198 research outputs found
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 ) 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, .
The behavior of in the domain of thermal velocities ()
can be characterized by the two first non-trivial coefficients ( and
) 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 -dependence of and , to report new
computer simulations results of and for two-dimensional systems,
and to investigate the possibility of proposing theoretical estimates of
and 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 to a
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 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 . In this paper we
have inverted the Fourier transform to express in the form of an
infinite series of exponentially decaying terms. The dominant high energy tail
is exponential, , where and the amplitude is given in terms of a converging
sum. This is explicitly shown in the totally inelastic limit ()
and in the quasi-elastic limit (). 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 around a crossover velocity , where .
In this crossover region the distribution function is extremely small, .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 $R_g \sim \lambda_0\
\epsilon^{-1/2}\exp(|a|/\sqrt{\epsilon})\epsilon\ll 1\lambda_0a$ 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 is found below which the initial conditions are relevant
for the long time dynamics of the system. For 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 growth law at
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