Fracture in disordered media is a complex problem for which a definitive physical and theoretical treatment is still lacking. We view earthquakes (EQ's) as large-scale fracture phenomena in the Earth's heterogeneous crust. Our main observational tool is the monitoring of the microfractures, which occur in the prefocal area before the final breakup, by recording their kHz-MHz electromagnetic (EM) emissions, with the MHz radiation appearing earlier than the kHz. Two fundamental questions (unanswered yet) that scientists in this field ought to address are as follows. (i) Is there a way of estimating the time to global failure? (ii) Is the evolution towards global failure irreversible after the appearance of distinguishing features in the preseismic EM time series? We attempt to put forward physically powerful arguments with regard to answering these two basic questions. Our approach will be in terms of critical phase transitions in statistical physics, drawing on recently published results. We obtain two major results. First, the initial MHz part of the preseismic emission, which has anti-persistent behavior, is triggered by microfractures in the highly disordered system that surrounds the essentially homogeneous "backbone asperities" within the prefocal area and could be described in analogy with a thermal continuous phase transition. However, the analysis reveals that the system is gradually driven out of equilibrium. Considerations of the symmetry-breaking and "intermittent dynamics of critical fluctuations" method estimate the time beyond which the process generating the preseismic EM emission could continue only as a nonequilibrium instability. Second, the abrupt emergence of strong kHz emission in the tail of the precursory radiation, showing strong persistent behavior, is thought to be due to the fracture of the high-strength "backbones". The associated phase of the EQ nucleation is a nonequilibrium process without any footprint of an equilibrium thermal phase transition. The family of asperities sustains the system. Physically, the appearance of persistent properties may indicate that the process acquires a self-regulating character and to a great degree the property of irreversibility, one of the important components of predictive capability. We address the role of the order of material heterogeneity on the transition from anti-persistent to persistent behavior.

Abstract. Ultra low frequency-ULF (1 Hz or lower), kHz and MHz electromagnetic (EM) anomalies were recorded prior to the L'Aquila catastrophic earthquake (EQ) that occurred on 6 April 2009. The detected anomalies followed this temporal scheme. The question effortlessly arises as to whether the observed anomalies before the L'Aquila EQ were seismogenic or not. The main goal of this work is to provide some insight into this issue. More precisely, the main aims of this contribution are threefold: How can we recognize an EM observation as pre-seismic one? We aim, through a multidisciplinary analysis to provide some elements of a definition. How can we link an individual EM anomaly with a distinctive stage of the EQ preparation process? The present analysis is consistent with the hypothesis that the kHz EM anomalies were associated with the fracture of asperities that were distributed along the L'Aquila fault sustaining the system, while the MHz EM anomalies could be triggered by fractures in the highly disordered system that surrounded the backbone of asperities of the activated fault. How can we identify precursory symptoms in an individual EM precursor that indicate that the occurrence of the EQ is unavoidable? We clearly state that the detection of a MHz EM precursor does not mean that the occurrence of EQ is unavoidable; the Correspondence to: K. Eftaxias (ceftax@phys.uoa.gr) abrupt emergence of kHz EM emissions indicate the fracture of asperities. The observed ULF EM anomaly supports the hypothesis of a relationship between processes produced by increasing tectonic stresses in the Earth's crust and attendant EM interactions between the crust and ionosphere. We emphasize that we attempt to specify not only whether or not a single EM anomaly is pre-seismic in itself, but mainly whether a combination of emergent ULF, MHz and kHz EM anomalies could be characterized as pre-earthquake.

A theoretical scheme which relates multiparticle states generated in ultrarelativistic nuclear collisions to a QCD phase transition is considered in the framework of the universality class provided by the 3-D Ising model. Two different evolution scenarios for the QGP system are examined. The statistical mechanics of the critical state is accounted for in terms of (critical) cluster formation consistent with suitably cast effective action functionals, one for each considered type of expansion. Fractal properties associated with these clusters, characterizing the density fluctuations near the QCD critical point, are determined. Monte-Carlo simulations are employed to generate events, pertaining to the total system, which correspond to signals associated with unconventional sources of pion production

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Abstract. Precursory fracture induced electromagnetic (EM) emissions, rooted in opening cracks and ranging from MHz to kHz, with the MHz appearing earlier, are produced and detected both at laboratory and geophysical scale. Recently, we have proposed the following two epochs/stages model of EQ generation: (i) The final kHz part is triggered by the fracture of high strength and large asperities that are distributed along the activated fault and sustain the system. (ii) The initial MHz part is thought to be due to the fracture of highly heterogeneous system that surrounds the family of asperities. Interestingly, the MHz EM time-series can be described in analogy with a thermal second order phase transition. Herein we focus on the MHz pre-seismic activity, and especially on the naturally arising question: what is the physical mechanism that organizes the heterogeneous system in its critical state? Combining ideas of Levy and Tsallis statistics and criticality with features hidden in the precursory MHz time-series we argue that a Levy walk type mechanism can organize the heterogeneous system to criticality. Based on a numerically produced truncated Levy walk, we propose a way to estimate in the stage of critical fluctuations: (i) the associated Levy index-a, which describes quantitatively the underlying Levy dynamics, and (ii) the range of values where the nonextesitive Tsallis index q is restricted. We also show that the kHz EM activity could not be described by a truncated Levy mechanism. This result further indicates an abrupt sweep of the population of asperities that sustain the system.

Abstract. Ultra low frequency, kHz and MHz electromagnetic (EM) anomalies were recorded prior to the L'Aquila catastrophic earthquake that occurred on 6 April 2009. The main aims of this paper are threefold: (i) suggest a procedure for the designation of detected EM anomalies as seismogenic ones. We do not expect to be able to provide a succinct and solid definition of a pre-seismic EM emission. Instead, we aim, through a multidisciplinary analysis, to provide the elements of a definition. (ii) Link the detected MHz and kHz EM anomalies with equivalent last stages of the earthquake preparation process. (iii) Put forward physically meaningful arguments for quantifying the time to global failure and the identification of distinguishing features beyond which the evolution towards global failure becomes irreversible. We emphasize that we try to specify not only whether a single EM anomaly is pre-seismic in itself, but also whether a combination of kHz, MHz, and ULF EM anomalies can be characterized as pre-seismic. The entire procedure unfolds in two consecutive parts. Here in Part 1 we focus on the detected kHz EM anomaly, which play a crucial role in our approach to these challenges. We try to discriminate clearly this anomaly from background noise. For this purpose, we analyze the data successively in terms of various concepts of entropy and information theory including, Shannon n-block entropy, conditional entropy, entropy of the Correspondence to: K. Eftaxias (ceftax@phys.uoa.gr) source, Kolmogorov-Sinai entropy, T -entropy, approximate entropy, fractal spectral analysis, R/S analysis and detrended fluctuation analysis. We argue that this analysis reliably distinguishes the candidate kHz EM precursor from the noise: the launch of anomalies from the normal state is combined by a simultaneous appearance of a significantly higher level of organization, and persistency. This finding indicates that the process in which the anomalies are rooted is governed by a positive feedback mechanism. This mechanism induces a non-equilibrium process, i.e., a catastrophic event. This conclusion is supported by the fact that the two crucial signatures included in the kHz EM precursor are also hidden in other quite different, complex catastrophic events as predicted by the theory of complex systems. However, our view is that such an analysis by itself cannot establish a kHz EM anomaly as a precursor. It likely offers necessary but not sufficient criteria in order to recognize an anomaly as preseismic. In Part 2 we aim to provide sufficient criteria: the fracture process is characterized by fundamental universally valid scaling relationships which should be reflected in a real fracto-electromagnetic activity. Moreover, we aim to answer the following two key questions: (i) How can we link an individual EM precursor with a distinctive stage of the EQ preparation process; and (ii) How can we identify precursory symptoms in EM observations that indicate that the occurrence of the EQ is unavoidable.

Abstract. Many aspects of earthquake generation still escape our full understanding. Observations of electromagnetic emissions preceding significant earthquakes provide one of the few cases of premonitory events that are possibly related to a subsequent earthquake. Understanding the factors that control electromagnetic precursors generation seems to be important for determining how significant earthquakes nucleate. Here we report the results of a comprehensive study of the appearance of individual patterns in candidate electromagnetic precursors possibly indicating the breaking of backbone of large and strong asperities that sustain the activated fault. The search of precursory patterns is mainly based on well documented scaling properties of fault surface topology. More precisely, we argue that the candidate electromagnetic precursors might be originated during the slipping of two rough and rigid fractional-Brownian-motion-type profiles one over the other, with a roughness which is consistent with field and laboratory studies. The results also imply that the activation of a single earthquake (fault) is a reduced selfaffine image of the whole regional seismicity and a magnified self-affine image of the laboratory seismicity.

A detailed study of correlated scalars, produced in collisions of nuclei and associated with the σ-field fluctuations, (δσ) 2 =< σ 2 >, at the QCD critical point (critical fluctuations), is performed on the basis of a critical event generator (Critical Monte-Carlo) developed in our previous work.The aim of this analysis is to reveal suitable observables of critical QCD in the multiparticle environment of simulated events and select appropriate signatures of the critical point, associated with new and strong effects in nuclear collisions.The existence of a critical point in the phase diagram of QCD, for nonzero baryonic density, is of fundamental significance for our understanding of strong interactions and so its experimental verification has become an issue of high priority [1]. For this purpose an extensive programme of event-by-event searches for critical fluctuations in the pion sector is in progress in experiments with heavy ions from SPS to RHIC energies [2]. In [3] we have emphasized, however, that in order to reveal critical density fluctuations in multiparticle environment, one has to look for unconventional properties in the momentum distribution of reconstructed dipions (π + π − -pairs) [9] with invariant mass just above the two-pion threshold.In fact, the QCD critical point, if it exists, communicates with a zero mass scalar field (σfield) which at lower temperatures (T < T c ) may reach the two-pion threshold and decay in very short time scales owing to the fact that its coupling to the two-pion system is strong. Obviously, the fundamental, underlying pattern of σ-field fluctuations, built-up near the critical point by the universal critical exponents of QCD [3], is phenomenologically within reach if and only if the study of correlated sigmas, reconstructed near the two-pion threshold, becomes feasible. In the present work we perform a detailed feasibility study of the observables related to the detection of the QCD critical point in nuclear collisions. In