295 research outputs found
Diffusion of a passive scalar by convective flows under parametric disorder
We study transport of a weakly diffusive pollutant (a passive scalar) by
thermoconvective flow in a fluid-saturated horizontal porous layer heated from
below under frozen parametric disorder. In the presence of disorder (random
frozen inhomogeneities of the heating or of macroscopic properties of the
porous matrix), spatially localized flow patterns appear below the convective
instability threshold of the system without disorder. Thermoconvective flows
crucially effect the transport of a pollutant along the layer, especially when
its molecular diffusion is weak. The effective (or eddy) diffusivity also
allows to observe the transition from a set of localized currents to an almost
everywhere intense "global" flow. We present results of numerical calculation
of the effective diffusivity and discuss them in the context of localization of
fluid currents and the transition to a "global" flow. Our numerical findings
are in a good agreement with the analytical theory we develop for the limit of
a small molecular diffusivity and sparse domains of localized currents. Though
the results are obtained for a specific physical system, they are relevant for
a broad variety of fluid dynamical systems.Comment: 12 pages, 4 figures, the revised version of the paper for J. Stat.
Mech. (Special issue for proceedings of 5th Intl. Conf. on Unsolved Problems
on Noise and Fluctuations in Physics, Biology & High Technology, Lyon
(France), June 2-6, 2008
Advectional enhancement of eddy diffusivity under parametric disorder
Frozen parametric disorder can lead to appearance of sets of localized
convective currents in an otherwise stable (quiescent) fluid layer heated from
below. These currents significantly influence the transport of an admixture (or
any other passive scalar) along the layer. When the molecular diffusivity of
the admixture is small in comparison to the thermal one, which is quite typical
in nature, disorder can enhance the effective (eddy) diffusivity by several
orders of magnitude in comparison to the molecular diffusivity. In this paper
we study the effect of an imposed longitudinal advection on delocalization of
convective currents, both numerically and analytically; and report subsequent
drastic boost of the effective diffusivity for weak advection.Comment: 14 pages, 6 figures, for Topical Issue of Physica Scripta "2nd Intl.
Conf. on Turbulent Mixing and Beyond
Noise sensitivity of sub- and supercritically bifurcating patterns with group velocities close to the convective-absolute instability
The influence of small additive noise on structure formation near a forwards
and near an inverted bifurcation as described by a cubic and quintic Ginzburg
Landau amplitude equation, respectively, is studied numerically for group
velocities in the vicinity of the convective-absolute instability where the
deterministic front dynamics would empty the system.Comment: 16 pages, 7 Postscript figure
Breathing and randomly walking pulses in a semilinear Ginzburg-Landau system
A system consisting of the cubic complex Ginzburg-Landau equation which is
linearly coupled to an additional linear dissipative equation, is considered.
The model was introduced earlier in the context of dual-core nonlinear optical
fibers with one active and one passive cores. We argue that it may also
possibly describe traveling-wave convection in a channel with an inner vertical
partition. By means of systematic simulations, we find new types of stable
localized excitations, which exist in the system in addition to the earlier
found stationary pulses. The new localized excitations include pulses existing
on top of a small-amplitude background (that may be regular or chaotic) {\em
above} the threshold of instability of the zero solution, and breathers into
which stationary pulses are transformed through a Hopf bifurcation below the
zero-solution instability threshold. A sharp border between the stable
stationary pulses and breathers, precluding their coexistence, is identified.
Stable bound states of two breathers with a phase shift between their
internal vibrations are found too. Above the threshold, the pulses are standing
if the small-amplitude background oscillations are regular; if the background
is chaotic, the pulses are randomly walking. With the increase of the system's
size, more randomly walking pulses are spontaneously generated. The random walk
of different pulses in a multi-pulse state is synchronized (but not completely)
due to their mutual repulsion. At a large overcriticality, the multi-pulse
state goes over into a spatiotemporal chaos.Comment: 16page,12figure
Sources and sinks separating domains of left- and right-traveling waves: Experiment versus amplitude equations
In many pattern forming systems that exhibit traveling waves, sources and
sinks occur which separate patches of oppositely traveling waves. We show that
simple qualitative features of their dynamics can be compared to predictions
from coupled amplitude equations. In heated wire convection experiments, we
find a discrepancy between the observed multiplicity of sources and theoretical
predictions. The expression for the observed motion of sinks is incompatible
with any amplitude equation description.Comment: 4 pages, RevTeX, 3 figur
Thermally Induced Fluctuations Below the Onset of Rayleigh-B\'enard Convection
We report quantitative experimental results for the intensity of
noise-induced fluctuations below the critical temperature difference for Rayleigh-B\'enard convection. The structure factor of the fluctuating
convection rolls is consistent with the expected rotational invariance of the
system. In agreement with predictions based on stochastic hydrodynamic
equations, the fluctuation intensity is found to be proportional to
where . The
noise power necessary to explain the measurements agrees with the prediction
for thermal noise. (WAC95-1)Comment: 13 pages of text and 4 Figures in a tar-compressed and uuencoded file
(using uufiles package). Detailed instructions of unpacking are include
Phase chaos in the anisotropic complex Ginzburg-Landau Equation
Of the various interesting solutions found in the two-dimensional complex
Ginzburg-Landau equation for anisotropic systems, the phase-chaotic states show
particularly novel features. They exist in a broader parameter range than in
the isotropic case, and often even broader than in one dimension. They
typically represent the global attractor of the system. There exist two
variants of phase chaos: a quasi-one dimensional and a two-dimensional
solution. The transition to defect chaos is of intermittent type.Comment: 4 pages RevTeX, 5 figures, little changes in figures and references,
typos removed, accepted as Rapid Commun. in Phys. Rev.
Higgs production and decay: Analytic results at next-to-leading order QCD
The virtual two-loop corrections for Higgs production in gluon fusion are
calculated analytically in QCD for arbitrary Higgs and quark masses. Both
scalar and pseudo-scalar Higgs bosons are considered. The results are obtained
by expanding the known one-dimensional integral representation in terms of
m_H/m_q, and matching it with a suitably chosen ansatz of Harmonic
Polylogarithms. This ansatz is motivated by the known analytic result for the
Higgs decay rate into two photons. The method also allows us to check this
result and to extend it to the pseudo-scalar decay rate.Comment: LaTeX, 16 pages, 5 figures (8 eps-files
Modeling oscillatory Microtubule--Polymerization
Polymerization of microtubules is ubiquitous in biological cells and under
certain conditions it becomes oscillatory in time. Here simple reaction models
are analyzed that capture such oscillations as well as the length distribution
of microtubules. We assume reaction conditions that are stationary over many
oscillation periods, and it is a Hopf bifurcation that leads to a persistent
oscillatory microtubule polymerization in these models. Analytical expressions
are derived for the threshold of the bifurcation and the oscillation frequency
in terms of reaction rates as well as typical trends of their parameter
dependence are presented. Both, a catastrophe rate that depends on the density
of {\it guanosine triphosphate} (GTP) liganded tubulin dimers and a delay
reaction, such as the depolymerization of shrinking microtubules or the decay
of oligomers, support oscillations. For a tubulin dimer concentration below the
threshold oscillatory microtubule polymerization occurs transiently on the
route to a stationary state, as shown by numerical solutions of the model
equations. Close to threshold a so--called amplitude equation is derived and it
is shown that the bifurcation to microtubule oscillations is supercritical.Comment: 21 pages and 12 figure
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