A Unified Elementary Approach to the Dyson, Morris, Aomoto, and Forrester Constant Term Identities

We introduce an elementary method to give unified proofs of the Dyson, Morris, and Aomoto identities for constant terms of Laurent polynomials. These identities can be expressed as equalities of polynomials and thus can be proved by verifying them for sufficiently many values, usually at negative integers where they vanish. Our method also proves some special cases of the Forrester conjecture.Comment: 20 page

Vortices in Superfluid Fermi Gases through the BEC to BCS Crossover

We have analyzed a single vortex at T=0 in a 3D superfluid atomic Fermi gas across a Feshbach resonance. On the BCS side, the order parameter varies on two scales: $k_{F}^{-1}$ and the coherence length $\xi$, while only variation on the scale of $\xi$ is seen away from the BCS limit. The circulating current has a peak value $j_{max}$ which is a non-monotonic function of $1/k_F a_s$ implying a maximum critical velocity $\sim v_F$ at unitarity. The number of fermionic bound states in the core decreases as we move from the BCS to BEC regime. Remarkably, a bound state branch persists even on the BEC side reflecting the composite nature of bosonic molecules.Comment: 4 Pages, 4 Figure

Universal velocity distributions in an experimental granular fluid

We present experimental results on the velocity statistics of a uniformly heated granular fluid, in a quasi-2D configuration. We find the base state, as measured by the single particle velocity distribution $f(c)$, to be universal over a wide range of filling fractions and only weakly dependent on all other system parameters. There is a consistent overpopulation in the distribution's tails, which scale as $f\propto\exp(\mathrm{const.}\times c^{-3/2})$. More importantly, the high probability central region of $f(c)$, at low velocities, deviates from a Maxwell-Boltzmann by a second order Sonine polynomial with a single adjustable parameter, in agreement with recent theoretical analysis of inelastic hard spheres driven by a stochastic thermostat. To our knowledge, this is the first time that Sonine deviations have been measured in an experimental system.Comment: 13 pages, 15 figures, with minor corrections, submitted to Phys. Rev.

Energy non-equipartition in systems of inelastic, rough spheres

We calculate and verify with simulations the ratio between the average translational and rotational energies of systems with rough, inelastic particles, either forced or freely cooling. The ratio shows non-equipartition of energy. In stationary flows, this ratio depends mainly on the particle roughness, but in nonstationary flows, such as freely cooling granular media, it also depends strongly on the normal dissipation. The approach presented here unifies and simplifies different results obtained by more elaborate kinetic theories. We observe that the boundary induced energy flux plays an important role.Comment: 4 pages latex, 4 embedded eps figures, accepted by Phys Rev

The Class 0 Protostar BHR71: Herschel Observations and Dust Continuum Models

We use Herschel spectrophotometry of BHR71, an embedded Class 0 protostar, to provide new constraints on its physical properties. We detect 645 (non-unique) spectral lines amongst all spatial pixels. At least 61 different spectral lines originate from the central region. A CO rotational diagram analysis shows four excitation temperature components, 43 K, 197 K, 397 K, and 1057 K. Low-J CO lines trace the outflow while the high-J CO lines are centered on the infrared source. The low-excitation emission lines of H2O trace the large-scale outflow, while the high-excitation emission lines trace a small-scale distribution around the equatorial plane. We model the envelope structure using the dust radiative transfer code, Hyperion, incorporating rotational collapse, an outer static envelope, outflow cavity, and disk. The evolution of a rotating collapsing envelope can be constrained by the far-infrared/millimeter SED along with the azimuthally-averaged radial intensity profile, and the structure of the outflow cavity plays a critical role at shorter wavelengths. Emission at 20-40 um requires a cavity with a constant-density inner region and a power-law density outer region. The best fit model has an envelope mass of 19 solar mass inside a radius of 0.315 pc and a central luminosity of 18.8 solar luminosity. The time since collapse began is 24630-44000 yr, most likely around 36000 yr. The corresponding mass infall rate in the envelope (1.2x10$^{-5}$ solar mass per year) is comparable to the stellar mass accretion rate, while the mass loss rate estimated from the CO outflow is 20% of the stellar mass accretion rate. We find no evidence for episodic accretion.Comment: Accepted for publication in ApJ. 33 pages; 34 figures; 4 table

Human African trypanosomiasis : the current situation in endemic regions and the risks for non-endemic regions from imported cases

Human African trypanosomiasis (HAT) is caused by Trypanosoma brucei gambiense and T. b. rhodesiense and caused devastating epidemics during the 20th century. Due to effective control programs implemented in the last two decades, the number of reported cases has fallen to a historically low level. Although fewer than 977 cases were reported in 2018 in endemic countries, HAT is still a public health problem in endemic regions until it is completely eliminated. In addition, almost 150 confirmed HAT cases were reported in non-endemic countries in the last three decades. The majority of non-endemic HAT cases were reported in Europe, United States and South Africa, due to historical alliances, economic links or geographic proximity to disease endemic countries. Furthermore, with the implementation of the “Belt and Road” project, sporadic imported HAT cases have been reported in China as a warning sign of tropical diseases prevention. In this paper, we explore and interpret the data on HAT incidence and find no positive correlation between the number of HAT cases from endemic and non-endemic countries.This data will provide useful information for better understanding the imported cases of HAT globally in the post-elimination phase

SCOZA for Monolayer Films

We show the way in which the self-consistent Ornstein-Zernike approach (SCOZA) to obtaining structure factors and thermodynamics for Hamiltonian models can best be applied to two-dimensional systems such as thin films. We use the nearest-neighbor lattice gas on a square lattice as an illustrative example.Comment: 10 pages, 5 figure

Existence and stability of multiple solutions to the gap equation

We argue by way of examples that, as a nonlinear integral equation, the gap equation can and does possess many physically distinct solutions for the dressed-quark propagator. The examples are drawn from a class that is successful in describing a broad range of hadron physics observables. We apply the homotopy continuation method to each of our four exemplars and thereby find all solutions that exist within the interesting domains of light current-quark masses and interaction strengths; and simultaneously provide an explanation of the nature and number of the solutions, many of which may be associated with dynamical chiral symmetry breaking. Introducing a stability criterion based on the scalar and pseudoscalar susceptibilities we demonstrate, however, that for any nonzero current-quark mass only the regular Nambu solution of the gap equation is stable against perturbations. This guarantees that the existence of multiple solutions to the gap equation cannot complicate the description of phenomena in hadron physics.Comment: 14 pages, 15 figure