1,115 research outputs found
The complex scaling behavior of non--conserved self--organized critical systems
The Olami--Feder--Christensen earthquake model is often considered the
prototype dissipative self--organized critical model. It is shown that the size
distribution of events in this model results from a complex interplay of
several different phenomena, including limited floating--point precision.
Parallels between the dynamics of synchronized regions and those of a system
with periodic boundary conditions are pointed out, and the asymptotic avalanche
size distribution is conjectured to be dominated by avalanches of size one,
with the weight of larger avalanches converging towards zero as the system size
increases.Comment: 4 pages revtex4, 5 figure
Asperity characteristics of the Olami-Feder-Christensen model of earthquakes
Properties of the Olami-Feder-Christensen (OFC) model of earthquakes are
studied by numerical simulations. The previous study indicated that the model
exhibits ``asperity''-like phenomena, {\it i.e.}, the same region ruptures many
times near periodically [T.Kotani {\it et al}, Phys. Rev. E {\bf 77}, 010102
(2008)]. Such periodic or characteristic features apparently coexist with
power-law-like critical features, {\it e.g.}, the Gutenberg-Richter law
observed in the size distribution. In order to clarify the origin and the
nature of the asperity-like phenomena, we investigate here the properties of
the OFC model with emphasis on its stress distribution. It is found that the
asperity formation is accompanied by self-organization of the highly
concentrated stress state. Such stress organization naturally provides the
mechanism underlying our observation that a series of asperity events repeat
with a common epicenter site and with a common period solely determined by the
transmission parameter of the model. Asperity events tend to cluster both in
time and in space
The Network of Epicenters of the Olami-Feder-Christensen Model of Earthquakes
We study the dynamics of the Olami-Feder-Christensen (OFC) model of
earthquakes, focusing on the behavior of sequences of epicenters regarded as a
growing complex network. Besides making a detailed and quantitative study of
the effects of the borders (the occurrence of epicenters is dominated by a
strong border effect which does not scale with system size), we examine the
degree distribution and the degree correlation of the graph. We detect sharp
differences between the conservative and nonconservative regimes of the model.
Removing border effects, the conservative regime exhibits a Poisson-like degree
statistics and is uncorrelated, while the nonconservative has a broad
power-law-like distribution of degrees (if the smallest events are ignored),
which reproduces the observed behavior of real earthquakes. In this regime the
graph has also a unusually strong degree correlation among the vertices with
higher degree, which is the result of the existence of temporary attractors for
the dynamics: as the system evolves, the epicenters concentrate increasingly on
fewer sites, exhibiting strong synchronization, but eventually spread again
over the lattice after a series of sufficiently large earthquakes. We propose
an analytical description of the dynamics of this growing network, considering
a Markov process network with hidden variables, which is able to account for
the mentioned properties.Comment: 9 pages, 10 figures. Smaller number of figures, and minor text
corrections and modifications. For version with full resolution images see
http://fig.if.usp.br/~tpeixoto/cond-mat-0602244.pd
Simulation study of spatio-temporal correlations of earthquakes as a stick-slip frictional instability
Spatio-temporal correlations of earthquakes are studied numerically on the
basis of the one-dimensional spring-block (Burridge-Knopoff) model. As large
events approach, the frequency of smaller events gradually increases, while,
just before the mainshock, it is dramatically suppressed in a close vicinity of
the epicenter of the upcoming mainshock, a phenomenon closely resembling the
``Mogi doughnut'
Missing physics in stick-slip dynamics of a model for peeling of an adhesive tape
It is now known that the equations of motion for the contact point during
peeling of an adhesive tape mounted on a roll introduced earlier are singular
and do not support dynamical jumps across the two stable branches of the peel
force function. By including the kinetic energy of the tape in the Lagrangian,
we derive equations of motion that support stick-slip jumps as a natural
consequence of the inherent dynamics. In the low mass limit, these equations
reproduce solutions obtained using a differential-algebraic algorithm
introduced for the earlier equations. Our analysis also shows that mass of the
ribbon has a strong influence on the nature of the dynamics.Comment: Accepted for publication in Phys. Rev. E (Rapid Communication
Scaling and Correlation Functions in a Model of a Two-dimensional Earthquake Fault
We study numerically a two-dimensional version of the Burrige-Knopoff model.
We calculate spatial and temporal correlation functions and compare their
behavior with the results found for the one-dimensional model. The
Gutenberg-Richter law is only obtained for special choices of parameters in the
relaxation function. We find that the distribution of the fractal dimension of
the slip zone exhibits two well-defined peaks coeersponding to intermediate
size and large events.Comment: 14 pages, 23 Postscript figure
Towards a modeling of the time dependence of contact area between solid bodies
I present a simple model of the time dependence of the contact area between
solid bodies, assuming either a totally uncorrelated surface topography, or a
self affine surface roughness. The existence of relaxation effects (that I
incorporate using a recently proposed model) produces the time increase of the
contact area towards an asymptotic value that can be much smaller than
the nominal contact area. For an uncorrelated surface topography, the time
evolution of is numerically found to be well fitted by expressions of
the form [, where the exponent depends on
the normal load as , with close to 0.5. In
particular, when the contact area is much lower than the nominal area I obtain
, i.e., a logarithmic time increase of the
contact area, in accordance with experimental observations. The logarithmic
increase for low loads is also obtained analytically in this case. For the more
realistic case of self affine surfaces, the results are qualitatively similar.Comment: 18 pages, 9 figure
Constructing seasonally adjusted data with time-varying confidence intervals
Seasonal adjustment methods transform observed time series data into estimated data, where these estimated data are constructed such that they show no or almost no seasonal variation. An advantage of model-based methods is that these can provide confidence intervals around the seasonally adjusted data. One particularly useful time series model for seasonal adjustment is the basic structural time series [BSM] model. The usual premise of the BSM is that the variance of each of the components is constant. In this paper we address the possibility that the variance of the trend component in a macro-economic time series in some way depends on the business cycle. One reason for doing so is that one can expect that there is more uncertainty in recession periods. We extend the BSM by allowing for a business-cycle dependent variance in the level equation. Next we show how this affects the confidence intervals of seasonally adjusted data. We apply our extended BSM to monthly US unemployment and we show that the estimated confidence intervals for seasonally adjusted unemployment change with past changes in the oil price
Distribution of epicenters in the Olami-Feder-Christensen model
We show that the well established Olami-Feder-Christensen (OFC) model for the
dynamics of earthquakes is able to reproduce a new striking property of real
earthquake data. Recently, it has been pointed out by Abe and Suzuki that the
epicenters of earthquakes could be connected in order to generate a graph, with
properties of a scale-free network of the Barabasi-Albert type. However, only
the non conservative version of the Olami-Feder-Christensen model is able to
reproduce this behavior. The conservative version, instead, behaves like a
random graph. Besides indicating the robustness of the model to describe
earthquake dynamics, those findings reinforce that conservative and non
conservative versions of the OFC model are qualitatively different. Also, we
propose a completely new dynamical mechanism that, even without an explicit
rule of preferential attachment, generates a free scale network. The
preferential attachment is in this case a ``by-product'' of the long term
correlations associated with the self-organized critical state. The detailed
study of the properties of this network can reveal new aspects of the dynamics
of the OFC model, contributing to the understanding of self-organized
criticality in non conserving models.Comment: 7 pages, 7 figure
Near mean-field behavior in the generalized Burridge-Knopoff earthquake model with variable range stress transfer
Simple models of earthquake faults are important for understanding the
mechanisms for their observed behavior in nature, such as Gutenberg-Richter
scaling. Because of the importance of long-range interactions in an elastic
medium, we generalize the Burridge-Knopoff slider-block model to include
variable range stress transfer. We find that the Burridge-Knopoff model with
long-range stress transfer exhibits qualitatively different behavior than the
corresponding long-range cellular automata models and the usual
Burridge-Knopoff model with nearest-neighbor stress transfer, depending on how
quickly the friction force weakens with increasing velocity. Extensive
simulations of quasiperiodic characteristic events, mode-switching phenomena,
ergodicity, and waiting-time distributions are also discussed. Our results are
consistent with the existence of a mean-field critical point and have important
implications for our understanding of earthquakes and other driven dissipative
systems.Comment: 24 pages 12 figures, revised version for Phys. Rev.
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