1,499 research outputs found
Universal Scaling Properties in Large Assemblies of Simple Dynamical Units Driven by Long-Wave Random Forcing
Large assemblies of nonlinear dynamical units driven by a long-wave
fluctuating external field are found to generate strong turbulence with scaling
properties. This type of turbulence is so robust that it persists over a finite
parameter range with parameter-dependent exponents of singularity, and is
insensitive to the specific nature of the dynamical units involved. Whether or
not the units are coupled with their neighborhood is also unimportant. It is
discovered numerically that the derivative of the field exhibits strong spatial
intermittency with multifractal structure.Comment: 10 pages, 7 figures, submitted to PR
On the critical nature of plastic flow: one and two dimensional models
Steady state plastic flows have been compared to developed turbulence because
the two phenomena share the inherent complexity of particle trajectories, the
scale free spatial patterns and the power law statistics of fluctuations. The
origin of the apparently chaotic and at the same time highly correlated
microscopic response in plasticity remains hidden behind conventional
engineering models which are based on smooth fitting functions. To regain
access to fluctuations, we study in this paper a minimal mesoscopic model whose
goal is to elucidate the origin of scale free behavior in plasticity. We limit
our description to fcc type crystals and leave out both temperature and rate
effects. We provide simple illustrations of the fact that complexity in rate
independent athermal plastic flows is due to marginal stability of the
underlying elastic system. Our conclusions are based on a reduction of an
over-damped visco-elasticity problem for a system with a rugged elastic energy
landscape to an integer valued automaton. We start with an overdamped one
dimensional model and show that it reproduces the main macroscopic
phenomenology of rate independent plastic behavior but falls short of
generating self similar structure of fluctuations. We then provide evidence
that a two dimensional model is already adequate for describing power law
statistics of avalanches and fractal character of dislocation patterning. In
addition to capturing experimentally measured critical exponents, the proposed
minimal model shows finite size scaling collapse and generates realistic shape
functions in the scaling laws.Comment: 72 pages, 40 Figures, International Journal of Engineering Science
for the special issue in honor of Victor Berdichevsky, 201
Pulsar State Switching from Markov Transitions and Stochastic Resonance
Markov processes are shown to be consistent with metastable states seen in
pulsar phenomena, including intensity nulling, pulse-shape mode changes,
subpulse drift rates, spindown rates, and X-ray emission, based on the
typically broad and monotonic distributions of state lifetimes. Markovianity
implies a nonlinear magnetospheric system in which state changes occur
stochastically, corresponding to transitions between local minima in an
effective potential. State durations (though not transition times) are thus
largely decoupled from the characteristic time scales of various magnetospheric
processes. Dyadic states are common but some objects show at least four states
with some transitions forbidden. Another case is the long-term intermittent
pulsar B1931+24 that has binary radio-emission and torque states with wide, but
non-monotonic duration distributions. It also shows a quasi-period of
days in a 13-yr time sequence, suggesting stochastic resonance in a Markov
system with a forcing function that could be strictly periodic or
quasi-periodic. Nonlinear phenomena are associated with time-dependent activity
in the acceleration region near each magnetic polar cap. The polar-cap diode is
altered by feedback from the outer magnetosphere and by return currents from an
equatorial disk that may also cause the neutron star to episodically charge and
discharge. Orbital perturbations in the disk provide a natural periodicity for
the forcing function in the stochastic resonance interpretation of B1931+24.
Disk dynamics may introduce additional time scales in observed phenomena.
Future work can test the Markov interpretation, identify which pulsar types
have a propensity for state changes, and clarify the role of selection effects.Comment: 25 pages, 6 figures, submitted to the Astrophysical Journa
Testing the SOC hypothesis for the magnetosphere
As noted by Chang, the hypothesis of Self-Organised Criticality provides a
theoretical framework in which the low dimensionality seen in magnetospheric
indices can be combined with the scaling seen in their power spectra and the
recently-observed plasma bursty bulk flows. As such, it has considerable
appeal, describing the aspects of the magnetospheric fuelling:storage:release
cycle which are generic to slowly-driven, interaction-dominated, thresholded
systems rather than unique to the magnetosphere. In consequence, several recent
numerical "sandpile" algorithms have been used with a view to comparison with
magnetospheric observables. However, demonstration of SOC in the magnetosphere
will require further work in the definition of a set of observable properties
which are the unique "fingerprint" of SOC. This is because, for example, a
scale-free power spectrum admits several possible explanations other than SOC.
A more subtle problem is important for both simulations and data analysis
when dealing with multiscale and hence broadband phenomena such as SOC. This is
that finite length systems such as the magnetosphere or magnetotail will by
definition give information over a small range of orders of magnitude, and so
scaling will tend to be narrowband. Here we develop a simple framework in which
previous descriptions of magnetospheric dynamics can be described and
contrasted. We then review existing observations which are indicative of SOC,
and ask if they are sufficient to demonstrate it unambiguously, and if not,
what new observations need to be made?Comment: 29 pages, 0 figures. Based on invited talk at Spring American
Geophysical Union Meeting, 1999. Journal of Atmospheric and Solar Terrestrial
Physics, in pres
A minimal integer automaton behind crystal plasticity
Power law fluctuations and scale free spatial patterns are known to
characterize steady state plastic flow in crystalline materials. In this Letter
we study the emergence of correlations in a simple Frenkel-Kontorova (FK) type
model of 2D plasticity which is largely free of arbitrariness, amenable to
analytical study and is capable of generating critical exponents matching
experiments. Our main observation concerns the possibility to reduce continuum
plasticity to an integer valued automaton revealing inherent discreteness of
the plastic flow.Comment: 4 pages, 5 figure
A Coupled Map Lattice Model for Rheological Chaos in Sheared Nematic Liquid Crystals
A variety of complex fluids under shear exhibit complex spatio-temporal
behaviour, including what is now termed rheological chaos, at moderate values
of the shear rate. Such chaos associated with rheological response occurs in
regimes where the Reynolds number is very small. It must thus arise as a
consequence of the coupling of the flow to internal structural variables
describing the local state of the fluid. We propose a coupled map lattice (CML)
model for such complex spatio-temporal behaviour in a passively sheared nematic
liquid crystal, using local maps constructed so as to accurately describe the
spatially homogeneous case. Such local maps are coupled diffusively to nearest
and next nearest neighbours to mimic the effects of spatial gradients in the
underlying equations of motion. We investigate the dynamical steady states
obtained as parameters in the map and the strength of the spatial coupling are
varied, studying local temporal properties at a single site as well as
spatio-temporal features of the extended system. Our methods reproduce the full
range of spatio-temporal behaviour seen in earlier one-dimensional studies
based on partial differential equations. We report results for both the one and
two-dimensional cases, showing that spatial coupling favours uniform or
periodically time-varying states, as intuitively expected. We demonstrate and
characterize regimes of spatio-temporal intermittency out of which chaos
develops. Our work suggests that such simplified lattice representations of the
spatio-temporal dynamics of complex fluids under shear may provide useful
insights as well as fast and numerically tractable alternatives to continuum
representations.Comment: 32 pages, single column, 20 figure
25 Years of Self-Organized Criticality: Solar and Astrophysics
Shortly after the seminal paper {\sl "Self-Organized Criticality: An
explanation of 1/f noise"} by Bak, Tang, and Wiesenfeld (1987), the idea has
been applied to solar physics, in {\sl "Avalanches and the Distribution of
Solar Flares"} by Lu and Hamilton (1991). In the following years, an inspiring
cross-fertilization from complexity theory to solar and astrophysics took
place, where the SOC concept was initially applied to solar flares, stellar
flares, and magnetospheric substorms, and later extended to the radiation belt,
the heliosphere, lunar craters, the asteroid belt, the Saturn ring, pulsar
glitches, soft X-ray repeaters, blazars, black-hole objects, cosmic rays, and
boson clouds. The application of SOC concepts has been performed by numerical
cellular automaton simulations, by analytical calculations of statistical
(powerlaw-like) distributions based on physical scaling laws, and by
observational tests of theoretically predicted size distributions and waiting
time distributions. Attempts have been undertaken to import physical models
into the numerical SOC toy models, such as the discretization of
magneto-hydrodynamics (MHD) processes. The novel applications stimulated also
vigorous debates about the discrimination between SOC models, SOC-like, and
non-SOC processes, such as phase transitions, turbulence, random-walk
diffusion, percolation, branching processes, network theory, chaos theory,
fractality, multi-scale, and other complexity phenomena. We review SOC studies
from the last 25 years and highlight new trends, open questions, and future
challenges, as discussed during two recent ISSI workshops on this theme.Comment: 139 pages, 28 figures, Review based on ISSI workshops "Self-Organized
Criticality and Turbulence" (2012, 2013, Bern, Switzerland
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