407 research outputs found
Networks as Renormalized Models for Emergent Behavior in Physical Systems
Networks are paradigms for describing complex biological, social and
technological systems. Here I argue that networks provide a coherent framework
to construct coarse-grained models for many different physical systems. To
elucidate these ideas, I discuss two long-standing problems. The first concerns
the structure and dynamics of magnetic fields in the solar corona, as
exemplified by sunspots that startled Galileo almost 400 years ago. We
discovered that the magnetic structure of the corona embodies a scale free
network, with spots at all scales. A network model representing the
three-dimensional geometry of magnetic fields, where links rewire and nodes
merge when they collide in space, gives quantitative agreement with available
data, and suggests new measurements. Seismicity is addressed in terms of
relations between events without imposing space-time windows. A metric
estimates the correlation between any two earthquakes. Linking strongly
correlated pairs, and ignoring pairs with weak correlation organizes the
spatio-temporal process into a sparse, directed, weighted network. New scaling
laws for seismicity are found. For instance, the aftershock decay rate
decreases as 1/t in time up to a correlation time, t[omori]. An estimate from
the data gives t[omori] to be about one year for small magnitude 3 earthquakes,
about 1400 years for the Landers event, and roughly 26,000 years for the
earthquake causing the 2004 Asian tsunami. Our results confirm Kagan's
conjecture that aftershocks can rumble on for centuries.Comment: For the Proceedings of the Erice workshop on Complexity,
Metastability and Nonextensivity (2004), 12 page
Mass Extinctions vs. Uniformitarianism in Biological Evolution
It is usually believed that Darwin's theory leads to a smooth gradual
evolution, so that mass extinctions must be caused by external shocks. However,
it has recently been argued that mass extinctions arise from the intrinsic
dynamics of Darwinian evolution. Species become extinct when swept by
intermittent avalanches propagating through the global ecology. These ideas are
made concrete through studies of simple mathematical models of coevolving
species. The models exhibit self-organized criticality and describe some
general features of the extinction pattern in the fossil record.Comment: 17 pages uuencoded with style file lamuphys.sty. 9 figures not
included but can be obtained via [email protected]. to appear in ``Physics
of Biological Systems'' Lecture Notes in Physics (Springer-Verlag, Heidelberg
, 1996
Self-Organized Criticality and Noise in Traffic
Phantom traffic jams may emerge ``out of nowhere'' from small fluctuations
rather than being triggered by large, exceptional events. We show how phantom
jams arise in a model of single lane highway traffic, which mimics human
driving behavior. Surprisingly, the optimal state of highest efficiency, with
the largest throughput, is a critical state with traffic jams of all sizes. We
demonstrate that open systems self-organize to the most efficient state. In the
model we study, this critical state is a percolation transition for the phantom
traffic jams. At criticality, the individual jams have a complicated fractal
structure where cars follow an intermittent stop and go pattern. We
analytically derive the form of the corresponding power spectrum to be
with exactly. This theoretical prediction agrees
with our numerical simulations and with observations of noise in real
traffic.Comment: 13 pages, uuencoded with style file mprocl.sty. 6 Figures not
included but can be mailed on request. Will appear in ``Traffic and Granular
Flow,'' eds. D.E. Wolf, M. Schreckenberg, and A. Bachem (World Scientific,
Singapore, 1996.
Complex networks of earthquakes and aftershocks
We invoke a metric to quantify the correlation between any two earthquakes.
This provides a simple and straightforward alternative to using space-time
windows to detect aftershock sequences and obviates the need to distinguish
main shocks from aftershocks. Directed networks of earthquakes are constructed
by placing a link, directed from the past to the future, between pairs of
events that are strongly correlated. Each link has a weight giving the relative
strength of correlation such that the sum over the incoming links to any node
equals unity for aftershocks, or zero if the event had no correlated
predecessors. A correlation threshold is set to drastically reduce the size of
the data set without losing significant information. Events can be aftershocks
of many previous events, and also generate many aftershocks. The probability
distribution for the number of incoming and outgoing links are both scale free,
and the networks are highly clustered. The Omori law holds for aftershock rates
up to a decorrelation time that scales with the magnitude, , of the
initiating shock as with .
Another scaling law relates distances between earthquakes and their aftershocks
to the magnitude of the initiating shock. Our results are inconsistent with the
hypothesis of finite aftershock zones. We also find evidence that seismicity is
dominantly triggered by small earthquakes. Our approach, using concepts from
the modern theory of complex networks, together with a metric to estimate
correlations, opens up new avenues of research, as well as new tools to
understand seismicity.Comment: 12 pages, 12 figures, revtex
A simple model for self organization of bipartite networks
We suggest a minimalistic model for directed networks and suggest an
application to injection and merging of magnetic field lines. We obtain a
network of connected donor and acceptor vertices with degree distribution
, and with dynamical reconnection events of size occurring
with frequency that scale as . This suggest that the model is in
the same universality class as the model for self organization in the solar
atmosphere suggested by Hughes et al.(PRL {\bf 90} 131101)
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