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Register a new userAn Observational Test of the Critical Earthquake Concept
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We test the concept that seismicity prior to a large earthquake can be understood in terms of the statistical physics of a critical phase transition. In this model, the cumulative seismic strain release increases as a power-law time-to-failure before the final event. Furthermore, the region of correlated seismicity predicted by this model is much greater than would be predicted from simple elasto-dynamic interactions. We present a systematic procedure to test for the accelerating seismicity predicted by the critical point model and to identify the region approaching criticality, based on a comparison between the observed cumulative energy (Benioff strain) release and the power-law behavior predicted by theory. This method is used to find the critical region before all earthquakes along the San Andreas system since 1950 with M 6.5. The statistical significance of our results is assessed by performing the same procedure on a large number of randomly generated synthetic catalogs. The null hypothesis, that the observed acceleration in all these earthquakes could result from spurious patterns generated by our procedure in purely random catalogs, is rejected with 99.5% confidence. An empirical relation between the logarithm of the critical region radius (R) and the magnitude of the final event (M) is found, such that log R mu 0.5 M, suggesting that the largest probable event in a given region scales with the size of the regional fault network.
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We report new tests of the critical earthquake concepts performed on rockbursts in deep South African mines. We extend the concept of an optimal time and space correlation region and test it on the eight main shocks of our catalog provided by ISSI. In a first test, we use the simplest signature of criticality in terms of a power law time-to-failure formula. Notwithstanding the fact that the search for the optimal correlation size is performed with this simple power law, we find evidence both for accelerated seismicity and for the presence of logperiodic behavior with a prefered scaling factor close to 2. We then propose a new algorithm based on a space and time smoothing procedure, which is also intended to account for the finite range and time mechanical interactions between events. This new algorithm provides a much more robust and efficient construction of the optimal correlation region, which allows us the use of the logperiodic formula directly in the search process. In this preliminary work, we have only tested the new algorithm on the largest event on the catalog. The result is of remarkable good quality with a dramatic improvement in accuracy and robustness. This confirms the potential importance of logperiodic signals. Our study opens the road for an efficient implemention of a systematic testing procedure of real-time predictions.
We propose a new test of the critical earthquake model based on the hypothesis that precursory earthquakes are ``actors that create fluctuations in the stress field which exhibit an increasing correlation length as the critical large event becomes imminent. Our approach constitutes an attempt to build a more physically-based cumulative function in the spirit of but improving on the cumulative Benioff strain used in previous works documenting the phenomenon of accelerated seismicity. Using a space and time dependent visco-elastic Green function in a two-layer model of the Earth lithosphere, we compute the spatio-temporal stress fluctuations induced by every earthquake precursor and estimate, through an appropriate wavelet transform, the contribution of each event to the correlation properties of the stress field around the location of the main shock at different scales. Our physically-based definition of the cumulative stress function adding up the contribution of stress loads by all earthquakes preceding a main shock seems to be unable to reproduce an acceleration of the cumulative stress nor an increase of the stress correlation length similar to those observed previously for the cumulative Benioff strain. Either earthquakes are ``witnesses of large scale tectonic organization and/or the triggering Green function requires much more than just visco-elastic stress transfers.
Finite systems may undergo first or second order phase transitions under not isovolumetric but isobaric condition. The `analyticity of a finite-system partition function has been argued to imply universal values for isobaric critical exponents, $alpha_{{scriptscriptstyle{P}}}$, $beta_{{scriptscriptstyle{P}}}$ and $gamma_{{scriptscriptstyle{P}}}$. Here we test this prediction by analyzing NIST REFPROP data for twenty major molecules, including $mathrm{H_{2}O, CO_{2}, O_{2}}$, etc. We report they are consistent with the prediction for temperature range, $10^{-5} <|T/T_{c}-1|<10^{-3}$. For each molecule, there appears to exist a characteristic natural number, $n=2,3,4,5,6$, which determines all the critical exponents for $T<T_{c}$ as $alpha_{{scriptscriptstyle{P}}}=gamma_{{scriptscriptstyle{P}}}=frac{n}{n+1}$ and $beta_{{scriptscriptstyle{P}}}=delta^{-1}=frac{1}{n+1}$. For the opposite $T>T_{c}$, all the fluids seem to indicate the universal value of ${n=2}$.
Thermal energy agitates all matter and its competition with ordering tendencies is one of the most fundamental organizing principles in the physical world. Thus, it is natural to enquire if an effective temperature could result when external energy input enhances agitation. Potentially this could extend the insights of statistical thermodynamics to nonequilibrium systems, but despite proposals that the effective temperature concept may apply to synthetic active matter, biological motors, granular materials and turbulent fluids, its predictive value remains unclear. Here, combining computer simulations and imaging experiments, we design a two-component system of driven Janus colloids such that collisions produced by external energy sources play the role of temperature, and in this system we demonstrate quantitative agreement with hallmarks of statistical thermodynamics for binary phase behavior: the archetypal phase diagram with equilibrium critical exponents, Gaussian displacement distributions, fluctuation-dissipation relations, and capillarity. These quantitative analogies to equilibrium expectations, observed in this decidedly nonequilibrium system, constitute an existence proof from which to compare future theories of nonequilibrium, but limitations of this concept are also highlighted.
We have experimentally checked the Jarzynski equality and the Crooks relation on the thermal fluctuations of a macroscopic mechanical oscillator in contact with a heat reservoir. We found that, independently of the time scale and amplitude of the driving force, both relations are satisfied. These results give credit, at least in the case of Gaussian fluctuations, to the use of these relations in biological and chemical systems to estimate the free energy difference between two equilibrium states. An alternative method to estimate of the free nergy difference in isothermal process is proposed too.
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