provide frameworks that guide action, it would be expected that Ghana’s infrastructure policies address these problems. The study explores the relationship between infrastructure and rural poverty reduction, and the adequacy of Ghana’s infrastructure policy environment in contributing to rural poverty reduction
Low temperature specific heat and possible gap to magnetic excitations in the Heisenberg pyrochlore antiferromagnet Gd2Sn207
The Gd2Sn2O7 pyrochlore Heisenberg antiferromagnet displays a phase
transition to a four sublattice Neel ordered state at a temperature near 1 K.
Despite the seemingly conventional nature of the ordered state, the specific
heat has been found to be described in the temperature range 350-800 mK by an
anomalous T-squared power law. A similar temperature dependence has also been
reported for Gd2Ti2O7, another pyrochlore Heisenberg material. Such anomalous
T-squared behavior in Cv has been argued to be correlated to an unusual
energy-dependence of the density of states which also seemingly manifests
itself in low-temperature spin fluctuations found in muon spin relaxation
experiments. In this paper, we report calculations of Cv that consider spin
wave like excitations out of the Neel order observed in Gd2Sn2O7 and argue that
the parametric T-squared behavior does not reflect the true low-energy
excitations of Gd2Sn2O7. Rather, we find that the low-energy excitations of
this material are antiferromagnetic magnons gapped by single-ion and dipolar
anisotropy effects, and that the lowest temperature of 350 mK considered in
previous specific heat measurements accidentally happens to coincide with a
crossover temperature below which magnons become thermally activated and Cv
takes an exponential form. We argue that further specific heat measurements
that extend down to at least 100 mK are required in order to ascribe an
unconventional description of magnetic excitations out of the ground state of
Gd2Sn2O7 or to invalidate the standard picture of gapped excitations proposed
herein.Comment: 12 pages, 13 figures; shortened introduction and added 1 figur
On homogenization of electromagnetic crystals formed by uniaxial resonant scatterers
Dispersion properties of electromagnetic crystals formed by small uniaxial
resonant scatterers (magnetic or electric) are studied using the local field
approach. The goal of the study is to determine the conditions under which the
homogenization of such crystals can be made. Therefore the consideration is
limited by the frequency region where the wavelength in the host medium is
larger than the lattice periods. It is demonstrated that together with known
restriction for the homogenization related with the large values of the
material parameters there is an additional restriction related with their small
absolute values. From the other hand, the homogenization becomes allowed in
both cases of large and small material parameters for special directions of
propagation. Two unusual effects inherent to the crystals under consideration
are revealed: flat isofrequency contour which allows subwavelength imaging
using canalization regime and birefringence of extraordinary modes which can be
used for beam splitting.Comment: 16 pages, 12 figures, submitted to PR
Spatiotemporal Response of Crystals in X-ray Bragg Diffraction
The spatiotemporal response of crystals in x-ray Bragg diffraction resulting
from excitation by an ultra-short, laterally confined x-ray pulse is studied
theoretically. The theory presents an extension of the analysis in symmetric
reflection geometry [1] to the generic case, which includes Bragg diffraction
both in reflection (Bragg) and transmission (Laue) asymmetric scattering
geometries. The spatiotemporal response is presented as a product of a
crystal-intrinsic plane wave spatiotemporal response function and an envelope
function defined by the crystal-independent transverse profile of the incident
beam and the scattering geometry. The diffracted wavefields exhibit amplitude
modulation perpendicular to the propagation direction due to both angular
dispersion and the dispersion due to Bragg's law. The characteristic measure of
the spatiotemporal response is expressed in terms of a few parameters: the
extinction length, crystal thickness, Bragg angle, asymmetry angle, and the
speed of light. Applications to self-seeding of hard x-ray free electron lasers
are discussed, with particular emphasis on the relative advantages of using
either the Bragg or Laue scattering geometries. Intensity front inclination in
asymmetric diffraction can be used to make snapshots of ultra-fast processes
with femtosecond resolution
Statistical-mechanical theory of the overall magnetic properties of mesocrystals
The mesocrystal showing both electrorheological and magnetorheological
effects is called electro-magnetorheological (EMR) solids. Prediction of the
overall magnetic properties of the EMR solids is a challenging task due to the
coexistence of the uniaxially anisotropic behavior and structural transition as
well as long-range interaction between the suspended particles. To consider the
uniaxial anisotropy effect, we present an anisotropic Kirkwood-Fr\"{o}hlich
equation for calculating the effective permeabilities by adopting an explicit
characteristic spheroid rather than a characteristic sphere used in the
derivation of the usual Kirkwood-Fr\"{o}hlich equation. Further, by applying an
Ewald-Kornfeld formulation we are able to investigate the effective
permeability by including the structural transition and long-range interaction
explicitly. Our theory can reduce to the usual Kirkwood-Fr\"{o}hlich equation
and Onsager equation naturally. To this end, the numerical simulation shows the
validity of monitoring the structure of EMR solids by detecting their effective
permeabilities.Comment: 14 pages, 1 figur
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