11,744 research outputs found
Instability of spatial patterns and its ambiguous impact on species diversity
Self-arrangement of individuals into spatial patterns often accompanies and
promotes species diversity in ecological systems. Here, we investigate pattern
formation arising from cyclic dominance of three species, operating near a
bifurcation point. In its vicinity, an Eckhaus instability occurs, leading to
convectively unstable "blurred" patterns. At the bifurcation point, stochastic
effects dominate and induce counterintuitive effects on diversity: Large
patterns, emerging for medium values of individuals' mobility, lead to rapid
species extinction, while small patterns (low mobility) promote diversity, and
high mobilities render spatial structures irrelevant. We provide a quantitative
analysis of these phenomena, employing a complex Ginzburg-Landau equation.Comment: 4 pages, 3 figures and supplementary information. To appear in Phys.
Rev. Lett
Breaking Kelvin: Circulation conservation and vortex breakup in MHD at low Magnetic Prandtl Number
In this paper we examine the role of weak magnetic fields in breaking
Kelvin's circulation theorem and in vortex breakup in two-dimensional
magnetohydrodynamics for the physically important case of a low magnetic
Prandtl number (low ) fluid. We consider three canonical inviscid solutions
for the purely hydrodynamical problem, namely a Gaussian vortex, a circular
vortex patch and an elliptical vortex patch. We examine how magnetic fields
lead to an initial loss of circulation and attempt to derive scaling
laws for the loss of circulation as a function of field strength and diffusion
as measured by two non-dimensional parameters. We show that for all cases the
loss of circulation depends on the integrated effects of the Lorentz force,
with the patch cases leading to significantly greater circulation loss. For the
case of the elliptical vortex the loss of circulation depends on the total area
swept out by the rotating vortex and so this leads to more efficient
circulation loss than for a circular vortex.Comment: 21 pages, 12 figure
On Predicting the Solar Cycle using Mean-Field Models
We discuss the difficulties of predicting the solar cycle using mean-field
models. Here we argue that these difficulties arise owing to the significant
modulation of the solar activity cycle, and that this modulation arises owing
to either stochastic or deterministic processes. We analyse the implications
for predictability in both of these situations by considering two separate
solar dynamo models. The first model represents a stochastically-perturbed flux
transport dynamo. Here even very weak stochastic perturbations can give rise to
significant modulation in the activity cycle. This modulation leads to a loss
of predictability. In the second model, we neglect stochastic effects and
assume that generation of magnetic field in the Sun can be described by a fully
deterministic nonlinear mean-field model -- this is a best case scenario for
prediction. We designate the output from this deterministic model (with
parameters chosen to produce chaotically modulated cycles) as a target
timeseries that subsequent deterministic mean-field models are required to
predict. Long-term prediction is impossible even if a model that is correct in
all details is utilised in the prediction. Furthermore, we show that even
short-term prediction is impossible if there is a small discrepancy in the
input parameters from the fiducial model. This is the case even if the
predicting model has been tuned to reproduce the output of previous cycles.
Given the inherent uncertainties in determining the transport coefficients and
nonlinear responses for mean-field models, we argue that this makes predicting
the solar cycle using the output from such models impossible.Comment: 22 Pages, 5 Figures, Preprint accepted for publication in Ap
In--out intermittency in PDE and ODE models
We find concrete evidence for a recently discovered form of intermittency,
referred to as in--out intermittency, in both PDE and ODE models of mean field
dynamos. This type of intermittency (introduced in Ashwin et al 1999) occurs in
systems with invariant submanifolds and, as opposed to on--off intermittency
which can also occur in skew product systems, it requires an absence of skew
product structure. By this we mean that the dynamics on the attractor
intermittent to the invariant manifold cannot be expressed simply as the
dynamics on the invariant subspace forcing the transverse dynamics; the
transverse dynamics will alter that tangential to the invariant subspace when
one is far enough away from the invariant manifold.
Since general systems with invariant submanifolds are not likely to have skew
product structure, this type of behaviour may be of physical relevance in a
variety of dynamical settings.
The models employed here to demonstrate in--out intermittency are
axisymmetric mean--field dynamo models which are often used to study the
observed large scale magnetic variability in the Sun and solar-type stars. The
occurrence of this type of intermittency in such models may be of interest in
understanding some aspects of such variabilities.Comment: To be published in Chaos, June 2001, also available at
http://www.eurico.web.co
Astrophysical Fluid Dynamics via Direct Statistical Simulation
In this paper we introduce the concept of Direct Statistical Simulation (DSS)
for astrophysical flows. This technique may be appropriate for problems in
astrophysical fluids where the instantaneous dynamics of the flows are of
secondary importance to their statistical properties. We give examples of such
problems including mixing and transport in planets, stars and disks. The method
is described for a general set of evolution equations, before we consider the
specific case of a spectral method optimised for problems on a spherical
surface. The method is illustrated for the simplest non-trivial example of
hydrodynamics and MHD on a rotating spherical surface. We then discuss possible
extensions of the method both in terms of computational methods and the range
of astrophysical problems that are of interest.Comment: 26 pages, 11 figures, added clarifying remarks and references, and
corrected typos. This version is accepted for publication in The
Astrophysical Journa
Gaussian approximations for stochastic systems with delay: chemical Langevin equation and application to a Brusselator system
We present a heuristic derivation of Gaussian approximations for stochastic
chemical reaction systems with distributed delay. In particular we derive the
corresponding chemical Langevin equation. Due to the non-Markovian character of
the underlying dynamics these equations are integro-differential equations, and
the noise in the Gaussian approximation is coloured. Following on from the
chemical Langevin equation a further reduction leads to the linear-noise
approximation. We apply the formalism to a delay variant of the celebrated
Brusselator model, and show how it can be used to characterise noise-driven
quasi-cycles, as well as noise-triggered spiking. We find surprisingly
intricate dependence of the typical frequency of quasi-cycles on the delay
period.Comment: 14 pages, 9 figure
The Nonlinear Evolution of Instabilities Driven by Magnetic Buoyancy: A New Mechanism for the Formation of Coherent Magnetic Structures
Motivated by the problem of the formation of active regions from a
deep-seated solar magnetic field, we consider the nonlinear three-dimensional
evolution of magnetic buoyancy instabilities resulting from a smoothly
stratified horizontal magnetic field. By exploring the case for which the
instability is continuously driven we have identified a new mechanism for the
formation of concentrations of magnetic flux.Comment: Published in ApJL. Version with colour figure
Turbulence transition in the asymptotic suction boundary layer
We study the transition to turbulence in the asymptotic suction boundary
layer (ASBL) by direct numerical simulation. Tracking the motion of
trajectories intermediate between laminar and turbulent states we can identify
the invariant object inside the laminar-turbulent boundary, the edge state. In
small domains, the flow behaves like a travelling wave over short time
intervals. On longer times one notes that the energy shows strong bursts at
regular time intervals. During the bursts the streak structure is lost, but it
reforms, translated in the spanwise direction by half the domain size. Varying
the suction velocity allows to embed the flow into a family of flows that
interpolate between plane Couette flow and the ASBL. Near the plane Couette
limit, the edge state is a travelling wave. Increasing the suction, the
travelling wave and a symmetry-related copy of it undergo a saddle-node
infinite-period (SNIPER) bifurcation that leads to bursting and
discrete-symmetry shifts. In wider domains, the structures localize in the
spanwise direction, and the flow in the active region is similar to the one in
small domains. There are still periodic bursts at which the flow structures are
shifted, but the shift-distance is no longer connected to a discrete symmetry
of the flow geometry. Two different states are found by edge tracking
techniques, one where structures are shifted to the same side at every burst
and one where they are alternatingly shifted to the left and to the right.Comment: Conference TSFP8, Poitiers 2013. TSFP-8 conference proceedings 2013,
http://www.tsfp-conference.org/proceedings
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Audio-guided mindfulness training in schools and its effect on academic attainment: Contributing to theory and practice
We report the results of a randomized trial (N = 337) examining the effectiveness of a daily audio-guided MBI in raising academic achievement in 16 volunteer classrooms across two socio-demographically diverse United States primary schools. The study's findings were that, over the intervention period, improvements in Math scores, Social Studies scores and Grade Point Averages (GPA) were generally higher for students in intervention classrooms. However, confidence intervals were wide and there was pre-existing variability between schools and grades, resulting in few significant differences as a result of the intervention and generally low effect sizes. Through a careful discussion of the study's results, the paper contributes to theory by generating a comprehensive agenda for follow-up research. The study also contributes to practice by reporting on the effectiveness of technology-enabled mindfulness training because participating teachers seemed able to implement the intervention with almost no further training or need for hiring external mindfulness experts
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