A study of non-extensivity in the Earth’s magnetosphere

Magnetic storms are undoubtedly among the most important phenomena in space physics and also a central subject of space weather. The non-extensive Tsallis entropy has been recently introduced, as an effective complexity measure for the analysis of the geomagnetic activity D _st index. Tsallis entropy has been shown to sensitively detect the complexity dissimilarity between pre-storm activity and intense magnetic storms in the Earth’s magnetosphere. Here, we show that the D _st time series obey a modified form of the Gutenberg-Richter law for the case of non-extensive statistics, thus providing evidence for universality in magnetic storm and earthquake occurrence.     

Study of solar features causing GMSs with 250γ<<Emphasis Type="Italic">H</Emphasis><400γ

The effect of solar features on geospheric conditions leading to geomagnetic storms (GMSs) with planetary index,A ^P ≥ 20 and the range of horizontal component of the Earth’s magnetic fieldH such that 250γ <H < 400γ has been investigated using interplanetary magnetic field (IMF), solar wind plasma (SWP) and solar geophysical data (SGD) during the period 1978–99. Statistically, it is observed that maximum number of GMSs have occurred during the maximum solar activity years of 21st and 22nd solar cycles. A peculiar result has been observed during the years 1982, 1994 when sunspot numbers (SSNs) decrease very rapidly while numbers of GMSs increase. No distinct association between yearly occurrence of disturbed days and SSNs is observed. Maximum number of disturbed days have occurred during spring and rainy seasons showing a seasonal variation of disturbed days. No significant correlation between magnitude (intensity) of GMSs and importance ofH _α , X-ray solar flares has been observed. Maximum number of GMSs is associated with solar flares of lower importance, i.e., SF during the period 1978-93.H _α , X-ray solar flares occurred within lower helio-latitudes, i.e., (0–30)°N to (0–30)°S are associated with GMSs. NoH _α , X-ray solar flares have occurred beyond 40°N or 40°S in association with GMSs. In helio-latitude range (10–40)°N to (10–40)°S, the 89.5% concentration of active prominences and disappearing filaments (APDFs) are associated with GMSs. Maximum number of GMSs are associated with solar flares. Coronal mass ejections (CMEs) are related with eruptive prominences, solar flares, type IV radio burst and they occur at low helio-latitude. It is observed that CMEs related GMS events are not always associated with high speed solar wind streams (HSSWSs). In many individual events, the travel time between the explosion on the Sun and maximum activity lies between 58 and 118 h causing GMSs at the Earth.     

Applications of non-linear methods in astronomy

In this review I discuss catastrophes, bifurcations and strange attractors in a non-mathematical manner by giving very simple examples that st ill contain the essence of the phenomenon. The salientresults of the applications of these non-linear methods in astrophysics are reviewed and include such diverse phenomena as solar flares and loop brightenings (catastrophes), formation of binaries and cyclic stellar winds (bifurcations) and the solar cycle and galactic dynamics (strange attractors). Emphasis is laid on the unifying concept of non-linearity in (simple) differential equatio ns that can be the framework for understanding and predicting such diverse phenomena as mentioned above. Finally there is a discussion on the concept of intrinsic unpredictability (as a result on non-linearity), the limit it sets to the use of numerical models and the way it contradicts our intuiti ve notions on deterministic systems.     

Ionospheric effects of geomagnetic storms at mid latitudes

Previously, we studied the ionospheric effects of the sequence of geomagnetic storms on September 9–14, 2005 using a global self-consistent model “Thermosphere-Ionosphere-Protonosphere” (GSM TIP). Differences between the predicted and observed effects of the ionospheric storms may be due to the use of the three-hour K _p index of geomagnetic activity in modeling the time dependence of model input parameters, use of the dipole approximation of the geomagnetic field, and disregard in simulations for solar flares that occurred during this period. We tried to eliminate two of these three reasons. First, we used the A _E index of geomagnetic activity with minute resolution in modeling the time dependence of the model input parameters. Second, we took into account the effects of solar flares. In addition, GSM TIP model was supplemented by an empirical model describing the precipitation of high-energy electrons. The results of the simulation of the behavior of various ionospheric parameters over the Yakutsk, Irkutsk, Millstone Hill, and Arecibo stations on September 9 and 10, 2005 in the new formulation of the problem, presented in the current work, are in better agreement with the available experimental data than the results of previous calculations.     

Tsallis non-extensive statistics,intermittent turbulence,SOC and chaos in the solar plasma. Part two: Solar flares dynamics

In this study which is the continuation of the first part (Pavlos et al. 2012) [1], the nonlinear analysis of the solar flares index is embedded in the non-extensive statistical theory of Tsallis (1988) [3]. The q$q$-triplet of Tsallis, as well as the correlation dimension and the Lyapunov exponent spectrum were estimated for the singular value decomposition (SVD) components of the solar flares timeseries. Also the multifractal scaling exponent spectrum f(a)$f\left(a\right)$, the generalized Renyi dimension spectrum D(q)$D\left(q\right)$ and the spectrum J(p)$J\left(p\right)$ of the structure function exponents were estimated experimentally and theoretically by using theq$q$-entropy principle included in Tsallis non-extensive statistical theory, following Arimitsu and Arimitsu (2000) [25]. Our analysis showed clearly the following: (a) a phase transition process in the solar flare dynamics from a high dimensional non-Gaussian self-organized critical (SOC) state to a low dimensional also non-Gaussian chaotic state, (b) strong intermittent solar corona turbulence and an anomalous (multifractal) diffusion solar corona process, which is strengthened as the solar corona dynamics makes a phase transition to low dimensional chaos, (c) faithful agreement of Tsallis non-equilibrium statistical theory with the experimental estimations of the functions: (i) non-Gaussian probability distribution function P(x)$P\left(x\right)$, (ii) f(a)$f\left(a\right)$ and D(q)$D\left(q\right)$, and (iii) J(p)$J\left(p\right)$ for the solar flares timeseries and its underlying non-equilibrium solar dynamics, and (d) the solar flare dynamical profile is revealed similar to the dynamical profile of the solar corona zone as far as the phase transition process from self-organized criticality (SOC) to chaos state. However the solar low corona (solar flare) dynamical characteristics can be clearly discriminated from the dynamical characteristics of the solar convection zone.     

Effect of the electromagnetic field of an eruptive prominence on coronal and chromospheric plasmas (CME and Hα emission formation)

The frozen- in chromospheric and coronal plasma motions during an eruption of a filament with a magnetic field configuration described by the inverse polarity model are considered. At the initial stage of the filament motion the magnetic field compresses the chromospheric gas within two strips located symmetrically about the inversion line. The compression is accompanied by plasma heating and emission enhancement in the lineH _α. The distance between the strips increases with filament altitude above the photosphere. This mechanism is sufficient to describe the dynamics ofH _α emission kernels in two- ribbon flares. In the corona region in which the magnetic pressure of the filament field is greater than the gas pressure, plasma rarefaction and cavity formation occur. Near the boundary β=1the plasma is decelerated and its density increases, which corresponds to the formation of an outer shell of the CME.     

Heat-transfer mechanisms in solar flares. 1: Classical and anomalous heat conduction

In the context of the problem of energy transport in solar flares, simplified analytical models have been developed that describe plasma heating in the solar atmosphere by heat fluxes from the super-hot (T _e ≳ 10⁸ K) reconnecting current layer. It is shown that the applicability conditions of common heat conduction produced by Coulomb collisions of electrons in plasma are not fulfilled in solar flares. The heat flux calculated using the classical Fourier’s law proves to be significantly higher than the real energy fluxes known from modern multi-wavelength observations of flares. The so called anomalous flux produced by interaction of free electrons with ion acoustic waves in a plasma is critically analyzed. The question of what the dominant mechanism of heat transfer in solar flares is requires additional consideration [1].     

Correct thermodynamic forces in Tsallis thermodynamics: connection with Hill nanothermodynamics

The equivalence between Tsallis thermodynamics and Hill's nanothermodynamics is established. The correct thermodynamic forces in Tsallis thermodynamics are pointed out. Through this connection we also find a general expression for the entropic index q which we illustrate with two physical examples, allowing in both cases to relate q to the underlying dynamics of the Hamiltonian systems.     

Low-frequency resonance of domain walls in the iron garnet Tb3Fe5O12 near the magnetic compensation point

The vibrational motion dynamics of domain walls (DWs) in the iron garnet Tb₃Fe₅O₁₂, a low-frequency magnetic field, and the temperature range 200–295 K (which includes the magnetic compensation point of this ferrimagnet, T _c ≈ 249 K) is studied by a magnetooptical method. The temperature dependence of the DW vibration amplitude in this garnet crystal near T _c has a resonance character. A theoretical model of the magnetic resonance of DWs is proposed to interpret the obtained experimental results; according to this model, the DW mass tends to infinity and the resonance frequency tends to zero when temperature approaches the magnetic compensation point.     

Magnetic Phase Transitions in Nanoclusters and Nanostructures

New phenomena – the first order magnetic phase transitions were observed in nanoclusters and nanostructures. For isolated ferrihydrite nanoclusters (d ～ 1–2 nm) in porous materials, for α-,γ-Fe₂O₃ nanoclusters (d ～ 20–50 nm) and for composites of nanostructured metallic Eu with additives of α-, γ-Fe₂O₃ nanoclusters and adamantane the critical temperatures (T _C, T _N) and magnetic cluster critical sizes (R _cr) were determined by means of thermodynamic models and Mössbauer spectroscopy. The first order magnetic phase transitions (jump-like) proceed by such a way when magnetization and magnetic order disappear by jump without superparamagnetic relaxation. According to thermodynamic model predictions the cluster and interface defects were suggested to play the main role in magnetic behavior. Thus, for the defective α-, γ-Fe₂O₃ nanoclusters, at R ≤ R _cr, the presence of the first order (jump-like) magnetic phase transition was described in terms of magnetic critical size of cluster. The action of high pressure (up to 2 GPa) with shear (120–240°) was effective for defect generation and nanostructure formation. For nanosystems including iron oxide nanoclusters, adamantane and metallic europium and subjected to shear stress under high pressure loading the critical value of defect density was estimated by the study of the character of magnetic phase transition. First-to-second-order (nanostructured metallic Eu) and second-to-first-order (α-, γ-ferric oxide nanoclusters) changes of the character of magnetic phase transition were shown to accompany by the variation of critical temperatures compared to the corresponding bulk values.     

The Results of Studying Nonstationary Processes on the Sun by Radioastronomical Methods

This paper presents the results of studies of solar phenomena performed at the Radiophysical Research Institute (NIRFI) in the last years and based on the data of measuring the solar microwave radiation. We obtained new results concerning fragmentation of the regions of initial energy release during solar flares, their spatial and temporal dynamics, the physical conditions in flaring loops, the dynamics of energetic particles accelerated during flares, and the characteristics of sporadic radio emission during the formation and propagation of coronal mass ejections in the lower layers of the solar atmosphere.     

Short-time dynamics of Fe2/V13 magnetic superlattice models

Critical relaxation from a low-temperature fully ordered state of Fe₂/V₁₃ iron-vanadium magnetic superlattice models has been studied using the method of short-time dynamics. Systems with three variants of the ratio R of inter-to intralayer exchange coupling have been considered. Particles with N = 262144 spins have been simulated with periodic boundary conditions. Calculations have been performed using the standard Metropolis algorithm of the Monte Carlo method. The static critical exponents of magnetization and correlation radius, as well as the dynamic critical exponent, have been calculated for three R values. It is established that a small decrease in the exchange ratio (from R = 1.0 to 0.8) does not significantly influence the character of the short-time dynamics in the models studied. A further significant decrease in this ratio (to R = 0.01), for which a transition from three-dimensional to quasi-two-dimensional magnetism is possible, leads to significant changes in the dynamic behavior of iron-vanadium magnetic superlattice models.     

Stock market and motion of a variable mass spring

We establish an analogy between the motion of spring whose mass increases linearly with time and volatile stock market dynamics within an economic model based on simple temporal demand and supply functions [E. Canessa, J. Phys. A 33 (2000) 3637]. The total system energy E_t is shown to be proportional to a decreasing time dependent spring constant k_t. This model allows to derive log-periodicity cos[log(t−t_c)] on commodity prices and oscillations (surplus and shortages) in the level of stocks. We also made an attempt to connect these results to the Tsallis statistics parameter q based on a possible force-entropy correlation [E. Canessa, Physica A 341(2004) 165] and find that the Tsallis second entropic term relates to the square of the demand (or supply) function.     

Superstring induced mass and magnetic moment of the neutrino and the time modulation of the solar neutrino flux

The new Yukawa couplings involving heavy matter E₆ fields predicted in the framework of superstring theories are considered as a source of mass and magnetic moment for the neutrino. Given the experimental bound m_ve < 46 eV bounds are derived on the neutrino magnetic moment thus generated. Finally, a scenario is produced where the induced magnetic moment has the correct magnitude (∼10⁻¹¹ μ_B) to explain an alleged depletion or solar neutrino flux during periods of maximum solar activity.     

Density operators that extremize Tsallis entropy and thermal stability effects

Quite general, analytical (both exact and approximate) forms for discrete probability distributions (PDs) that maximize Tsallis entropy for a fixed variance are here investigated. They apply, for instance, in a wide variety of scenarios in which the system is characterized by a series of discrete eigenstates of the Hamiltonian. Using these discrete PDs as “weights” leads to density operators of a rather general character. The present study allows one to vividly exhibit the effects of non-extensivity. Varying Tsallis’ non-extensivity index q one is seen to pass from unstable to stable systems and even to unphysical situations of infinite energy.     

On the possibility of determining the diffusion length of excitons in semiconductors from photomagnetic measurement data

The effect of a magnetic field on the photocurrent I_ph in Si and GaAs solar cells is investigated. It is shown that the observed change in the photocurrent I_ph of the solar cells in response to a magnetic field can be caused by a decrease in the diffusion length of excitons L_exc. A simplified model of the photomagnetic experiment is proposed to estimate the diffusion length of excitons L_exc and the contribution made by excitons to the photocurrent of the solar cells.     

Investigation of stimulated dynamics in strongly anisotropic high-temperature superconductors system Bi-Pb-Sr-Ca-Cu-O

It is used the mechanical method of Abrikosov vortex stimulated dynamics investigation in superconductors. With its help it was studied relaxation phenomena in vortex matter of high-temperature superconductors. It established that pulsed magnetic fields change the course of relaxation processes taking place in vortex matter. The study of the influence of magnetic pulses differing by their durations and amplitudes on vortex system of strongly anisotropic high-temperature superconductors system Bi_1.7Pb_0.3Sr₂Ca₂Cu₃O_10−δ showed the presence of threshold phenomena. The small duration pulses do not change the course of relaxation processes taking place in vortex matter. When the duration of pulses exceeds some critical value (threshold), then their influence changes the course of relaxation process which is revealed by stepwise change of relaxing mechanical moment τrel. These investigations showed that the time for formatting of Abrikosov vortex lattice in Bi_1.7Pb_0.3Sr₂Ca₂Cu₃O_10−δ is of the order of 150 μs which on the order of value exceeds the time necessary for formation of a single vortex observed in isotropic high-temperature superconductor HoBa₂Cu₃O_7−δ and on two orders exceeds the creation time of a single vortex observed in classical type II superconductors.     

Magnetic-field-controlled phase separation in manganites: Electron magnetic resonance study

The electron magnetic resonance spectra of Sm_1?x Sr _x MnO₃ (x = 0.30, 0.40, 0.45) manganites have been studied. At temperatures that are higher than the Curie point by several tens of kelvins, samples with x = 0.40 and 0.45 exhibit a ferromagnetic resonance (FMR) spectrum imposed on their usual EPR spectrum. The FMR spectrum appears as the applied magnetic field H exceeds a certain critical field H _c , which decreases upon cooling and becomes zero at T = T _C . These results agree with the magnetic-measurement data and indicate the magnetic-field-induced nucleation and growth of ferromagnetic domains in a paramagnetic matrix. In the initial growth stage, the volume of the ferromagnetic domains is proportional to (H ? H _c )^β, where β = 4.0 ± 0.3, and it changes in phase with magnetic field modulation up to a frequency of 100 kHz. In the same field and temperature ranges, hysteretic phenomena and narrow unstable spectral lines are detected; these lines indicate a dynamic character of the phase separation. The results obtained are interpreted in terms of the competition of different types of magnetic and charge ordering.     

Solar-neutrino variations: A manifestation of nonzero neutrino mass and magnetic moment, and mixing

Time variations of solar neutrino flux are investigated on the basis of available Homestake experimental data for more than two solar cycles (1970–1994). At first, we determine (with the weight-time function by taking into account ³⁷Ar decay), for each solar neutrino run n, the effective Earth’s heliolatitude L _eff(n), the effective Zurich sunspots number Z _eff(n), the effective latitude of sunspots distribution Λ_eff(n), and the effective surfaces of sunspots in different heliolatitude belts. Then, we consider the correlation of solar-electron-neutrino fluxes with these parameters for different periods of solar activity. It is found that correlation coefficients change sign in different periods of solar activity, so that for total period 1970–1994 the correlation coefficient is very small. The obtained information indicates that a neutrino should have nonzero mass and nonzero magnetic moment.