182 research outputs found
Wavelength limits on isobaricity of perturbations in a thermally unstable radiatively cooling medium
Nonlinear evolution of one-dimensional planar perturbations in an optically
thin radiatively cooling medium in the long-wavelength limit is studied
numerically. The accepted cooling function generates in thermal equilibrium a
bistable equation of state . The unperturbed state is taken close to
the upper (low-density) unstable state with infinite compressibility
(). The evolution is shown to proceed in three different stages.
At first stage, pressure and density set in the equilibrium equation of state,
and velocity profile steepens gradually as in case of pressure-free flows. At
second stage, those regions of the flow where anomalous pressure (i.e. with
negative compressibility) holds, create velocity profile more sharp than in
pressure-free case, which in turn results in formation of a very narrow
(short-wavelength) region where gas separates the equilibrium equation of state
and pressure equilibrium sets in rapidly. On this stage, variation in pressure
between narrow dense region and extended environment does not exceed more than
0.01 of the unperturbed value. On third stage, gas in the short-wavelength
region reaches the second (high-density) stable state, and pressure balance
establishes through the flow with pressure equal to the one in the unperturbed
state. In external (long-wavelength) regions, gas forms slow isobaric inflow
toward the short-wavelength layer. The duration of these stages decreases when
the ratio of the acoustic time to the radiative cooling time increases. Limits
in which nonlinear evolution of thermally unstable long-wavelength
perturbations develops in isobaric regime are obtained.Comment: 21 pages with 7 figures, Revtex, accepted in Physics of Plasma
Reducing multiphoton ionization in a linearly polarized microwave field by local control
We present a control procedure to reduce the stochastic ionization of
hydrogen atom in a strong microwave field by adding to the original Hamiltonian
a comparatively small control term which might consist of an additional set of
microwave fields. This modification restores select invariant tori in the
dynamics and prevents ionization. We demonstrate the procedure on the
one-dimensional model of microwave ionization.Comment: 8 page
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
Attempted density blowup in a freely cooling dilute granular gas: hydrodynamics versus molecular dynamics
It has been recently shown (Fouxon et al. 2007) that, in the framework of
ideal granular hydrodynamics (IGHD), an initially smooth hydrodynamic flow of a
granular gas can produce an infinite gas density in a finite time. Exact
solutions that exhibit this property have been derived. Close to the
singularity, the granular gas pressure is finite and almost constant. This work
reports molecular dynamics (MD) simulations of a freely cooling gas of nearly
elastically colliding hard disks, aimed at identifying the "attempted" density
blowup regime. The initial conditions of the simulated flow mimic those of one
particular solution of the IGHD equations that exhibits the density blowup. We
measure the hydrodynamic fields in the MD simulations and compare them with
predictions from the ideal theory. We find a remarkable quantitative agreement
between the two over an extended time interval, proving the existence of the
attempted blowup regime. As the attempted singularity is approached, the
hydrodynamic fields, as observed in the MD simulations, deviate from the
predictions of the ideal solution. To investigate the mechanism of breakdown of
the ideal theory near the singularity, we extend the hydrodynamic theory by
accounting separately for the gradient-dependent transport and for finite
density corrections.Comment: 11 pages, 9 figures, accepted for publication on Physical Review
On population extinction risk in the aftermath of a catastrophic event
We investigate how a catastrophic event (modeled as a temporary fall of the
reproduction rate) increases the extinction probability of an isolated
self-regulated stochastic population. Using a variant of the Verhulst logistic
model as an example, we combine the probability generating function technique
with an eikonal approximation to evaluate the exponentially large increase in
the extinction probability caused by the catastrophe. This quantity is given by
the eikonal action computed over "the optimal path" (instanton) of an effective
classical Hamiltonian system with a time-dependent Hamiltonian. For a general
catastrophe the eikonal equations can be solved numerically. For simple models
of catastrophic events analytic solutions can be obtained. One such solution
becomes quite simple close to the bifurcation point of the Verhulst model. The
eikonal results for the increase in the extinction probability caused by a
catastrophe agree well with numerical solutions of the master equation.Comment: 11 pages, 11 figure
Hydrodynamic singularities and clustering in a freely cooling inelastic gas
We employ hydrodynamic equations to follow the clustering instability of a
freely cooling dilute gas of inelastically colliding spheres into a
well-developed nonlinear regime. We simplify the problem by dealing with a
one-dimensional coarse-grained flow. We observe that at a late stage of the
instability the shear stress becomes negligibly small, and the gas flows solely
by inertia. As a result the flow formally develops a finite time singularity,
as the velocity gradient and the gas density diverge at some location. We argue
that flow by inertia represents a generic intermediate asymptotic of unstable
free cooling of dilute inelastic gases.Comment: 4 pages, 4 figure
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
Fluctuations of Current in Non-Stationary Diffusive Lattice Gases
We employ the macroscopic fluctuation theory to study fluctuations of
integrated current in one-dimensional lattice gases with a step-like initial
density profile. We analytically determine the variance of the current
fluctuations for a class of diffusive processes with a density-independent
diffusion coefficient, but otherwise arbitrary. Our calculations rely on a
perturbation theory around the noiseless hydrodynamic solution. We consider
both quenched and annealed types of averaging (the initial condition is allowed
to fluctuate in the latter situation). The general results for the variance are
specialized to a few interesting models including the symmetric exclusion
process and the Kipnis-Marchioro-Presutti model. We also probe large deviations
of the current for the symmetric exclusion process. This is done by numerically
solving the governing equations of the macroscopic fluctuation theory using an
efficient iteration algorithm.Comment: Slightly extended version. 12 pages, 6 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
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