5,342 research outputs found
Hierarchy of Temporal Responses of Multivariate Self-Excited Epidemic Processes
We present the first exact analysis of some of the temporal properties of
multivariate self-excited Hawkes conditional Poisson processes, which
constitute powerful representations of a large variety of systems with bursty
events, for which past activity triggers future activity. The term
"multivariate" refers to the property that events come in different types, with
possibly different intra- and inter-triggering abilities. We develop the
general formalism of the multivariate generating moment function for the
cumulative number of first-generation and of all generation events triggered by
a given mother event (the "shock") as a function of the current time . This
corresponds to studying the response function of the process. A variety of
different systems have been analyzed. In particular, for systems in which
triggering between events of different types proceeds through a one-dimension
directed or symmetric chain of influence in type space, we report a novel
hierarchy of intermediate asymptotic power law decays of the rate of triggered events as a function of the
distance of the events to the initial shock in the type space, where for the relevant long-memory processes characterizing many natural
and social systems. The richness of the generated time dynamics comes from the
cascades of intermediate events of possibly different kinds, unfolding via a
kind of inter-breeding genealogy.Comment: 40 pages, 8 figure
Power Law Distributions of Seismic Rates
We report an empirical determination of the probability density functions
of the number of earthquakes in finite space-time
windows for the California catalog. We find a stable power law tail
with exponent for all
space ( to km) and time intervals (0.1 to 1000
days). These observations, as well as the non-universal dependence on
space-time windows for all different space-time windows simultaneously, are
explained by solving one of the most used reference model in seismology (ETAS),
which assumes that each earthquake can trigger other earthquakes. The data
imposes that active seismic regions are Cauchy-like fractals, whose exponent
is well-constrained by the seismic rate data.Comment: 5 pages with 1 figur
Vere-Jones' Self-Similar Branching Model
Motivated by its potential application to earthquake statistics, we study the
exactly self-similar branching process introduced recently by Vere-Jones, which
extends the ETAS class of conditional branching point-processes of triggered
seismicity. One of the main ingredient of Vere-Jones' model is that the power
law distribution of magnitudes m' of daughters of first-generation of a mother
of magnitude m has two branches m'm with
exponent beta+d, where beta and d are two positive parameters. We predict that
the distribution of magnitudes of events triggered by a mother of magnitude
over all generations has also two branches m'm
with exponent beta+h, with h= d \sqrt{1-s}, where s is the fraction of
triggered events. This corresponds to a renormalization of the exponent d into
h by the hierarchy of successive generations of triggered events. The empirical
absence of such two-branched distributions implies, if this model is seriously
considered, that the earth is close to criticality (s close to 1) so that beta
- h \approx \beta + h \approx \beta. We also find that, for a significant part
of the parameter space, the distribution of magnitudes over a full catalog
summed over an average steady flow of spontaneous sources (immigrants)
reproduces the distribution of the spontaneous sources and is blind to the
exponents beta, d of the distribution of triggered events.Comment: 13 page + 3 eps figure
New possibility of the ground state of quarter-filled one-dimensional strongly correlated electronic system interacting with localized spins
We study numerically the ground state properties of the one-dimensional
quarter-filled strongly correlated electronic system interacting
antiferromagnetically with localized spins. It is shown that the
charge-ordered state is significantly stabilized by the introduction of
relatively small coupling with the localized spins. When the coupling becomes
large the spin and charge degrees of freedom behave quite independently and the
ferromagnetism is realized. Moreover, the coexistence of ferromagnetism with
charge order is seen under strong electronic interaction. Our results suggest
that such charge order can be easily controlled by the magnetic field, which
possibly give rise to the giant negative magnetoresistance, and its relation to
phthalocyanine compounds is discussed.Comment: 5pages, 4figure
Variational ground states of the two-dimensional Hubbard model
Recent refinements of analytical and numerical methods have improved our
understanding of the ground-state phase diagram of the two-dimensional (2D)
Hubbard model. Here we focus on variational approaches, but comparisons with
both Quantum Cluster and Gaussian Monte Carlo methods are also made. Our own
ansatz leads to an antiferromagnetic ground state at half filling with a
slightly reduced staggered order parameter (as compared to simple mean-field
theory). Away from half filling, we find d-wave superconductivity, but confined
to densities where the Fermi surface passes through the antiferromagnetic zone
boundary (if hopping between both nearest-neighbour and next-nearest-neighbour
sites is considered). Our results agree surprisingly well with recent numerical
studies using the Quantum Cluster method. An interesting trend is found by
comparing gap parameters (antiferromagnetic or superconducting) obtained with
different variational wave functions. They vary by an order of magnitude and
thus cannot be taken as a characteristic energy scale. In contrast, the order
parameter is much less sensitive to the degree of sophistication of the
variational schemes, at least at and near half filling.Comment: 18 pages, 4 figures, to be published in New J. Phy
Intercluster Correlation in Seismicity
Mega et al.(cond-mat/0212529) proposed to use the ``diffusion entropy'' (DE)
method to demonstrate that the distribution of time intervals between a large
earthquake (the mainshock of a given seismic sequence) and the next one does
not obey Poisson statistics. We have performed synthetic tests which show that
the DE is unable to detect correlations between clusters, thus negating the
claimed possibility of detecting an intercluster correlation. We also show that
the LR model, proposed by Mega et al. to reproduce inter-cluster correlation,
is insufficient to account for the correlation observed in the data.Comment: Comment on Mega et al., Phys. Rev. Lett. 90. 188501 (2003)
(cond-mat/0212529
Invariant manifolds and orbit control in the solar sail three-body problem
In this paper we consider issues regarding the control and orbit transfer of solar sails in the circular restricted Earth-Sun system. Fixed points for solar sails in this system have the linear dynamical properties of saddles crossed with centers; thus the fixed points are dynamically unstable and control is required. A natural mechanism of control presents itself: variations in the sail's orientation. We describe an optimal controller to control the sail onto fixed points and periodic orbits about fixed points. We find this controller to be very robust, and define sets of initial data using spherical coordinates to get a sense of the domain of controllability; we also perform a series of tests for control onto periodic orbits. We then present some mission strategies involving transfer form the Earth to fixed points and onto periodic orbits, and controlled heteroclinic transfers between fixed points on opposite sides of the Earth. Finally we present some novel methods to finding periodic orbits in circumstances where traditional methods break down, based on considerations of the Center Manifold theorem
Generating Functions and Stability Study of Multivariate Self-Excited Epidemic Processes
We present a stability study of the class of multivariate self-excited Hawkes
point processes, that can model natural and social systems, including
earthquakes, epileptic seizures and the dynamics of neuron assemblies, bursts
of exchanges in social communities, interactions between Internet bloggers,
bank network fragility and cascading of failures, national sovereign default
contagion, and so on. We present the general theory of multivariate generating
functions to derive the number of events over all generations of various types
that are triggered by a mother event of a given type. We obtain the stability
domains of various systems, as a function of the topological structure of the
mutual excitations across different event types. We find that mutual triggering
tends to provide a significant extension of the stability (or subcritical)
domain compared with the case where event types are decoupled, that is, when an
event of a given type can only trigger events of the same type.Comment: 27 pages, 8 figure
A possible phase diagram of a t-J ladder model
We investigate a t-J ladder model by numerical diagonalization method. By
calculating correlation functions and assuming the Luttinger liquid relation,
we obtained a possible phase diagram of the ground state as a function of J/t
and electron density . We also found that behavior of correlation functions
seems to consist with the prediction of Luttinger liquid relation. The result
suggests that the superconducting phase appear in the region of for high electron density and for low electron density.Comment: Latex, 10 pages, figures available upon reques
Effects of Fermi surface and superconducting gap structure in the field-rotational experiments: A possible explanation of the cusp-like singularity in YNiBC
We have studied the field-orientational dependence of zero-energy density of
states (FODOS) for a series of systems with different Fermi surface and
superconducting gap structures. Instead of phenomenological Doppler-shift
method, we use an approximate analytical solution of Eilenberger equation
together with self-consistent determination of order parameter and a
variational treatment of vortex lattice. First, we compare zero-energy density
of states (ZEDOS) when a magnetic field is applied in the nodal direction
() and in the antinodal direction (), by taking
account of the field-angle dependence of order parameter. As a result, we found
that there exists a crossover magnetic field so that for for , consistent with our previous analyses. Next, we showed that and the
shape of FODOS are determined by contribution from the small part of Fermi
surface where Fermi velocity is parallel to field-rotational plane. In
particular, we found that is lowered and FODOS has broader minima, when a
superconducting gap has point nodes, in contrast to the result of the
Doppler-shift method. We also studied the effects of in-plane anisotropy of
Fermi surface. We found that in-plane anisotropy of quasi-two dimensional Fermi
surface sometimes becomes larger than the effects of Doppler-shift and can
destroy the Doppler-shift predominant region. In particular, this tendency is
strong in a multi-band system where superconducting coherence lengths are
isotropic. Finally, we addressed the problem of cusp-like singularity in
YNiBC and present a possible explanation of this phenomenon.Comment: 13pages, 23figure
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