1,932 research outputs found
Phase separation of a driven granular gas in annular geometry
This work investigates phase separation of a monodisperse gas of
inelastically colliding hard disks confined in a two-dimensional annulus, the
inner circle of which represents a "thermal wall". When described by granular
hydrodynamic equations, the basic steady state of this system is an azimuthally
symmetric state of increased particle density at the exterior circle of the
annulus. When the inelastic energy loss is sufficiently large, hydrodynamics
predicts spontaneous symmetry breaking of the annular state, analogous to the
van der Waals-like phase separation phenomenon previously found in a driven
granular gas in rectangular geometry. At a fixed aspect ratio of the annulus,
the phase separation involves a "spinodal interval" of particle area fractions,
where the gas has negative compressibility in the azimuthal direction. The heat
conduction in the azimuthal direction tends to suppress the instability, as
corroborated by a marginal stability analysis of the basic steady state with
respect to small perturbations. To test and complement our theoretical
predictions we performed event-driven molecular dynamics (MD) simulations of
this system. We clearly identify the transition to phase separated states in
the MD simulations, despite large fluctuations present, by measuring the
probability distribution of the amplitude of the fundamental Fourier mode of
the azimuthal spectrum of the particle density. We find that the instability
region, predicted from hydrodynamics, is always located within the phase
separation region observed in the MD simulations. This implies the presence of
a binodal (coexistence) region, where the annular state is metastable. The
phase separation persists when the driving and elastic walls are interchanged,
and also when the elastic wall is replaced by weakly inelastic one.Comment: 9 pages, 10 figures, to be published in PR
Solution of a statistical mechanics model for pulse formation in lasers
We present a rigorous statistical-mechanics theory of nonlinear many mode
laser systems. An important example is the passively mode-locked laser that
promotes pulse operation when a saturable absorber is placed in the cavity. It
was shown by Gordon and Fischer [1] that pulse formation is a first-order phase
transition of spontaneous ordering of modes in an effective "thermodynamic"
system, in which intracavity noise level is the effective temperature. In this
paper we present a rigorous solution of a model of passive mode locking. We
show that the thermodynamics depends on a single parameter, and calculate
exactly the mode-locking point. We find the phase diagram and calculate
statistical quantities, including the dependence of the intracavity power on
the gain saturation function, and finite size corrections near the transition
point. We show that the thermodynamics is independent of the gain saturation
mechanism and that it is correctly reproduced by a mean field calculation. The
outcome is a new solvable statistical mechanics system with an unstable
self-interaction accompanied by a natural global power constraint, and an exact
description of an important many mode laser system.Comment: 10 pages, 3 figures, RevTe
Emergence of stability in a stochastically driven pendulum: beyond the Kapitsa effect
We consider a prototypical nonlinear system which can be stabilized by
multiplicative noise: an underdamped non-linear pendulum with a stochastically
vibrating pivot. A numerical solution of the pertinent Fokker-Planck equation
shows that the upper equilibrium point of the pendulum can become stable even
when the noise is white, and the "Kapitsa pendulum" effect is not at work. The
stabilization occurs in a strong-noise regime where WKB approximation does not
hold.Comment: 4 pages, 7 figure
Critical Behavior of Light
Light is shown to exhibit critical and tricritical behavior in passive
mode-locked lasers with externally injected pulses. It is a first and unique
example of critical phenomena in a one-dimensional many body light-mode system.
The phase diagrams consist of regimes with continuous wave, driven para-pulses,
spontaneous pulses via mode condensation, and heterogeneous pulses, separated
by phase transition lines which terminate with critical or tricritical points.
Enhanced nongaussian fluctuations and collective dynamics are observed at the
critical and tricritical points, showing a mode system analog of the critical
opalescence phenomenon. The critical exponents are calculated and shown to
comply with the mean field theory, which is rigorous in the light system.Comment: RevTex, 5 pages, 3 figure
Extinction of metastable stochastic populations
We investigate extinction of a long-lived self-regulating stochastic
population, caused by intrinsic (demographic) noise. Extinction typically
occurs via one of two scenarios depending on whether the absorbing state n=0 is
a repelling (scenario A) or attracting (scenario B) point of the deterministic
rate equation. In scenario A the metastable stochastic population resides in
the vicinity of an attracting fixed point next to the repelling point n=0. In
scenario B there is an intermediate repelling point n=n_1 between the
attracting point n=0 and another attracting point n=n_2 in the vicinity of
which the metastable population resides. The crux of the theory is WKB method
which assumes that the typical population size in the metastable state is
large. Starting from the master equation, we calculate the quasi-stationary
probability distribution of the population sizes and the (exponentially long)
mean time to extinction for each of the two scenarios. When necessary, the WKB
approximation is complemented (i) by a recursive solution of the
quasi-stationary master equation at small n and (ii) by the van Kampen
system-size expansion, valid near the fixed points of the deterministic rate
equation. The theory yields both entropic barriers to extinction and
pre-exponential factors, and holds for a general set of multi-step processes
when detailed balance is broken. The results simplify considerably for
single-step processes and near the characteristic bifurcations of scenarios A
and B.Comment: 19 pages, 7 figure
Electrical conductivity beyond linear response in layered superconductors under magnetic field
The time-dependent Ginzburg-Landau approach is used to investigate nonlinear
response of a strongly type-II superconductor. The dissipation takes a form of
the flux flow which is quantitatively studied beyond linear response. Thermal
fluctuations, represented by the Langevin white noise, are assumed to be strong
enough to melt the Abrikosov vortex lattice created by the magnetic field into
a moving vortex liquid and marginalize the effects of the vortex pinning by
inhomogeneities. The layered structure of the superconductor is accounted for
by means of the Lawrence-Doniach model. The nonlinear interaction term in
dynamics is treated within Gaussian approximation and we go beyond the often
used lowest Landau level approximation to treat arbitrary magnetic fields. The
I-V curve is calculated for arbitrary temperature and the results are compared
to experimental data on high- superconductor
YBaCuO.Comment: 8 pages, 3 figure
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