253 research outputs found
Rank-Ordering Statistics of Extreme Events: Application to the Distribution of Large Earthquakes
Rank-ordering statistics provides a perspective on the rare, largest elements
of a population, whereas the statistics of cumulative distributions are
dominated by the more numerous small events. The exponent of a power law
distribution can be determined with good accuracy by rank-ordering statistics
from the observation of only a few tens of the largest events. Using analytical
results and synthetic tests, we quantify the systematic and the random errors.
We also study the case of a distribution defined by two branches, each having
a power law distribution, one defined for the largest events and the other for
smaller events, with application to the World-Wide (Harvard) and Southern
California earthquake catalogs. In the case of the Harvard moment catalog, we
make more precise earlier claims of the existence of a transition of the
earthquake magnitude distribution between small and large earthquakes; the
-values are for large shallow earthquakes and for smaller shallow earthquakes. However, the cross-over
magnitude between the two distributions is ill-defined. The data available at
present do not provide a strong constraint on the cross-over which has a
probability of being between magnitudes and for shallow
earthquakes; this interval may be too conservatively estimated. Thus, any
influence of a universal geometry of rupture on the distribution of earthquakes
world-wide is ill-defined at best. We caution that there is no direct evidence
to confirm the hypothesis that the large-moment branch is indeed a power law.
In fact, a gamma distribution fits the entire suite of earthquake moments from
the smallest to the largest satisfactorily. There is no evidence that the
earthquakes of the Southern California catalog have a distribution with tw
From a systems theory of sociology to modeling the onset and evolution of criminality
This paper proposes a systems theory approach to the modeling of onset and
evolution of criminality in a territory, which aims at capturing the complexity
features of social systems. Complexity is related to the fact that individuals
have the ability to develop specific heterogeneously distributed strategies,
which depend also on those expressed by the other individuals. The modeling is
developed by methods of generalized kinetic theory where interactions and
decisional processes are modeled by theoretical tools of stochastic game
theory.Comment: 20 page
"Universal" Distribution of Inter-Earthquake Times Explained
We propose a simple theory for the ``universal'' scaling law previously
reported for the distributions of waiting times between earthquakes. It is
based on a largely used benchmark model of seismicity, which just assumes no
difference in the physics of foreshocks, mainshocks and aftershocks. Our
theoretical calculations provide good fits to the data and show that
universality is only approximate. We conclude that the distributions of
inter-event times do not reveal more information than what is already known
from the Gutenberg-Richter and the Omori power laws. Our results reinforces the
view that triggering of earthquakes by other earthquakes is a key physical
mechanism to understand seismicity.Comment: 4 pages with two figure
Persistence and Quiescence of Seismicity on Fault Systems
We study the statistics of simulated earthquakes in a quasistatic model of
two parallel heterogeneous faults within a slowly driven elastic tectonic
plate. The probability that one fault remains dormant while the other is active
for a time Dt following the previous activity shift is proportional to the
inverse of Dt to the power 1+x, a result that is robust in the presence of
annealed noise and strength weakening. A mean field theory accounts for the
observed dependence of the persistence exponent x as a function of
heterogeneity and distance between faults. These results continue to hold if
the number of competing faults is increased. This is related to the persistence
phenomenon discovered in a large variety of systems, which specifies how long a
relaxing dynamical system remains in a neighborhood of its initial
configuration. Our persistence exponent is found to vary as a function of
heterogeneity and distance between faults, thus defining a novel universality
class.Comment: 4 pages, 3 figures, Revte
Scale free networks of earthquakes and aftershocks
We propose a new metric to quantify the correlation between any two
earthquakes. The metric consists of a product involving the time interval and
spatial distance between two events, as well as the magnitude of the first one.
According to this metric, events typically are strongly correlated to only one
or a few preceding ones. Thus a classification of events as foreshocks, main
shocks or aftershocks emerges automatically without imposing predefined
space-time windows. To construct a network, each earthquake receives an
incoming link from its most correlated predecessor. The number of aftershocks
for any event, identified by its outgoing links, is found to be scale free with
exponent . The original Omori law with emerges as a
robust feature of seismicity, holding up to years even for aftershock sequences
initiated by intermediate magnitude events. The measured fat-tailed
distribution of distances between earthquakes and their aftershocks suggests
that aftershock collection with fixed space windows is not appropriate.Comment: 7 pages and 7 figures. Submitte
What is life? A perspective of the mathematical kinetic theory of active particles
The modeling of living systems composed of many interacting entities is treated in this paper with the aim of describing their collective behaviors. The mathematical approach is developed within the general framework of the kinetic theory of active particles. The presentation is in three parts. First, we derive the mathematical tools, subsequently, we show how the method can be applied to a number of case studies related to well defined living systems, and finally, we look ahead to research perspectives
On the Occurrence of Finite-Time-Singularities in Epidemic Models of Rupture, Earthquakes and Starquakes
We present a new kind of critical stochastic finite-time-singularity, relying
on the interplay between long-memory and extreme fluctuations. We illustrate it
on the well-established epidemic-type aftershock (ETAS) model for aftershocks,
based solely on the most solidly documented stylized facts of seismicity
(clustering in space and in time and power law Gutenberg-Richter distribution
of earthquake energies). This theory accounts for the main observations (power
law acceleration and discrete scale invariant structure) of critical rupture of
heterogeneous materials, of the largest sequence of starquakes ever attributed
to a neutron star as well as of earthquake sequences.Comment: Revtex document of 4 pages including 1 eps figur
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