284 research outputs found
Navier-Stokes hydrodynamics of thermal collapse in a freely cooling granular gas
We employ Navier-Stokes granular hydrodynamics to investigate the long-time
behavior of clustering instability in a freely cooling dilute granular gas in
two dimensions. We find that, in circular containers, the homogeneous cooling
state (HCS) of the gas loses its stability via a sub-critical pitchfork
bifurcation. There are no time-independent solutions for the gas density in the
supercritical region, and we present analytical and numerical evidence that the
gas develops thermal collapse unarrested by heat diffusion. To get more
insight, we switch to a simpler geometry of a narrow-sector-shaped container.
Here the HCS loses its stability via a transcritical bifurcation. For some
initial conditions a time-independent inhomogeneous density profile sets in,
qualitatively similar to that previously found in a narrow-channel geometry.
For other initial conditions, however, the dilute gas develops thermal collapse
unarrested by heat diffusion. We determine the dynamic scalings of the flow
close to collapse analytically and verify them in hydrodynamic simulations. The
results of this work imply that, in dimension higher than one, Navier-Stokes
hydrodynamics of a dilute granular gas is prone to finite-time density blowups.
This provides a natural explanation to the formation of densely packed clusters
of particles in a variety of initially dilute granular flows.Comment: 18 pages, 19 figure
Far-from-equilibrium Ostwald ripening in electrostatically driven granular powders
We report the first experimental study of cluster size distributions in
electrostatically driven granular submonolayers. The cluster size distribution
in this far-from-equilibrium process exhibits dynamic scaling behavior
characteristic of the (nearly equilibrium) Ostwald ripening, controlled by the
attachment and detachment of the "gas" particles. The scaled size distribution,
however, is different from the classical Wagner distribution obtained in the
limit of a vanishingly small area fraction of the clusters. A much better
agreement is found with the theory of Conti et al. [Phys. Rev. E 65, 046117
(2002)] which accounts for the cluster merger.Comment: 5 pages, to appear in PR
Towards a continuum theory of clustering in a freely cooling inelastic gas
We performed molecular dynamics simulations to investigate the clustering
instability of a freely cooling dilute gas of inelastically colliding disks in
a quasi-one-dimensional setting. We observe that, as the gas cools, the shear
stress becomes negligibly small, and the gas flows by inertia only. Finite-time
singularities, intrinsic in such a flow, are arrested only when close-packed
clusters are formed. We observe that the late-time dynamics of this system are
describable by the Burgers equation with vanishing viscosity, and predict the
long-time coarsening behavior.Comment: 7 pages, 5 eps figures, to appear in Europhys. Let
Thermal Instability-Induced Interstellar Turbulence
We study the dynamics of phase transitions in the interstellar medium by
means of three-dimensional hydrodynamic numerical simulations. We use a
realistic cooling function and generic nonequilibrium initial conditions to
follow the formation history of a multiphase medium in detail in the absence of
gravity. We outline a number of qualitatively distinct stages of this process,
including a linear isobaric evolution, transition to an isochoric regime,
formation of filaments and voids (also known as "thermal" pancakes), the
development and decay of supersonic turbulence, an approach to pressure
equilibrium, and final relaxation of the multiphase medium. We find that 1%-2%
of the initial thermal energy is converted into gas motions in one cooling
time. The velocity field then randomizes into turbulence that decays on a
dynamical timescale E_k ~ t^-n, 1 < n < 2. While not all initial conditions
yield a stable two-phase medium, we examine such a case in detail. We find that
the two phases are well mixed with the cold clouds possessing a fine-grained
structure near our numerical resolution limit. The amount of gas in the
intermediate unstable phase roughly tracks the rms turbulent Mach number,
peaking at 25% when M_rms ~ 8, decreasing to 11% when M_rms ~ 0.4.Comment: To appear in the ApJ Letters, April 2002; 5 pages, 3 color figures,
mpeg animations available at http://akpc.ucsd.edu/ThermalLetter/thermal.htm
Formation and evolution of density singularities in hydrodynamics of inelastic gases
We use ideal hydrodynamics to investigate clustering in a gas of
inelastically colliding spheres. The hydrodynamic equations exhibit a new type
of finite-time density blowup, where the gas pressure remains finite. The
density blowups signal formation of close-packed clusters. The blowup dynamics
are universal and describable by exact analytic solutions continuable beyond
the blowup time. These solutions show that dilute hydrodynamic equations yield
a powerful effective description of a granular gas flow with close-packed
clusters, described as finite-mass point-like singularities of the density.
This description is similar in spirit to the description of shocks in ordinary
ideal gas dynamics.Comment: 4 pages, 3 figures, final versio
Normal scaling in globally conserved interface-controlled coarsening of fractal clusters
Globally conserved interface-controlled coarsening of fractal clusters
exhibits dynamic scale invariance and normal scaling. This is demonstrated by a
numerical solution of the Ginzburg-Landau equation with a global conservation
law. The sharp-interface limit of this equation is volume preserving motion by
mean curvature. The scaled form of the correlation function has a power-law
tail accommodating the fractal initial condition. The coarsening length
exhibits normal scaling with time. Finally, shrinking of the fractal clusters
with time is observed. The difference between global and local conservation is
discussed.Comment: 4 pages, 3 eps figure
A nonlinear theory of non-stationary low Mach number channel flows of freely cooling nearly elastic granular gases
We use hydrodynamics to investigate non-stationary channel flows of freely
cooling dilute granular gases. We focus on the regime where the sound travel
time through the channel is much shorter than the characteristic cooling time
of the gas. As a result, the gas pressure rapidly becomes almost homogeneous,
while the typical Mach number of the flow drops well below unity. Eliminating
the acoustic modes, we reduce the hydrodynamic equations to a single nonlinear
and nonlocal equation of a reaction-diffusion type in Lagrangian coordinates.
This equation describes a broad class of channel flows and, in particular, can
follow the development of the clustering instability from a weakly perturbed
homogeneous cooling state to strongly nonlinear states. If the heat diffusion
is neglected, the reduced equation is exactly soluble, and the solution
develops a finite-time density blowup. The heat diffusion, however, becomes
important near the attempted singularity. It arrests the density blowup and
brings about novel inhomogeneous cooling states (ICSs) of the gas, where the
pressure continues to decay with time, while the density profile becomes
time-independent. Both the density profile of an ICS, and the characteristic
relaxation time towards it are determined by a single dimensionless parameter
that describes the relative role of the inelastic energy loss and heat
diffusion. At large values of this parameter, the intermediate cooling dynamics
proceeds as a competition between low-density regions of the gas. This
competition resembles Ostwald ripening: only one hole survives at the end.Comment: 20 pages, 15 figures, final versio
Psychological Safety and Communication Difficulties of Teachers and Students During Long-term Online Training
Due to the growing concerns related to the psychological well-being of students and teachers during a long and intensive online training, it becomes necessary for teachers, psychologists, practitioners to take measures to prevent threats to online communication and identify personal resources of psychological security in the online environment.The purpose of the study was to identify the communicative difficulties of long-term online learning during the COVID-19 pandemic, and the personal resources of students and teachers that contribute to ensuring their psychological safety.The study was conducted in February-March 2022. The study sample included 132 students and 40 teachers of the Faculty of Psychology of the Russian State Social University (Moscow). The following techniques were used: “The test of hardiness” (S. Muddy, in the Russian-language adaptation of E.N. Osin, E.I. Rasskazova), “The scale of subjective well-being” (A. Perrudet-Badoux, G.A. Mendelssohn, J. Chiche, in the Russian-language adaptation of M.V. Sokolova), “Methodology for assessing the level of sociability” (V.F. Ryakhovsky), questionnaires “Difficulties of online communication” for students and teachers. The empirical data obtained were interpreted and processed using qualitative and quantitative methods of analysis, including: descriptive statistics, frequency analysis, Spearman correlation analysis. The study showed that during the long-term distance learning, students and teachers experienced significant difficulties in online educational communication, had low levels of subjective well-being, resilience and sociability. These personal qualities are systemic in nature, interrelated and can act as resources to ensure the psychological safety of subjects of education, prevention or coping with difficulties of online communication and hybrid forms of learning.The data obtained make it necessary for teachers to create psychodidactic conditions for a safe online educational environment in which students will be involved as subjects of education, will be able to freely share their opinions and not be afraid to make a mistake, will feel belonging to a group and protected from verbal aggression
Weak selection and stability of localized distributions in Ostwald ripening
We support and generalize a weak selection rule predicted recently for the
self-similar asymptotics of the distribution function (DF) in the
zero-volume-fraction limit of Ostwald ripening (OR). An asymptotic perturbation
theory is developed that, when combined with an exact invariance property of
the system, yields the selection rule, predicts a power-law convergence towards
the selected self-similar DF and agrees well with our numerical simulations for
the interface- and diffusion-controlled OR.Comment: 4 pages, 2 figures, submitted to PR
Phase fluctuations in the ABC model
We analyze the fluctuations of the steady state profiles in the modulated
phase of the ABC model. For a system of sites, the steady state profiles
move on a microscopic time scale of order . The variance of their
displacement is computed in terms of the macroscopic steady state profiles by
using fluctuating hydrodynamics and large deviations. Our analytical prediction
for this variance is confirmed by the results of numerical simulations
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