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Here we suggest a new procedure through which one can identify when the accumulation of stresses before major earthquakes (EQs) (of magnitude M 8.2 or larger) occurs. By analyzing the seismicity in the frame of natural time, which is a new concept of time introduced in 2001, we study the evolution of the fluctuations of the entropy change of seismicity under time reversal for various scales of different length i (number of events). We find that anomalous intersections between scales of different lengths i are observed upon approaching an extraordinary major EQ occurrence. The investigation is presented for the seismicity in Japan since 1984 including the M9 Tohoku EQ on 11 March 2011, which is the largest EQ ever recorded there., Comment: 6 pages, 5 figures

By applying natural time analysis to the time series of earthquakes, we find that the order parameter of seismicity exhibits a unique change approximately at the date(s) at which Seismic Electric Signals (SES) activities have been reported to initiate. In particular, we show that the fluctuations of the order parameter of seismicity in Japan exhibits a clearly detectable minimum approximately at the time of the initiation of the SES activity observed almost two months before the onset of the Volcanic-seismic swarm activity in 2000 in the Izu Island region, Japan. To the best of our knowledge, this is the first time that, well before the occurrence of major earthquakes, anomalous changes are found to appear almost simultaneously in two independent datasets of different geophysical observables (geoelectrical measurements, seismicity). In addition, we show that these two phenomena are also linked closely in space., Comment: 18 pages, 8 figures, 1 table

A characteristic change of seismicity has been recently uncovered when the precursory Seismic Electric Signals activities initiate before an earthquake occurrence. In particular, the fluctuations of the order parameter of seismicity exhibit a simultaneous distinct minimum upon analyzing the seismic catalogue in a new time domain termed natural time and employing a sliding natural time window comprising a number of events that would occur in a few months. Here, we focus on the minima preceding all earthquakes of magnitude 8 (and 9) class that occurred in Japanese area from 1 January 1984 to 11 March 2011 (the day of the M9 Tohoku earthquake). By applying Detrended Fluctuation Analysis to the earthquake magnitude time series, we find that each of these minima is preceded as well as followed by characteristic changes of temporal correlations between earthquake magnitudes. In particular, we identify the following three main features. The minima are observed during periods when long range correlations have been developed, but they are preceded by a stage in which an evident anti-correlated behavior appears. After the minima, the long range correlations break down to an almost random behavior turning to anti-correlation. The minima that precede M$\geq$7.8 earthquakes are distinguished from other minima which are either non-precursory or followed by smaller earthquakes., Comment: 21 pages, 8 figures, 5 tables

The bulk moduli of PbS$_{x}$Se$_{1-x}$, PbS$_{x}$Te$_{1-x}$, and PbSe$_{x}$Te$_{1-x}$ have been recently determined [E. Skordas, Materials Science in Semiconductor Processing 43 (2016) 65-68] by employing a thermodynamical model, the so called $cB\Omega$ model, which has been found to give successful results in several applications of defects in solids. Here, we suggest an alternative procedure for this determination which combines the $cB\Omega$ model with the modified Born theory. The results are in satisfactory agreement with those deduced independently by the generalized gradient approximation approach., Comment: 11 pages, 1 figure

Since its introduction in 2001, natural time analysis has been applied to diverse fields with remarkable results. Its validity has not been doubted by any publication to date. Here, we indicate that frequently asked questions on the motivation and the foundation of natural time analysis are directly answered if one takes into account the following two key points that we have considered as widely accepted when natural time analysis was proposed: First, the aspects on the energy of a system forwarded by Max Planck in his Treatise on Thermodynamics. Second, the theorem on the characteristic functions of probability distributions which Gauss called Ein Sch\"ones Theorem der Wahrscheinlichkeitsrechnung (beautiful theorem of probability calculus). The case of the time series of earthquakes and of the precursory Seismic Electric Signals are discussed as typical examples., Comment: 17 pages including 1 figure. Accepted for publication in Acta Geophysica on May 1, 2015