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