203 research outputs found
Pattern fluctuations in transitional plane Couette flow
In wide enough systems, plane Couette flow, the flow established between two
parallel plates translating in opposite directions, displays alternatively
turbulent and laminar oblique bands in a given range of Reynolds numbers R. We
show that in periodic domains that contain a few bands, for given values of R
and size, the orientation and the wavelength of this pattern can fluctuate in
time. A procedure is defined to detect well-oriented episodes and to determine
the statistics of their lifetimes. The latter turn out to be distributed
according to exponentially decreasing laws. This statistics is interpreted in
terms of an activated process described by a Langevin equation whose
deterministic part is a standard Landau model for two interacting complex
amplitudes whereas the noise arises from the turbulent background.Comment: 13 pages, 11 figures. Accepted for publication in Journal of
statistical physic
Horseshoe patterns: visualizing partisan media trust in Germany
A trusted media is crucial for a politically informed citizenry, yet media trust has become fragile in many Western countries. An underexplored aspect is the link between media (dis)trust and populism. The authors visualize media trust across news outlets and partisanship in Germany, for both mainstream and “alternative” news sources. For each source, average trust is grouped by partisanship and sorted from left to right, allowing within-source comparisons. The authors find an intriguing horseshoe pattern for mainstream media sources, for which voters of both populist left-wing and right-wing parties express lower levels of trust. The underlying distribution of individual responses reveals that voters of the right-wing populist party are especially likely to “not at all” trust the mainstream outlets that otherwise enjoy high levels of trust. The media trust gap between populist and centrist voters disappears for alternative sources, for which trust is generally low
Magnons in real materials from density-functional theory
We present an implementation of the adiabatic spin-wave dynamics of Niu and
Kleinman. This technique allows to decouple the spin and charge excitations of
a many-electron system using a generalization of the adiabatic approximation.
The only input for the spin-wave equations of motion are the energies and Berry
curvatures of many-electron states describing frozen spin spirals. The latter
are computed using a newly developed technique based on constrained
density-functional theory, within the local spin density approximation and the
pseudo-potential plane-wave method. Calculations for iron show an excellent
agreement with experiments.Comment: 1 LaTeX file and 1 postscript figur
On the well-posedness of the stochastic Allen-Cahn equation in two dimensions
White noise-driven nonlinear stochastic partial differential equations
(SPDEs) of parabolic type are frequently used to model physical and biological
systems in space dimensions d = 1,2,3. Whereas existence and uniqueness of weak
solutions to these equations are well established in one dimension, the
situation is different for d \geq 2. Despite their popularity in the applied
sciences, higher dimensional versions of these SPDE models are generally
assumed to be ill-posed by the mathematics community. We study this discrepancy
on the specific example of the two dimensional Allen-Cahn equation driven by
additive white noise. Since it is unclear how to define the notion of a weak
solution to this equation, we regularize the noise and introduce a family of
approximations. Based on heuristic arguments and numerical experiments, we
conjecture that these approximations exhibit divergent behavior in the
continuum limit. The results strongly suggest that a series of published
numerical studies are problematic: shrinking the mesh size in these simulations
does not lead to the recovery of a physically meaningful limit.Comment: 21 pages, 4 figures; accepted by Journal of Computational Physics
(Dec 2011
Amplification of Fluctuations in Unstable Systems with Disorder
We study the early-stage kinetics of thermodynamically unstable systems with
quenched disorder. We show analytically that the growth of initial fluctuations
is amplified by the presence of disorder. This is confirmed by numerical
simulations of morphological phase separation (MPS) in thin liquid films and
spinodal decomposition (SD) in binary mixtures. We also discuss the
experimental implications of our results.Comment: 15 pages, 4 figure
Mean flow and spiral defect chaos in Rayleigh-Benard convection
We describe a numerical procedure to construct a modified velocity field that
does not have any mean flow. Using this procedure, we present two results.
Firstly, we show that, in the absence of mean flow, spiral defect chaos
collapses to a stationary pattern comprising textures of stripes with angular
bends. The quenched patterns are characterized by mean wavenumbers that
approach those uniquely selected by focus-type singularities, which, in the
absence of mean flow, lie at the zig-zag instability boundary. The quenched
patterns also have larger correlation lengths and are comprised of rolls with
less curvature. Secondly, we describe how mean flow can contribute to the
commonly observed phenomenon of rolls terminating perpendicularly into lateral
walls. We show that, in the absence of mean flow, rolls begin to terminate into
lateral walls at an oblique angle. This obliqueness increases with Rayleigh
number.Comment: 14 pages, 19 figure
Spinodal Decomposition in a Binary Polymer Mixture: Dynamic Self Consistent Field Theory and Monte Carlo Simulations
We investigate how the dynamics of a single chain influences the kinetics of
early stage phase separation in a symmetric binary polymer mixture. We consider
quenches from the disordered phase into the region of spinodal instability. On
a mean field level we approach this problem with two methods: a dynamical
extension of the self consistent field theory for Gaussian chains, with the
density variables evolving in time, and the method of the external potential
dynamics where the effective external fields are propagated in time. Different
wave vector dependencies of the kinetic coefficient are taken into account.
These early stages of spinodal decomposition are also studied through Monte
Carlo simulations employing the bond fluctuation model that maps the chains --
in our case with 64 effective segments -- on a coarse grained lattice. The
results obtained through self consistent field calculations and Monte Carlo
simulations can be compared because the time, length, and temperature scales
are mapped onto each other through the diffusion constant, the chain extension,
and the energy of mixing. The quantitative comparison of the relaxation rate of
the global structure factor shows that a kinetic coefficient according to the
Rouse model gives a much better agreement than a local, i.e. wave vector
independent, kinetic factor. Including fluctuations in the self consistent
field calculations leads to a shorter time span of spinodal behaviour and a
reduction of the relaxation rate for smaller wave vectors and prevents the
relaxation rate from becoming negative for larger values of the wave vector.
This is also in agreement with the simulation results.Comment: Phys.Rev.E in prin
Theory of superfluidity and drag force in the one-dimensional Bose gas
The one-dimensional Bose gas is an unusual superfluid. In contrast to higher
spatial dimensions, the existence of non-classical rotational inertia is not
directly linked to the dissipationless motion of infinitesimal impurities.
Recently, experimental tests with ultracold atoms have begun and quantitative
predictions for the drag force experienced by moving obstacles have become
available. This topical review discusses the drag force obtained from linear
response theory in relation to Landau's criterion of superfluidity. Based upon
improved analytical and numerical understanding of the dynamical structure
factor, results for different obstacle potentials are obtained, including
single impurities, optical lattices and random potentials generated from
speckle patterns. The dynamical breakdown of superfluidity in random potentials
is discussed in relation to Anderson localization and the predicted
superfluid-insulator transition in these systems.Comment: 17 pages, 12 figures, mini-review prepared for the special issue of
Frontiers of Physics "Recent Progresses on Quantum Dynamics of Ultracold
Atoms and Future Quantum Technologies", edited by Profs. Lee, Ueda, and
Drummon
Electronic structure of overstretched DNA
Minuscule molecular forces can transform DNA into a structure that is
elongated by more than half its original length. We demonstrate that this
pronounced conformational transition is of relevance to ongoing experimental
and theoretical efforts to characterize the conducting properties of DNA wires.
We present quantum mechanical calculations for acidic, dry, poly(CG).poly(CG)
DNA which has undergone elongation of up to 90 % relative to its natural
length, along with a method for visualizing the effects of stretching on the
electronic eigenstates. We find that overstretching leads to a drastic drop of
the hopping matrix elements between localized occupied electronic states
suggesting a dramatic decrease in the conductivity through holes.Comment: 4 page
Relaxation phenomena at criticality
The collective behaviour of statistical systems close to critical points is
characterized by an extremely slow dynamics which, in the thermodynamic limit,
eventually prevents them from relaxing to an equilibrium state after a change
in the thermodynamic control parameters. The non-equilibrium evolution
following this change displays some of the features typically observed in
glassy materials, such as ageing, and it can be monitored via dynamic
susceptibilities and correlation functions of the order parameter, the scaling
behaviour of which is characterized by universal exponents, scaling functions,
and amplitude ratios. This universality allows one to calculate these
quantities in suitable simplified models and field-theoretical methods are a
natural and viable approach for this analysis. In addition, if a statistical
system is spatially confined, universal Casimir-like forces acting on the
confining surfaces emerge and they build up in time when the temperature of the
system is tuned to its critical value. We review here some of the theoretical
results that have been obtained in recent years for universal quantities, such
as the fluctuation-dissipation ratio, associated with the non-equilibrium
critical dynamics, with particular focus on the Ising model with Glauber
dynamics in the bulk. The non-equilibrium dynamics of the Casimir force acting
in a film is discussed within the Gaussian model.Comment: Talk delivered at Statphys23, Genova, Italy, July 9-13, 2007. 8
pages, 7 figure
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