1,721,015 research outputs found
Testing of the foreshock hypothesis within an epidemic like description of seismicity
No full textThe epidemic type aftershock sequence (ETAS) model provides a good description of the post-seismic spatio-temporal clustering of seismicity and is also able to capture some features of the increase of seismic activity caused by foreshocks. Recent results, however, have shown that the number of foreshocks observed in instrumental catalogues is significantly much larger than the one predicted by the ETAS model. Here we show that it is possible to keep an epidemic description of post-seismic activity and, at the same time, to incorporate pre-seismic temporal clustering, related to foreshocks. Taking also into-account the short-term incompleteness of instrumental catalogues, we present a model which achieves very good description of the southern California seismicity both on the aftershock and on the foreshock side. Our results indicate that the existence of a preparatory phase anticipating main shocks represents the most plausible explanation for the occurrence of foreshocks
b-More-Incomplete and b-More-Positive: Insights on a Robust Estimator of Magnitude Distribution
No full textThe b-value in earthquake magnitude-frequency distribution quantifies the relative frequency of large versus small earthquakes. Monitoring its evolution could provide fundamental insights into temporal variations of stress on different fault patches. However, genuine b-value changes are often difficult to distinguish from artificial ones induced by temporal variations of the detection threshold. A highly innovative and effective solution to this issue has recently been proposed by van der Elst (2021, https://doi.org/10.1029/2020jb021027) by means of the b-positive estimator, which is based on analyzing only the positive differences in magnitude between successive earthquakes. Here, we demonstrate the robustness of the estimator, which remains largely unaffected by detection issues due to the properties of conditional probability. We illustrate that this robustness can be further improved by considering positive differences in magnitude, not only between successive earthquakes but also between different pairs of earthquakes. This generalized approach, defined as the "b-more-positive estimator," enhances efficiency by providing a precise estimate of the b-value while including a larger number of earthquakes from an incomplete catalog. However, our analysis reveals that the accuracy of the b estimators diminishes when earthquakes below the completeness threshold are included in the catalog. This leads to the paradoxical observation that greater efficiency is achieved when the catalog is more incomplete. To address this, we introduce the "b-more-incomplete estimator," where the b-more-positive estimator is applied only after artificially filtering the instrumental catalog to make it more incomplete. Our findings show the superior efficiency of the b-more-incomplete method
Quasideterministic dynamics, memory effects, and lack of self-averaging in the relaxation of quenched ferromagnets
No full textWe discuss the interplay between the degree of dynamical stochasticity, memory persistence, and violation of the self-averaging property in the aging kinetics of quenched ferromagnets. We show that, in general, the longest possible memory effects, which correspond to the slowest possible temporal decay of the correlation function, are accompanied by the largest possible violation of self-averaging and a quasideterministic descent into the ergodic components. This phenomenon is observed in different systems, such as the Ising model with long-range interactions, including the mean-field, and the short-range random-field Ising model
Universality in the time correlations of the long-range 1d Ising model
No full textThe equilibrium and nonequilibrium properties of ferromagnetic systems may be affected by the long-range nature of the coupling interaction. Here we study the phase separation process of a one-dimensional Ising model in the presence of a power-law decaying coupling, J(r)=1/r1+σ with σ>0, and we focus on the two-time autocorrelation function C(t,tw)=⟨si(t)si(tw)⟩. We find that it obeys the scaling form C(t,tw)=f(L(tw)/L(t)), where L(t) is the typical domain size at time t, and where f(x) can only be of two types. For σ>1, when domain walls diffuse freely, f(x) falls in the nearest-neighbour (nn) universality class. Conversely, for σ≤1, when domain walls dynamics is driven, f(x) displays a new universal behavior. In particular, the so-called Fisher-Huse exponent, which characterizes the asymptotic behavior of f(x)≃x−λ for x≫1, is λ=1 in the nn universality class (σ>1) and λ=1/2 for σ≤1
One Dimensional Phase-Ordering in the Ising Model with Space Decaying Interactions
No full textThe study of the phase ordering kinetics of the ferromagnetic one-dimensional Ising model dates back to 1963 (R. J. Glauber, J. Math. Phys. 4, 294) for non conserved order parameter (NCOP) and to 1991 (S. J. Cornell, K. Kaski and R.B. Stinchcombe, Phys. Rev. B 44, 12263) for conserved order parameter (COP). The case of long range interactions J(r) has been widely studied at equilibrium but their effect on relaxation is a much less investigated field. Here we make a detailed numerical and analytical study of both cases, NCOP and COP. Many results are valid for any positive, decreasing coupling J(r), but we focus specifically on the exponential case, Jexp(r) = e-r/R with varying R> 0 , and on the integrable power law case, Jpow(r) = 1 / r1+σ with σ> 0. We find that the asymptotic growth law L(t) is the usual algebraic one, L(t) ∼ t1/z, of the corresponding model with nearest neighbouring interaction (zNCOP= 2 and zCOP= 3) for all models except Jpow for small σ: in the non conserved case when σ≤ 1 (zNCOP= σ+ 1) and in the conserved case when σ→ 0 + (zCOP= 4 β+ 3 , where β= 1 / T is the inverse of the absolute temperature). The models with space decaying interactions also differ markedly from the ones with nearest neighbors due to the presence of many long-lasting preasymptotic regimes, such as an exponential mean-field behavior with L(t) ∼ et, a ballistic one with L(t) ∼ t, a slow (logarithmic) behavior L(t) ∼ ln t and one with L(t) ∼ t1/σ+1. All these regimes and their validity ranges have been found analytically and verified in numerical simulations. Our results show that the main effect of the conservation law is a strong slowdown of COP dynamics if interactions have an extended range. Finally, by comparing the Ising model at hand with continuum approaches based on a Ginzburg–Landau free energy, we discuss when and to which extent the latter represent a faithful description of the former
Slow relaxation in the large-N model for phase ordering
No full textThe basic features of the slow relaxation phenomenology arising in phase ordering processes are obtained analytically in the large-N model through the exact separation of the order parameter into the sum of thermal and condensation components. The aging contribution in the response function chi(ag)(t,t(w)) is found to obey a pattern of behavior, under variation of dimensionality, qualitatively similar to the one observed in Ising systems. There exists a critical dimensionality (d=4) above which chi(ag)(t,t(w)) is proportional to the defect density rho(D)(t), while for d<4 it vanishes more slowly than rho(D)(t) and at d=2 does not vanish. As in the Ising case, this behavior can be understood in terms of the dependence on dimensionality of the interplay between the defect density and the effective response associated to a single defect
Comment on "Scaling of the linear response in simple aging systems without disorder"
No full textWe have repeated the simulations of Henkel, Paessens, and Pleimling (HPP) [Phys. Rev. E 69, 056109 (2004)] for the field-cooled susceptibility chi(FC)(t)-chi(0)similar to t(-A) in the quench of ferromagnetic systems to and below T-C. We show that, contrary to the statement made by HPP, the exponent A coincides with the exponent a of the linear response function R(t,s)similar to s(-(1+a))f(R)(t/s). We point out what are the assumptions in the argument of HPP that lead them to the conclusion A < a
Correction to scaling in the response function of the two-dimensional kinetic Ising model
No full textThe aging part R-ag(t,s) of the impulsive response function of the two-dimensional ferromagnetic Ising model, quenched below the critical point, is studied numerically employing an algorithm without the imposition of the external field. We find that the simple scaling form R-ag(t,s)=s(-(1+a))f(t/s), which is usually believed to hold in the aging regime, is not obeyed. We analyze the data assuming the existence of a correction to scaling. We find a=0.273 +/- 0.006, in agreement with previous numerical results obtained from the zero field cooled magnetization. We investigate in detail also the scaling function f(t/s) and we compare the results with the predictions of analytical theories. We make an ansatz for the correction to scaling, deriving an analytical expression for R-ag(t,s). This gives a satisfactory qualitative agreement with the numerical data for R-ag(t,s) and for the integrated response functions. With the analytical model we explore the overall behavior, extrapolating beyond the time regime accessible with the simulations. We explain why the data for the zero field cooled susceptibility are not too sensitive to the existence of the correction to scaling in R-ag(t,s), making this quantity the most convenient for the study of the asymptotic scaling properties
Estimating the generation interval from the incidence rate, the optimal quarantine duration and the efficiency of fast switching periodic protocols for COVID‐19
Full text linkThe transmissibility of an infectious disease is usually quantified in terms of the reproduction
number Rt representing, at a given time, the average number of secondary cases caused by an
infected individual. Recent studies have enlightened the central role played by w(z), the distribution
of generation times z, namely the time between successive infections in a transmission chain. In
standard approaches this quantity is usually substituted by the distribution of serial intervals, which
is obtained by contact tracing after measuring the time between onset of symptoms in successive
cases. Unfortunately, this substitution can cause important biases in the estimate of Rt . Here we
present a novel method which allows us to simultaneously obtain the optimal functional form of
w(z) together with the daily evolution of Rt , over the course of an epidemic. The method uses, as
unique information, the daily series of incidence rate and thus overcomes biases present in standard
approaches. We apply our method to one year of data from COVID-19 officially reported cases in the
21 Italian regions, since the first confirmed case on February 2020. We find that w(z) has mean value
z ≃ 6 days with a standard deviation a ≃ 1 day, for all Italian regions, and these values are stable
even if one considers only the first 10 days of data recording. This indicates that an estimate of the
most relevant transmission parameters can be already available in the early stage of a pandemic. We
use this information to obtain the optimal quarantine duration and to demonstrate that, in the case
of COVID-19, post-lockdown mitigation policies, such as fast periodic switching and/or alternating
quarantine, can be very efficient
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