The paper reviews recent advances in studies of electric discharges in the stratosphere and mesosphere above thunderstorms, and their effects on the atmosphere. The primary focus is on the sprite discharge occurring in the mesosphere, which is the most commonly observed high altitude discharge by imaging cameras from the ground, but effects on the upper atmosphere by electromagnetic radiation from lightning are also considered. During the past few years, co-ordinated observations over Southern Europe have been made of a wide range of parameters related to sprites and their causative thunderstorms. Observations have been complemented by the modelling of processes ranging from the electric discharge to perturbations of trace gas concentrations in the upper atmosphere. Observations point to significant energy deposition by sprites in the neutral atmosphere as observed by infrasound waves detected at up to 1000 km distance, whereas elves and lightning have been shown significantly to affect ionization and heating of the lower ionosphere/mesosphere. Studies of the thunderstorm systems powering high altitude discharges show the important role of intracloud (IC) lightning in sprite generation as seen by the first simultaneous observations of IC activity, sprite activity and broadband, electromagnetic radiation in the VLF range. Simulations of sprite ignition suggest that, under certain conditions, energetic electrons in the runaway regime are generated in streamer discharges. Such electrons may be the source of X-and Gamma-rays observed in lightning, thunderstorms and the so-called Terrestrial Gamma-ray Flashes (TGFs) observed from space over thunderstorm regions. Model estimates of sprite perturbations to the global atmospheric electric circuit, trace gas concentrations and atmospheric dynamics suggest significant local perturbations, and possibly significant meso-scale effects, but negligible global effects.

No abstract

The adoption of the Kolmogorov-Sinai (KS) entropy is becoming a popular research tool among physicists, especially when applied to a dynamical system fitting the conditions of validity of the Pesin theorem. The study of time series that are a manifestation of system dynamics whose rules are either unknown or too complex for a mathematical treatment, is still a challenge since the KS entropy is not computable, in general, in that case. Here we present a plan of action based on the joint action of two procedures, both related to the KS entropy, but compatible with computer implementation through fast and efficient programs. The former procedure, called Compression Algorithm Sensitive To Regularity (CASToRe), establishes the amount of order by the numerical evaluation of algorithmic compressibility. The latter, called Complex Analysis of Sequences via Scaling AND Randomness Assessment (CASSANDRA), establishes the complexity degree through the numerical evaluation of the strength of an anomalous effect. This is the departure, of the diffusion process generated by the observed fluctuations, from ordinary Brownian motion. The CASSANDRA algorithm shares with CASToRe a connection with the Kolmogorov complexity. This makes both algorithms especially suitable to study the transition from dynamics to thermodynamics, and 1 the case of non-stationary time series as well. The benefit of the joint action of these two methods is proven by the analysis of artificial sequences with the same main properties as the real time series to which the joint use of these two methods will be applied in future research work.

In this letter we examine a model recently proposed to produce phase synchronization [K. Wood et al, Phys. Rev. Lett. 96, 145701 (2006)] and we show that the onset to synchronization corresponds to the emergence of an intermittent process that is non-Poisson and renewal at the same time. We argue that this makes the model appropriate for the physics of blinking quantum dots, and the dynamics of human brain as well.PACS numbers: 05.40.Fb,,82.20.Uv Phase synchronization of coupled clocks (oscillators) is a growing field of research, which is fast developing from the seminal work of Winfree [1] and Kuramoto [2]. Using the model of coupled clocks of these authors it is possible to derive [3] the Turing structure [4], which, in turn, triggered the research work in the field of diffusion reaction [5]. Physiologists are using a clock as a representation of a single neuron. In the work of Ref.[6] a neuron is a clock whose behavior is described by a chaotic attractor: the Rössler oscillator [7]. The authors of Ref.[8] and of Ref. [9] have shown that coupled stochastic clocks can show cooperative (synchronized) behavior. Brain functions, such as a cognitive act, rest on the cooperative behavior of a collection of many neurons [10]. The authors of Ref.[11] study the dynamic of the cooperation of a collection of many neurons by mapping the brain activity into a network. They find that the changes in the topology of the network describing the brain activity are driven by a non-Poisson renewal process operating in the non-ergodic regime [12]. A collection of Blinking Quantum Dots (BQDs) [13] has the same dynamical property as the brain activity. The non-Poisson non-ergodic character of the distribution of the sojourn times of the BQDs in the "light" and in the "dark" state is a well established property [13]. The renewal character of the BQDs dynamic has been established only recently [14].The similarity between the BQDs and the brain activity dynamics makes it plausible to search for a dynamic model accounting for both complex systems. In this Letter we show that a simplified version of the model of Ref.[9] affords significant suggestions on how to realize this important purpose. The authors of Ref.[9] use a system of coupled 3-state stochastic clocks, while we use a system coupled 2-state stochastic clocks. We shall prove that at the onset of phase synchronization the dynamics of the system has the same properties as the BQDs [13, 14] and brain dynamics [11]. They are non-Poisson renewal processes operating in the non-ergodic regime.We consider a Gibbs ensemble of systems with N 2-state stochastic clocks, each of them coupled to N c clocks. We denote by |1> and |2> the two states of the clock, corresponding to the phases Φ=0 and Φ=π, respectively. The master equation for a single clock of a system of the Gibbs ensemble is d dt P 1 = −g 12 P 1 + g 21 P 2 d dt P 2 = −g 21 P 2 + g 12 P 1 .(1) P 1 (P 2 ) is the probability of finding the clock in the state |1> (|2>), and g 12 (g 21 ) is the rate of transitions from the state...

We prove that the Lévy walk is characterized by bilinear scaling. This effect mirrors the existence of a form of aging that does not require the adoption of nonstationary conditions. DOI: 10.1103/PhysRevE.66.015101 PACS number͑s͒: 89.75.Da, 05.40.Fb, 05.45.Df, 05.45.Tp In the last few years Lévy flights and walks have become a popular field of investigation for physicists ͓1,2͔. They are as widely applied in nonlinear, fractal, chaotic, and turbulent systems as Brownian motion is in simpler systems. Their theoretical foundation rests on one hand on the generalized central limit theorem ͑GCLT͒ ͓3͔, and on the other hand, on the renormalization group ͑RG͒ ͓4͔ . The RG serves the purpose of explaining the physical origin for fluctuations with diverging second moment, and the GCLT proves that the diffusion process generated by these fluctuations is characterized by probability distribution functions ͑PDF͒ that are as stable as the Gaussian distributions generated by fluctuations with finite second moment. The GCLT refers to the case where the fluctuations are uncorrelated and the random walker, at regular intervals of time, makes jumps of arbitrarily large intensity. If the distribution of these jumps lengths is already stable, the resulting diffusion process is christened Lévy flight ͓1,2͔. This physical condition is judged to be unrealistic, and for this reason in the last 17 years Lévy diffusion has been studied under the form of Lévy walk ͓5-7͔, where a certain time is needed to complete each jump depending on its length, in this paper being proportional to it. Later research ͓2,8,9͔ has established that the Lévy walks are processes with memory. Here we plan to prove a further interesting property: Lévy walk is characterized by aging, reflected by the emergence of bilinear scaling, and aging is, quite surprisingly, compatible with the adoption of stationary conditions. Let us consider a sequence ͕ i ,s i ͖, with iϭ0,1, . . . ,ϱ. The numbers i are random numbers with the distribution density ͑1͒Note that we shall set Ͼ2 so as to ensure the mean time ͗͘ to exist and be finite: it is easy to prove that ͗͘ ϭT/(Ϫ2). The numbers s i have the values 1 and Ϫ1, determined by the coin tossing rule. Let us imagine two archetypal individuals, Jerry and Bob, in action to realize with this time series a diffusion process without age and with age, respectively. Both Bob and Jerry create first an infinite trajectory for the diffusion variable y(l), generated by the sequence ͕ i ,s i ͖, according to a criterion of their own choice. Note that for any sequence ͕ i ,s i ͖ there exists only one trajectory y(l). Then they consider the values that the trajectory y(t) gets at times L and Lϩt so as to create, for each L, a trajectory defined by xϭ0 at tϭ0 and x(t)ϭy(Tϩt) Ϫy(T) at tϾ0, and thus an infinite number of trajectories from the original single trajectory. Let us illustrate first the criterion adopted by Jerry to construct the trajectory y(l). The time l of Jerry is discrete, and it corresponds to the number of random drawin...

In this paper we show that both music composition and brain function, as revealed by the electroencephalogram ͑EEG͒ analysis, are renewal non-Poisson processes living in the nonergodic dominion. To reach this important conclusion we process the data with the minimum spanning tree method, so as to detect significant events, thereby building a sequence of times, which is the time series to analyze. Then we show that in both cases, EEG and music composition, these significant events are the signature of a non-Poisson renewal process. This conclusion is reached using a technique of statistical analysis recently developed by our group, the aging experiment ͑AE͒. First, we find that in both cases the distances between two consecutive events are described by nonexponential histograms, thereby proving the non-Poisson nature of these processes. The corresponding survival probabilities ⌿͑t͒ are well fitted by stretched exponentials ͓⌿͑t͒ ϰ exp (−͑␥t͒ ␣ ), with 0.5Ͻ ␣ Ͻ 1.͔ The second step rests on the adoption of AE, which shows that these are renewal processes. We show that the stretched exponential, due to its renewal character, is the emerging tip of an iceberg, whose underwater part has slow tails with an inverse power law structure with power index =1+␣. Adopting the AE procedure we find that both EEG and music composition yield Ͻ 2. On the basis of the recently discovered complexity matching effect, according to which a complex system S with S Ͻ 2 responds only to a complex driving signal P with P ഛ S , we conclude that the results of our analysis may explain the influence of music on the human brain.

We study the random growth of surfaces from within the perspective of a single column, namely, the fluctuation of the column height around the mean value, y͑t͒ϵh͑t͒ − ͗h͑t͒͘, which is depicted as being subordinated to a standard fluctuation-dissipation process with friction ␥. We argue that the main properties of Kardar-Parisi-Zhang theory, in one dimension, are derived by identifying the distribution of return times to y͑0͒ = 0, which is a truncated inverse power law, with the distribution of subordination times. The agreement of the theoretical prediction with the numerical treatment of the ͑1+1͒-dimensional model of ballistic deposition is remarkably good, in spite of the finite-size effects affecting this model. is an example of self-organization: As pointed out by Family [7], a growing surface spontaneously evolving into a steady state with universal fractal properties is similar to the mechanism of self-organized criticality [8]. The columns of the material growing due to the deposition of particles can be thought of as the individuals of a society. The joint action of the randomness driving the particle deposition and the interaction among columns results in the emergence of anomalous scaling coefficients, which can be interpreted as the signature of cooperation. However, only a little attention has been devoted so far to studying the dynamics of the single individuals of this society, namely, the single growing columns of the sample under study. Usually the authors of this field of research study the correlation among distinct columns [9] without paying attention to the dynamics of an individual. Yet, a single column is expected to carry information about cooperation.The single column perspective was recently adopted by Merikoski et al.[10] to study combustion fronts in paper. The individual property under observation iswhere h͑t͒ denotes the height of a single column at time t and ͗h͑t͒͘ the average over the heights of the columns of the whole sample. The authors of Ref.[10] record the times at which the variable y͑t͒ changes sign and builds up the corresponding time series t i so as to create the new time series The coefficient ␤ refers to the interface growth prior to saturation, a physical condition where the standard deviation of all L columns, the interface widthgrows as w͑L , t͒ ϰ t ␤ . Equation (2) establishes a connection between a single column property, D , and a collective property, ␤, thereby playing an important role for the perspective adopted in this paper. The theoretical foundation for this important relation is given in earlier papers [11][12][13][14] and has been more recently discussed by Majumdar [15].In this paper we prove that the KPZ condition emerges from the identification of D ͑͒ with the distribution function S ͑͒, the essential ingredient of the subordination theory [16][17][18] stemming from the original work of Montroll and Weiss [19]. In the subdiffusion case, anomalous diffusion is derived from the ordinary diffusion process by assuming that the time distance between on...

We address the study of sporadic randomness by means of the Manneville map. We point out that the Manneville map is the generator of fluctuations yielding the Lévy processes, and that these processes are currently regarded by some authors as statistical manifestations of a nonextensive form of thermodynamics. For this reason we study the sensitivity to initial conditions with the help of a nonextensive form of the Lyapunov coefficient. The purpose of this research is twofold. The former is to assess whether a finite diffusion coefficient might emerge from the nonextensive approach. This property, at first sight, seems to be plausible in the nonstationary case, where conventional Kolmogorov-Sinai analysis predicts a vanishing Lyapunov coefficient. The latter purpose is to confirm or reject conjectures about the nonextensive nature of Lévy processes. We find that the adoption of a nonextensive approach does not serve any predictive purpose: It does not even signal a transition from a stationary to a nonstationary regime. These conclusions are reached by means of both numerical and analytical calculations that shed light on why the Lévy processes do not imply any need to depart from the adoption of traditional complexity measures.