108 research outputs found
Self-similar aftershock rates
In many important systems exhibiting crackling noise --- intermittent
avalanche-like relaxation response with power-law and, thus, self-similar
distributed event sizes --- the "laws" for the rate of activity after large
events are not consistent with the overall self-similar behavior expected on
theoretical grounds. This is in particular true for the case of seismicity and
a satisfying solution to this paradox has remained outstanding. Here, we
propose a generalized description of the aftershock rates which is both
self-similar and consistent with all other known self-similar features.
Comparing our theoretical predictions with high resolution earthquake data from
Southern California we find excellent agreement, providing in particular clear
evidence for a unified description of aftershocks and foreshocks. This may
offer an improved way of time-dependent seismic hazard assessment and
earthquake forecasting
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
Nonequilibrium temperature response for stochastic overdamped systems
The thermal response of nonequilibrium systems requires the knowledge of
concepts that go beyond entropy production. This is showed for systems obeying
overdamped Langevin dynamics, either in steady states or going through a
relaxation process. Namely, we derive the linear response to perturbations of
the noise intensity, mapping it onto the quadratic response to a constant small
force. The latter, displaying divergent terms, is explicitly regularized with a
novel path-integral method. The nonequilibrium equivalents of heat capacity and
thermal expansion coefficient are two applications of this approach, as we show
with numerical examples.Comment: 23 pages, 2 figure
Models of DNA denaturation dynamics: universal properties
We briefly review some of the models used to describe DNA denaturation
dynamics, focusing on the value of the dynamical exponent , which governs
the scaling of the characteristic time as a function of the
sequence length . The models contain different degrees of simplifications,
in particular sometimes they do not include a description for helical
entanglement: we discuss how this aspect influences the value of , which
ranges from to . Connections with experiments are also
mentioned
Inflow rate, a time-symmetric observable obeying fluctuation relations
While entropy changes are the usual subject of fluctuation theorems, we seek
fluctuation relations involving time-symmetric quantities, namely observables
that do not change sign if the trajectories are observed backward in time. We
find detailed and integral fluctuation relations for the (time integrated)
difference between "entrance rate" and escape rate in mesoscopic jump systems.
Such "inflow rate", which is even under time reversal, represents the
discrete-state equivalent of the phase space contraction rate. Indeed, it
becomes minus the divergence of forces in the continuum limit to overdamped
diffusion. This establishes a formal connection between reversible
deterministic systems and irreversible stochastic ones, confirming that
fluctuation theorems are largely independent of the details of the underling
dynamics.Comment: v3: published version, slightly shorter title and abstrac
A thermodynamic uncertainty relation for a system with memory
We introduce an example of thermodynamic uncertainty relation (TUR) for
systems modeled by a one-dimensional generalised Langevin dynamics with memory,
determining the motion of a micro-bead driven in a complex fluid. Contrary to
TURs typically discussed in the previous years, our observables and the entropy
production rate are one-time variables. The bound to the signal-to-noise ratio
of such state-dependent observables only in some cases can be mapped to the
entropy production rate. For example, this is true in Markovian systems. Hence,
the presence of memory in the system complicates the thermodynamic
interpretation of the uncertainty relation
Thermal response in driven diffusive systems
Evaluating the linear response of a driven system to a change in environment
temperature(s) is essential for understanding thermal properties of
nonequilibrium systems. The system is kept in weak contact with possibly
different fast relaxing mechanical, chemical or thermal equilibrium reservoirs.
Modifying one of the temperatures creates both entropy fluxes and changes in
dynamical activity. That is not unlike mechanical response of nonequilibrium
systems but the extra difficulty for perturbation theory via path-integration
is that for a Langevin dynamics temperature also affects the noise amplitude
and not only the drift part. Using a discrete-time mesh adapted to the
numerical integration one avoids that ultraviolet problem and we arrive at a
fluctuation expression for its thermal susceptibility. The algorithm appears
stable under taking even finer resolution.Comment: 10 pages, 3 figure
Correlated earthquakes in a self-organized model
Motivated by the fact that empirical time series of earthquakes exhibit
long-range correlations in space and time and the Gutenberg-Richter
distribution of magnitudes, we propose a simple fault model that can account
for these types of scale-invariance. It is an avalanching process that displays
power-laws in the event sizes, in the epicenter distances as well as in the
waiting-time distributions, and also aftershock rates obeying a generalized
Omori law. We thus confirm that there is a relation between temporal and
spatial clustering of the activity in this kind of models. The fluctuating
boundaries of possible slipping areas show that the size of the largest
possible earthquake is not always maximal, and the average correlation length
is a fraction of the system size. This suggests that there is a concrete
alternative to the extreme interpretation of self-organized criticality as a
process in which every small event can cascade to an arbitrary large one: the
new picture includes fluctuating domains of coherent stress field as part of
the global self-organization. Moreover, this picture can be more easily
compared with other scenarios discussing fluctuating correlations lengths in
seismicity.Comment: 8 pages, 10 figure
The modified Sutherland--Einstein relation for diffusive nonequilibria
There remains a useful relation between diffusion and mobility for a Langevin
particle in a periodic medium subject to nonconservative forces. The usual
fluctuation-dissipation relation easily gets modified and the mobility matrix
is no longer proportional to the diffusion matrix, with a correction term
depending explicitly on the (nonequilibrium) forces. We discuss this correction
by considering various simple examples and we visualize the various
dependencies on the applied forcing and on the time by means of simulations.
For example, in all cases the diffusion depends on the external forcing more
strongly than does the mobility. We also give an explicit decomposition of the
symmetrized mobility matrix as the difference between two positive matrices,
one involving the diffusion matrix, the other force--force correlations
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