The second and third Sonine coefficients of a freely cooling granular gas revisited

In its simplest statistical-mechanical description, a granular fluid can be modeled as composed of smooth inelastic hard spheres (with a constant coefficient of normal restitution $\alpha$) whose velocity distribution function obeys the Enskog-Boltzmann equation. The basic state of a granular fluid is the homogeneous cooling state, characterized by a homogeneous, isotropic, and stationary distribution of scaled velocities, $F(\mathbf{c})$. The behavior of $F(\mathbf{c})$ in the domain of thermal velocities ($c\sim 1$) can be characterized by the two first non-trivial coefficients ($a_2$ and $a_3$) of an expansion in Sonine polynomials. The main goals of this paper are to review some of the previous efforts made to estimate (and measure in computer simulations) the $\alpha$-dependence of $a_2$ and $a_3$, to report new computer simulations results of $a_2$ and $a_3$ for two-dimensional systems, and to investigate the possibility of proposing theoretical estimates of $a_2$ and $a_3$ with an optimal compromise between simplicity and accuracy.Comment: 12 pages, 5 figures; v2: minor change

Assessment of mitral valve regurgitation by cardiovascular magnetic resonance imaging

Mitral regurgitation (MR) is a common valvular heart disease and is the second most frequent indication for heart valve surgery in Western countries. Echocardiography is the recommended first-line test for the assessment of valvular heart disease, but cardiovascular magnetic resonance imaging (CMR) provides complementary information, especially for assessing MR severity and to plan the timing of intervention. As new CMR techniques for the assessment of MR have arisen, standardizing CMR protocols for research and clinical studies has become important in order to optimize diagnostic utility and support the wider use of CMR for the clinical assessment of MR. In this Consensus Statement, we provide a detailed description of the current evidence on the use of CMR for MR assessment, highlight its current clinical utility, and recommend a standardized CMR protocol and report for MR assessment

The nature of transition circumstellar disks. I. The ophiuchus molecular cloud

We have obtained millimeter-wavelength photometry, high-resolution optical spectroscopy, and adaptive optics near-infrared imaging for a sample of 26 Spitzer-selected transition circumstellar disks. All of our targets are located in the Ophiuchus molecular cloud (d ∼ 125pc) and have spectral energy distributions (SEDs) suggesting the presence of inner opacity holes. We use these ground-based data to estimate the disk mass, multiplicity, and accretion rate for each object in our sample in order to investigate the mechanisms potentially responsible for their inner holes. We find that transition disks are a heterogeneous group of objects, with disk masses ranging from JUP and accretion rates ranging from JUP) and negligible accretion (<10-11 M ⊙yr-1), and are thus consistent with photoevaporating (or photoevaporated) disks. Four of these nine non-accreting objects have fractional disk luminosities <10-3 and could already be in a debris disk stage. Seventeen of our transition disks are accreting. Thirteen of these accreting objects are consistent with grain growth. The remaining four accreting objects have SEDs suggesting the presence of sharp inner holes, and thus are excellent candidates for harboring giant planets.Facultad de Ciencias Astronómicas y Geofísica

Kinetics of Ordering in Fluctuation-Driven First-Order Transitions: Simulations and Dynamical Renormalization

Many systems where interactions compete with each other or with constraints are well described by a model first introduced by Brazovskii. Such systems include block copolymers, alloys with modulated phases, Rayleigh-Benard Cells and type-I superconductors. The hallmark of this model is that the fluctuation spectrum is isotropic and has a minimum at a nonzero wave vector represented by the surface of a d-dimensional hyper-sphere. It was shown by Brazovskii that the fluctuations change the free energy structure from a $\phi ^{4}$ to a $\phi ^{6}$ form with the disordered state metastable for all quench depths. The transition from the disordered to the periodic, lamellar structure changes from second order to first order and suggests that the dynamics is governed by nucleation. Using numerical simulations we have confirmed that the equilibrium free energy function is indeed of a $\phi ^{6}$ form. A study of the dynamics, however, shows that, following a deep quench, the dynamics is described by unstable growth rather than nucleation. A dynamical calculation, based on a generalization of the Brazovskii calculations shows that the disordered state can remain unstable for a long time following the quench.Comment: 18 pages, 15 figures submitted to PR

Hilbert Lattice Equations

There are five known classes of lattice equations that hold in every infinite dimensional Hilbert space underlying quantum systems: generalised orthoarguesian, Mayet's E_A, Godowski, Mayet-Godowski, and Mayet's E equations. We obtain a result which opens a possibility that the first two classes coincide. We devise new algorithms to generate Mayet-Godowski equations that allow us to prove that the fourth class properly includes the third. An open problem related to the last class is answered. Finally, we show some new results on the Godowski lattices characterising the third class of equations.Comment: 24 pages, 3 figure

Exact steady state solution of the Boltzmann equation: A driven 1-D inelastic Maxwell gas

The exact nonequilibrium steady state solution of the nonlinear Boltzmann equation for a driven inelastic Maxwell model was obtained by Ben-Naim and Krapivsky [Phys. Rev. E 61, R5 (2000)] in the form of an infinite product for the Fourier transform of the distribution function $f(c)$. In this paper we have inverted the Fourier transform to express $f(c)$ in the form of an infinite series of exponentially decaying terms. The dominant high energy tail is exponential, $f(c)\simeq A_0\exp(-a|c|)$, where $a\equiv 2/\sqrt{1-\alpha^2}$ and the amplitude $A_0$ is given in terms of a converging sum. This is explicitly shown in the totally inelastic limit ($\alpha\to 0$) and in the quasi-elastic limit ($\alpha\to 1$). In the latter case, the distribution is dominated by a Maxwellian for a very wide range of velocities, but a crossover from a Maxwellian to an exponential high energy tail exists for velocities $|c-c_0|\sim 1/\sqrt{q}$ around a crossover velocity $c_0\simeq \ln q^{-1}/\sqrt{q}$, where $q\equiv (1-\alpha)/2\ll 1$. In this crossover region the distribution function is extremely small, $\ln f(c_0)\simeq q^{-1}\ln q$.Comment: 11 pages, 4 figures; a table and a few references added; to be published in PR

Foundations of Dissipative Particle Dynamics

We derive a mesoscopic modeling and simulation technique that is very close to the technique known as dissipative particle dynamics. The model is derived from molecular dynamics by means of a systematic coarse-graining procedure. Thus the rules governing our new form of dissipative particle dynamics reflect the underlying molecular dynamics; in particular all the underlying conservation laws carry over from the microscopic to the mesoscopic descriptions. Whereas previously the dissipative particles were spheres of fixed size and mass, now they are defined as cells on a Voronoi lattice with variable masses and sizes. This Voronoi lattice arises naturally from the coarse-graining procedure which may be applied iteratively and thus represents a form of renormalisation-group mapping. It enables us to select any desired local scale for the mesoscopic description of a given problem. Indeed, the method may be used to deal with situations in which several different length scales are simultaneously present. Simulations carried out with the present scheme show good agreement with theoretical predictions for the equilibrium behavior.Comment: 18 pages, 7 figure

The role of superficial geology in controlling groundwater recharge in the weathered crystalline basement of semi-arid Tanzania

Study region Little Kinyasungwe River Catchment, central semi-arid Tanzania. Study focus The structure and hydraulic properties of superficial geology can play a crucial role in controlling groundwater recharge in drylands. However, the pathways by which groundwater recharge occurs and their sensitivity to environmental change remain poorly resolved. Geophysical surveys using Electrical Resistivity Tomography (ERT) were conducted in the study region and used to delineate shallow subsurface stratigraphy in conjunction with borehole logs. Based on these results, a series of local-scale conceptual hydrogeological models was produced and collated to generate a 3D conceptual model of groundwater recharge to the wellfield. New hydrological insights for the region We propose that configurations of superficial geology control groundwater recharge in dryland settings as follows: 1) superficial sand deposits act as collectors and stores that slowly feed recharge into zones of active faulting; 2) these fault zones provide permeable pathways enabling greater recharge to occur; 3) ‘windows’ within layers of smectitic clay that underlie ephemeral streams may provide pathways for focused recharge via transmission losses; and 4) overbank flooding during high intensity precipitation events increases the probability of activating such permeable pathways. These conceptual models provide a physical basis to improve numerical models of groundwater recharge in drylands, and a conceptual framework to evaluate strategies (e.g., Managed Aquifer Recharge) to artificially enhance the availability of groundwater resources in these regions

Grain boundary pinning and glassy dynamics in stripe phases

We study numerically and analytically the coarsening of stripe phases in two spatial dimensions, and show that transient configurations do not achieve long ranged orientational order but rather evolve into glassy configurations with very slow dynamics. In the absence of thermal fluctuations, defects such as grain boundaries become pinned in an effective periodic potential that is induced by the underlying periodicity of the stripe pattern itself. Pinning arises without quenched disorder from the non-adiabatic coupling between the slowly varying envelope of the order parameter around a defect, and its fast variation over the stripe wavelength. The characteristic size of ordered domains asymptotes to a finite value $R_g \sim \lambda_0\ \epsilon^{-1/2}\exp(|a|/\sqrt{\epsilon})$, where$\epsilon\ll 1$is the dimensionless distance away from threshold,$\lambda_0$the stripe wavelength, and$a$ a constant of order unity. Random fluctuations allow defect motion to resume until a new characteristic scale is reached, function of the intensity of the fluctuations. We finally discuss the relationship between defect pinning and the coarsening laws obtained in the intermediate time regime.Comment: 17 pages, 8 figures. Corrected version with one new figur

Dynamics of systems with isotropic competing interactions in an external field: a Langevin approach

We study the Langevin dynamics of a ferromagnetic Ginzburg-Landau Hamiltonian with a competing long-range repulsive term in the presence of an external magnetic field. The model is analytically solved within the self consistent Hartree approximation for two different initial conditions: disordered or zero field cooled (ZFC), and fully magnetized or field cooled (FC). To test the predictions of the approximation we develop a suitable numerical scheme to ensure the isotropic nature of the interactions. Both the analytical approach and the numerical simulations of two-dimensional finite systems confirm a simple aging scenario at zero temperature and zero field. At zero temperature a critical field $h_c$ is found below which the initial conditions are relevant for the long time dynamics of the system. For $h < h_c$ a logarithmic growth of modulated domains is found in the numerical simulations but this behavior is not captured by the analytical approach which predicts a $t^1/2$ growth law at $T = 0$