Moduli of quantum Riemannian geometries on <= 4 points

We classify parallelizable noncommutative manifold structures on finite sets of small size in the general formalism of framed quantum manifolds and vielbeins introduced previously. The full moduli space is found for $\le 3$ points, and a restricted moduli space for 4 points. The topological part of the moduli space is found for $\le 9$ points based on the known atlas of regular graphs. We also discuss aspects of the quantum theory defined by functional integration.Comment: 34 pages ams-latex, 4 figure

Electromagnetism and Gauge Theory on the Permutation Group S3S_3

Using noncommutative geometry we do U(1) gauge theory on the permutation group $S_3$. Unlike usual lattice gauge theories the use of a nonAbelian group here as spacetime corresponds to a background Riemannian curvature. In this background we solve spin 0, 1/2 and spin 1 equations of motion, including the spin 1 or `photon' case in the presence of sources, i.e. a theory of classical electromagnetism. Moreover, we solve the U(1) Yang-Mills theory (this differs from the U(1) Maxwell theory in noncommutative geometry), including the moduli spaces of flat connections. We show that the Yang-Mills action has a simple form in terms of Wilson loops in the permutation group, and we discuss aspects of the quantum theory.Comment: 28 pages, LaTex as revised March 2001 -- expanded remarks in last section on the quantum theory, but no sig. change

The expected neutral frequency spectrum of linked sites

We present an exact, closed expression for the expected neutral Site Frequency Spectrum for two neutral sites, 2-SFS, without recombination. This spectrum is the immediate extension of the well known single site $\theta/f$ neutral SFS. Similar formulae are also provided for the case of the expected SFS of sites that are linked to a focal neutral mutation of known frequency. Formulae for finite samples are obtained by coalescent methods and remarkably simple expressions are derived for the SFS of a large population, which are also solutions of the multi-allelic Kolmogorov equations. Besides the general interest of these new spectra, they relate to interesting biological cases such as structural variants and introgressions. As an example, we present the expected neutral frequency spectrum of regions with a chromosomal inversion.Comment: 26 pages, 5 figure

Field Localization and Enhancement of Phase Locked Second and Third Harmonic Generation in Absorbing Semiconductor Cavities

We predict and experimentally observe the enhancement by three orders of magnitude of phase mismatched second and third harmonic generation in a GaAs cavity at 650nm and 433nm, respectively, well above the absorption edge. Phase locking between the pump and the harmonics changes the effective dispersion of the medium and inhibits absorption. Despite hostile conditions the harmonics become localized inside the cavity leading to relatively large conversion efficiencies. Field localization plays a pivotal role and ushers in a new class of semiconductor-based devices in the visible and UV ranges

Field theory for size- and charge asymmetric primitive model of electrolytes. Mean-field stability analysis and pretransitional effects

The primitive model of ionic systems is investigated within a field-theoretic description for the whole range of size-, \lambda, and charge, Z, ratios of the two ionic species. Two order parameters (OP) are identified, and their relations to physically relevant quantities are described for various values of \lambda and Z. Instabilities of the disordered phase associated with the two OP's are determined in the mean-field approximation. A gas-liquid separation occurs for any Z and \lambda different from 1. In addition, an instability with respect to various types of periodic ordering of the two kinds of ions is found

Theory of solvation in polar nematics

We develop a linear response theory of solvation of ionic and dipolar solutes in anisotropic, axially symmetric polar solvents. The theory is applied to solvation in polar nematic liquid crystals. The formal theory constructs the solvation response function from projections of the solvent dipolar susceptibility on rotational invariants. These projections are obtained from Monte Carlo simulations of a fluid of dipolar spherocylinders which can exist both in the isotropic and nematic phase. Based on the properties of the solvent susceptibility from simulations and the formal solution, we have obtained a formula for the solvation free energy which incorporates experimentally available properties of nematics and the length of correlation between the dipoles in the liquid crystal. Illustrative calculations are presented for the Stokes shift and Stokes shift correlation function of coumarin-153 in 4-n-pentyl-4'-cyanobiphenyl (5CB) and 4,4-n-heptyl-cyanopiphenyl (7CB) solvents as a function of temperature in both the nematic and isotropic phase.Comment: 19 pages, 9 figure

Mesoscopic theory for size- and charge- asymmetric ionic systems. I. Case of extreme asymmetry

A mesoscopic theory for the primitive model of ionic systems is developed for arbitrary size, $\lambda=\sigma_+/\sigma_-$, and charge, $Z=e_+/|e_-|$, asymmetry. Our theory is an extension of the theory we developed earlier for the restricted primitive model. The case of extreme asymmetries $\lambda\to\infty$ and $Z \to\infty$ is studied in some detail in a mean-field approximation. The phase diagram and correlation functions are obtained in the asymptotic regime $\lambda\to\infty$ and $Z \to\infty$, and for infinite dilution of the larger ions (volume fraction $n_p\sim 1/Z$ or less). We find a coexistence between a very dilute 'gas' phase and a crystalline phase in which the macroions form a bcc structure with the lattice constant $\approx 3.6\sigma_+$. Such coexistence was observed experimentally in deionized aqueous solutions of highly charged colloidal particles

Asymmetric Primitive-Model Electrolytes: Debye-Huckel Theory, Criticality and Energy Bounds

Debye-Huckel (DH) theory is extended to treat two-component size- and charge-asymmetric primitive models, focussing primarily on the 1:1 additive hard-sphere electrolyte with, say, negative ion diameters, a--, larger than the positive ion diameters, a++. The treatment highlights the crucial importance of the charge-unbalanced ``border zones'' around each ion into which other ions of only one species may penetrate. Extensions of the DH approach which describe the border zones in a physically reasonable way are exact at high $T$ and low density, $\rho$, and, furthermore, are also in substantial agreement with recent simulation predictions for \emph{trends} in the critical parameters, $T_c$ and $\rho_c$, with increasing size asymmetry. Conversely, the simplest linear asymmetric DH description, which fails to account for physically expected behavior in the border zones at low $T$, can violate a new lower bound on the energy (which applies generally to models asymmetric in both charge and size). Other recent theories, including those based on the mean spherical approximation, have predicted trends in the critical parameters quite opposite to those established by the simulations.Comment: to appear in Physical Review

Persistent left ventricular dysfunction after acute lymphocytic myocarditis: Frequency and predictors.

BACKGROUND: Persistent left ventricular (LV) systolic dysfunction in patients with acute lymphocytic myocarditis (LM) is widely unexplored. OBJECTIVES: To assess the frequency and predictors of persistent LV dysfunction in patients with LM and reduced LVEF at admission. METHODS AND RESULTS: We retrospectively evaluated 89 consecutive patients with histologically-proven acute myocarditis enrolled at three Italian referral hospitals. A subgroup of 48 patients with LM, baseline systolic impairment and an available echocardiographic assessment at 12 months (6-18) from discharge constituted the study population. The primary study end-point was persistent LV dysfunction, defined as LVEF <50% at 1-year, and was observed in 27/48 patients (56.3%). Higher LV end-diastolic diameter at admission (odds ratio [OR] 1.22, 95% confidence interval [CI] 1.04-1.43, p = 0.002), non-fulminant presentation (OR 8.46, 95% CI 1.28-55.75, p = 0.013) and presence of a poor lymphocytic infiltrate (OR 12.40, 95% CI 1.23-124.97, p = 0.010) emerged as independent predictors of persistent LV dysfunction at multivariate analysis (area under the curve 0.91, 95% CI 0.82-0.99). Pre-discharge LVEF was lower in patients with persistent LV dysfunction compared to the others (32%±8 vs. 53%±8, p <0.001), and this single variable showed the best accuracy in predicting the study end-point (area under the curve 0.95, 95% CI 0.89-1.00). CONCLUSIONS: More than half of patients presenting with acute LM and LVEF <50% who survive the acute phase show persistent LV dysfunction after 1-year from hospital discharge. Features of subacute inflammatory process and of established myocardial damage at initial hospitalization emerged as predictors of this end-point

Coexistence and Criticality in Size-Asymmetric Hard-Core Electrolytes

Liquid-vapor coexistence curves and critical parameters for hard-core 1:1 electrolyte models with diameter ratios lambda = sigma_{-}/\sigma_{+}=1 to 5.7 have been studied by fine-discretization Monte Carlo methods. Normalizing via the length scale sigma_{+-}=(sigma_{+} + sigma_{-})/2 relevant for the low densities in question, both Tc* (=kB Tc sigma_{+-}/q^2 and rhoc* (= rhoc sigma _{+-}^{3}) decrease rapidly (from ~ 0.05 to 0.03 and 0.08 to 0.04, respectively) as lambda increases. These trends, which unequivocally contradict current theories, are closely mirrored by results for tightly tethered dipolar dimers (with Tc* lower by ~ 0-11% and rhoc* greater by 37-12%).Comment: 4 pages, 5 figure