82 research outputs found
Spatial period-multiplying instabilities of hexagonal Faraday waves
A recent Faraday wave experiment with two-frequency forcing reports two types of `superlattice' patterns that display periodic spatial structures having two separate scales. These patterns both arise as secondary states once the primary hexagonal pattern becomes unstable. In one of these patterns (so-called `superlattice-II') the original hexagonal symmetry is broken in a subharmonic instability to form a striped pattern with a spatial scale increased by a factor of 2sqrt{3} from the original scale of the hexagons. In contrast, the time-averaged pattern is periodic on a hexagonal lattice with an intermediate spatial scale (sqrt{3} larger than the original scale) and apparently has 60 degree rotation symmetry. We present a symmetry-based approach to the analysis of this bifurcation. Taking as our starting point only the observed instantaneous symmetry of the superlattice-II pattern presented in and the subharmonic nature of the secondary instability, we show (a) that the superlattice-II pattern can bifurcate stably from standing hexagons; (b) that the pattern has a spatio-temporal symmetry not reported in [1]; and (c) that this spatio-temporal symmetry accounts for the intermediate spatial scale and hexagonal periodicity of the time-averaged pattern, but not for the apparent 60 degree rotation symmetry. The approach is based on general techniques that are readily applied to other secondary instabilities of symmetric patterns, and does not rely on the primary pattern having small amplitude
The benefits of maternal effects in novel and in stable environments
Natural selection favours phenotypes that match prevailing ecological conditions. A rapid process of adaptation is therefore required in changing environments. Maternal effects can facilitate such responses, but it is currently poorly understood under which circumstances maternal effects may accelerate or slow down the rate of phenotypic evolution. Here, we use a quantitative genetic model, including phenotypic plasticity and maternal effects, to suggest that the relationship between fitness and phenotypic variance plays an important role. Intuitive expectations that positive maternal effects are beneficial are supported following an extreme environmental shift, but, if too strong, that shift can also generate oscillatory dynamics that overshoot the optimal phenotype. In a stable environment, negative maternal effects that slow phenotypic evolution actually minimize variance around the optimum phenotype and thus maximize population mean fitness
Cross-Newell equations for hexagons and triangles
The Cross-Newell equations for hexagons and triangles are derived for general
real gradient systems, and are found to be in flux-divergence form. Specific
examples of complex governing equations that give rise to hexagons and
triangles and which have Lyapunov functionals are also considered, and explicit
forms of the Cross-Newell equations are found in these cases. The general
nongradient case is also discussed; in contrast with the gradient case, the
equations are not flux-divergent. In all cases, the phase stability boundaries
and modes of instability for general distorted hexagons and triangles can be
recovered from the Cross-Newell equations.Comment: 24 pages, 1 figur
Labyrinthic granular landscapes
We have numerically studied a model of granular landscape eroded by wind. We
show the appearance of labyrinthic patterns when the wind orientation turns by
. The occurence of such structures are discussed. Morever, we
introduce the density of ``defects'' as the dynamic parameter governing
the landscape evolution. A power law behavior of is found as a function
of time. In the case of wind variations, the exponent (drastically) shifts from
2 to 1. The presence of two asymptotic values of implies the
irreversibility of the labyrinthic formation process.Comment: 3 pages, 3 figure, RevTe
Ripple and kink dynamics
We propose a relevant modification of the Nishimori-Ouchi model [{\em Phys.
Rev. Lett.} {\bf 71}, 197 (1993)] for granular landscape erosion. We explicitly
introduce a new parameter: the angle of repose , and a new process:
avalanches. We show that the parameter leads to an asymmetry of the
ripples, as observed in natural patterns. The temporal evolution of the maximum
ripple height is limited and not linear, according to recent
observations. The ripple symmetry and the kink dynamics are studied and
discussed.Comment: 7 pages, 10 figure, RevTe
Minimal model for aeolian sand dunes
We present a minimal model for the formation and migration of aeolian sand
dunes. It combines a perturbative description of the turbulent wind velocity
field above the dune with a continuum saltation model that allows for
saturation transients in the sand flux. The latter are shown to provide the
characteristic length scale. The model can explain the origin of important
features of dunes, such as the formation of a slip face, the broken scale
invariance, and the existence of a minimum dune size. It also predicts the
longitudinal shape and aspect ratio of dunes and heaps, their migration
velocity and shape relaxation dynamics. Although the minimal model employs
non-local expressions for the wind shear stress as well as for the sand flux,
it is simple enough to serve as a very efficient tool for analytical and
numerical investigations and to open up the way to simulations of large scale
desert topographies.Comment: 19 pages, 22 figure
Dynamics of Void and its Shape in Redshift Space
We investigate the dynamics of a single spherical void embedded in a
Friedmann-Lema\^itre universe, and analyze the void shape in the redshift
space. We find that the void in the redshift space appears as an ellipse shape
elongated in the direction of the line of sight (i.e., an opposite deformation
to the Kaiser effect). Applying this result to observed void candidates at the
redshift z~1-2, it may provide us with a new method to evaluate the
cosmological parameters, in particular the value of a cosmological constant.Comment: 19 pages, 11 figure
The Quantum Mechanical Arrows of Time
The familiar textbook quantum mechanics of laboratory measurements
incorporates a quantum mechanical arrow of time --- the direction in time in
which state vector reduction operates. This arrow is usually assumed to
coincide with the direction of the thermodynamic arrow of the quasiclassical
realm of everyday experience. But in the more general context of cosmology we
seek an explanation of all observed arrows, and the relations between them, in
terms of the conditions that specify our particular universe. This paper
investigates quantum mechanical and thermodynamic arrows in a time-neutral
formulation of quantum mechanics for a number of model cosmologies in fixed
background spacetimes. We find that a general universe may not have well
defined arrows of either kind. When arrows are emergent they need not point in
the same direction over the whole of spacetime. Rather they may be local,
pointing in different directions in different spacetime regions. Local arrows
can therefore be consistent with global time symmetry.Comment: 9 pages, 4 figures, revtex4, typos correcte
A two-species model of a two-dimensional sandpile surface: a case of asymptotic roughening
We present and analyze a model of an evolving sandpile surface in (2 + 1)
dimensions where the dynamics of mobile grains ({\rho}(x, t)) and immobile
clusters (h(x, t)) are coupled. Our coupling models the situation where the
sandpile is flat on average, so that there is no bias due to gravity. We find
anomalous scaling: the expected logarithmic smoothing at short length and time
scales gives way to roughening in the asymptotic limit, where novel and
non-trivial exponents are found.Comment: 7 Pages, 6 Figures; Granular Matter, 2012 (Online
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