Condensation of Hard Spheres Under Gravity: Exact Results in One Dimension

We present exact results for the density profile of the one dimensional array of N hard spheres of diameter D and mass m under gravity g. For a strictly one dimensional system, the liquid-solid transition occurs at zero temperature, because the close-pakced density, $\phi_c$, is one. However, if we relax this condition slightly such that $phi_c=1-\delta$, we find a series of critical temperatures T_c^i=mgD(N+1-i)/\mu_o with \mu_o=const, at which the i-th particle undergoes the liquid-solid transition. The functional form of the onset temperature, T_c^1=mgDN/\mu_o, is consistent with the previous result [Physica A 271, 192 (1999)] obtained by the Enskog equation. We also show that the increase in the center of mass is linear in T before the transition, but it becomes quadratic in T after the transition because of the formation of solid near the bottom

Planning an integrated agriculture and health program and designing its evaluation: Experience from Western Kenya.

AbstractMulti-sectoral programs that involve stakeholders in agriculture, nutrition and health care are essential for responding to nutrition problems such as vitamin A deficiency among pregnant and lactating women and their infants in many poor areas of lower income countries. Yet planning such multi-sectoral programs and designing appropriate evaluations, to respond to different disciplinary cultures of evidence, remain a challenge. We describe the context, program development process, and evaluation design of the Mama SASHA project (Sweetpotato Action for Security and Health in Africa) which promoted production and consumption of a bio-fortified, orange-fleshed sweetpotato (OFSP). In planning the program we drew upon information from needs assessments, stakeholder consultations, and a first round of the implementation evaluation of a pilot project. The multi-disciplinary team worked with partner organizations to develop a program theory of change and an impact pathway which identified aspects of the program that would be monitored and established evaluation methods. Responding to the growing demand for greater rigour in impact evaluations, we carried out quasi-experimental allocation by health facility catchment area, repeat village surveys for assessment of change in intervention and control areas, and longitudinal tracking of individual mother-child pairs. Mid-course corrections in program implementation were informed by program monitoring, regular feedback from implementers and partners’ meetings. To assess economic efficiency and provide evidence for scaling we collected data on resources used and project expenses. Managing the multi-sectoral program and the mixed methods evaluation involved bargaining and trade-offs that were deemed essential to respond to the array of stakeholders, program funders and disciplines involved

Impurity Effects on the A_1-A_2 Splitting of Superfluid 3He in Aerogel

When liquid 3He is impregnated into silica aerogel a solid-like layer of 3He atoms coats the silica structure. The surface 3He is in fast exchange with the liquid on NMR timescales. The exchange coupling of liquid 3He quasiparticles with the localized 3He spins modifies the scattering of 3He quasiparticles by the aerogel structure. In a magnetic field the polarization of the solid spins gives rise to a splitting of the scattering cross-section of for `up' vs. `down' spin quasiparticles, relative to the polarization of the solid 3He. We discuss this effect, as well as the effects of non-magnetic scattering, in the context of a possible splitting of the superfluid transition for $\uparrow\uparrow$ vs. $\downarrow\downarrow$ Cooper pairs for superfluid 3He in aerogel, analogous to the A_1-A_2 splitting in bulk 3He. Comparison with the existing measurements of T_c for B< 5 kG, which show no evidence of an A_1-A_2 splitting, suggests a liquid-solid exchange coupling of order J = 0.1 mK. Measurements at higher fields, B > 20 kG, should saturate the polarization of the solid 3He and reveal the A_1-A_2 splitting.Comment: 7 pages, 3 figure

From Fractional Chern Insulators to a Fractional Quantum Spin Hall Effect

We investigate the algebraic structure of flat energy bands a partial filling of which may give rise to a fractional quantum anomalous Hall effect (or a fractional Chern insulator) and a fractional quantum spin Hall effect. Both effects arise in the case of a sufficiently flat energy band as well as a roughly flat and homogeneous Berry curvature, such that the global Chern number, which is a topological invariant, may be associated with a local non-commutative geometry. This geometry is similar to the more familiar situation of the fractional quantum Hall effect in two-dimensional electron systems in a strong magnetic field.Comment: 8 pages, 3 figure; published version with labels in Figs. 2 and 3 correcte

Displacive order–disorder behavior and intrinsic clustering of lattice distortions in bi‐substituted NaNbO3

Perovskite‐like NaNbO3‐Bi1/3NbO3 solid solutions are studied to understand the interactions between octahedral rotations, which dominate the structural behavior of NaNbO3 and displacive disorder of Bi present in Bi1/3NbO3. Models of instantaneous structures for representative compositions are obtained by refining atomic coordinates against X‐ray total scattering and extended X‐ray‐absorption fine structure data, with additional input obtained from transmission electron microscopy. A mixture of distinct cations and vacancies on the cuboctahedral A‐sites in Na1−3x Bix NbO3 (x ≤ 0.2) results in 3D nanoscale modulations of structural distortions. This phenomenon is determined by the inevitable correlations in the chemical composition of adjacent unit cells according to the structure type—an intrinsic property of any nonmolecular crystals. Octahedral rotations become suppressed as x increases. Out‐of‐phase rotations vanish for x > 0.1, whereas in‐phase tilts persist up to x = 0.2, although for this composition their correlation length becomes limited to the nanoscale. The loss of out‐of‐phase tilting is accompanied by qualitative changes in the probability density distributions for Bi and Nb, with both species becoming disordered over loci offset from the centers of their respective oxygen cages. Symmetry arguments are used to attribute this effect to different strengths of the coupling between the cation displacements and out‐of‐phase versus in‐phase rotations. The displacive disorder of Bi and Nb combined with nanoscale clustering of lattice distortions are primarily responsible for the anomalous broadening of the temperature dependence of the dielectric constant

Charge and Current Sum Rules in Quantum Media Coupled to Radiation

This paper concerns the equilibrium bulk charge and current density correlation functions in quantum media, conductors and dielectrics, fully coupled to the radiation (the retarded regime). A sequence of static and time-dependent sum rules, which fix the values of certain moments of the charge and current density correlation functions, is obtained by using Rytov's fluctuational electrodynamics. A technique is developed to extract the classical and purely quantum-mechanical parts of these sum rules. The sum rules are critically tested in the classical limit and on the jellium model. A comparison is made with microscopic approaches to systems of particles interacting through Coulomb forces only (the non-retarded regime). In contrast with microscopic results, the current-current correlation function is found to be integrable in space, in both classical and quantum regimes.Comment: 19 pages, 1 figur

Asymptotics and zeros of Sobolev orthogonal polynomials on unbounded supports

In this paper we present a survey about analytic properties of polynomials orthogonal with respect to a weighted Sobolev inner product such that the vector of measures has an unbounded support. In particular, we are focused in the study of the asymptotic behaviour of such polynomials as well as in the distribution of their zeros. Some open problems as well as some new directions for a future research are formulated.Comment: Changed content; 34 pages, 41 reference

Effective interaction between helical bio-molecules

The effective interaction between two parallel strands of helical bio-molecules, such as deoxyribose nucleic acids (DNA), is calculated using computer simulations of the "primitive" model of electrolytes. In particular we study a simple model for B-DNA incorporating explicitly its charge pattern as a double-helix structure. The effective force and the effective torque exerted onto the molecules depend on the central distance and on the relative orientation. The contributions of nonlinear screening by monovalent counterions to these forces and torques are analyzed and calculated for different salt concentrations. As a result, we find that the sign of the force depends sensitively on the relative orientation. For intermolecular distances smaller than $6\AA$ it can be both attractive and repulsive. Furthermore we report a nonmonotonic behaviour of the effective force for increasing salt concentration. Both features cannot be described within linear screening theories. For large distances, on the other hand, the results agree with linear screening theories provided the charge of the bio-molecules is suitably renormalized.Comment: 18 pages, 18 figures included in text, 100 bibliog

Renormalized Surface Charge Density for a Strongly Charged Plate in Asymmetric Electrolytes: Asymptotic Exact Results in Poisson Boltzmann Theory

The Poisson-Boltzmann equation for a strongly charged plate inside a generic charge-asymmetric electrolyte is solved using the method of asymptotic matching. Both near field and far field asymptotic behaviors of the potential are systematically analyzed. Using these expansions, the renormalized surface charge density is obtained as an asymptotic series in terms of the bare surface charge density.Comment: 11 pages, 4 eps figure