93 research outputs found
A stochastic theory for temporal fluctuations in self-organized critical systems
A stochastic theory for the toppling activity in sandpile models is
developed, based on a simple mean-field assumption about the toppling process.
The theory describes the process as an anti-persistent Gaussian walk, where the
diffusion coefficient is proportional to the activity. It is formulated as a
generalization of the It\^{o} stochastic differential equation with an
anti-persistent fractional Gaussian noise source. An essential element of the
theory is re-scaling to obtain a proper thermodynamic limit, and it captures
all temporal features of the toppling process obtained by numerical simulation
of the Bak-Tang-Wiesenfeld sandpile in this limit.Comment: 9 pages, 4 figure
Modeling temporal fluctuations in avalanching systems
We demonstrate how to model the toppling activity in avalanching systems by
stochastic differential equations (SDEs). The theory is developed as a
generalization of the classical mean field approach to sandpile dynamics by
formulating it as a generalization of Itoh's SDE. This equation contains a
fractional Gaussian noise term representing the branching of an avalanche into
small active clusters, and a drift term reflecting the tendency for small
avalanches to grow and large avalanches to be constricted by the finite system
size. If one defines avalanching to take place when the toppling activity
exceeds a certain threshold the stochastic model allows us to compute the
avalanche exponents in the continum limit as functions of the Hurst exponent of
the noise. The results are found to agree well with numerical simulations in
the Bak-Tang-Wiesenfeld and Zhang sandpile models. The stochastic model also
provides a method for computing the probability density functions of the
fluctuations in the toppling activity itself. We show that the sandpiles do not
belong to the class of phenomena giving rise to universal non-Gaussian
probability density functions for the global activity. Moreover, we demonstrate
essential differences between the fluctuations of total kinetic energy in a
two-dimensional turbulence simulation and the toppling activity in sandpiles.Comment: 14 pages, 11 figure
Critical fluctuations and anomalous transport in soft Yukawa-Langevin systems
Simulation of a Langevin-dynamics model demonstrates emergence of critical
fluctuations and anomalous grain transport which have been observed in
experiments on "soft" quasi-two-dimensional dusty plasma clusters. It has been
suggested that these anomalies derive from particular non-equilibrium physics,
but our model does not contain such physics: the grains are confined by an
external potential, interact via static Yukawa forces, and are subject to
stochastic heating and dissipation from neutrals. One remarkable feature is
emergence of leptokurtic probability distributions of grain displacements
on time-scales , where is the
time at which the standard deviation
approaches the mean inter-grain distance . Others are development of
humps in the distributions on multiples of , anomalous Hurst exponents,
and transitions from leptokurtic towards Gaussian displacement distributions on
time scales . The latter is a signature of intermittency,
here interpreted as a transition from bursty transport associated with hopping
on intermediate time scales to vortical flows on longer time scales.Comment: 12 pages, 9 figure
Temperature variability implies greater economic damages from climate change
A number of influential assessments of the economic cost of climate change rely on just a small number of coupled climate–economy models. A central feature of these assessments is their accounting of the economic cost of epistemic uncertainty—that part of our uncertainty stemming from our inability to precisely estimate key model parameters, such as the Equilibrium Climate Sensitivity. However, these models fail to account for the cost of aleatory uncertainty—the irreducible uncertainty that remains even when the true parameter values are known. We show how to account for this second source of uncertainty in a physically well-founded and tractable way, and we demonstrate that even modest variability implies trillions of dollars of previously unaccounted for economic damages
Two and three-dimensional oscillons in nonlinear Faraday resonance
We study 2D and 3D localised oscillating patterns in a simple model system
exhibiting nonlinear Faraday resonance. The corresponding amplitude equation is
shown to have exact soliton solutions which are found to be always unstable in
3D. On the contrary, the 2D solitons are shown to be stable in a certain
parameter range; hence the damping and parametric driving are capable of
suppressing the nonlinear blowup and dispersive decay of solitons in two
dimensions. The negative feedback loop occurs via the enslaving of the
soliton's phase, coupled to the driver, to its amplitude and width.Comment: 4 pages; 1 figur
Ultrashort filaments of light in weakly-ionized, optically-transparent media
Modern laser sources nowadays deliver ultrashort light pulses reaching few
cycles in duration, high energies beyond the Joule level and peak powers
exceeding several terawatt (TW). When such pulses propagate through
optically-transparent media, they first self-focus in space and grow in
intensity, until they generate a tenuous plasma by photo-ionization. For free
electron densities and beam intensities below their breakdown limits, these
pulses evolve as self-guided objects, resulting from successive equilibria
between the Kerr focusing process, the chromatic dispersion of the medium, and
the defocusing action of the electron plasma. Discovered one decade ago, this
self-channeling mechanism reveals a new physics, widely extending the frontiers
of nonlinear optics. Implications include long-distance propagation of TW beams
in the atmosphere, supercontinuum emission, pulse shortening as well as
high-order harmonic generation. This review presents the landmarks of the
10-odd-year progress in this field. Particular emphasis is laid to the
theoretical modeling of the propagation equations, whose physical ingredients
are discussed from numerical simulations. Differences between femtosecond
pulses propagating in gaseous or condensed materials are underlined. Attention
is also paid to the multifilamentation instability of broad, powerful beams,
breaking up the energy distribution into small-scale cells along the optical
path. The robustness of the resulting filaments in adverse weathers, their
large conical emission exploited for multipollutant remote sensing, nonlinear
spectroscopy, and the possibility to guide electric discharges in air are
finally addressed on the basis of experimental results.Comment: 50 pages, 38 figure
Recommended temperature metrics for carbon budget estimates, model evaluation and climate policy
Recent estimates of the amount of carbon dioxide that can still be emitted while achieving the Paris Agreement temperature goals are larger than previously thought. One potential reason for these larger estimates may be the different temperature metrics used to estimate the observed global mean warming for the historical period, as they affect the size of the remaining carbon budget. Here we explain the reasons behind these remaining carbon budget increases, and discuss how methodological choices of the global mean temperature metric and the reference period influence estimates of the remaining carbon budget. We argue that the choice of the temperature metric should depend on the domain of application. For scientific estimates of total or remaining carbon budgets, globally averaged surface air temperature estimates should be used consistently for the past and the future. However, when used to inform the achievement of the Paris Agreement goal, a temperature metric consistent with the science that was underlying and directly informed the Paris Agreement should be applied. The resulting remaining carbon budgets should be calculated using the appropriate metric or adjusted to reflect these differences among temperature metrics. Transparency and understanding of the implications of such choices are crucial to providing useful information that can bridge the science–policy gap
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