Jouni Takalo

Self-organized criticality in the substorm phenomenon and its relation to localized reconnection in the magnetospheric plasma sheet

Evidence is presented that suggests that there is a significant self-organized criticality (SOC) component in the dynamics of substorms in the magnetosphere. We assume that observations of bursty bulk flows, fast flows, localized dipolarizations, plasma turbulence, etc. show that multiple localized reconnection sites provide the basic avalanche phenomenon in the establishment of SOC in the plasma sheet. First results are presented from a study of this avalanche process based on this working assumption. A magnetic field reversal model is discussed. Resistivity, in this model, is self-consistently generated in response to the excitation of an idealized currentdriven instability. When forced by convection of magnetic flux into the field reversal region, the model yields rapid magnetic field annihilation through a dynamic behavior that is shown to exhibit many of the characteristics of SOC. Over a large range of forcing strengths, the annihilation rate is shown to self-adjust to balance the rate at which flux is convected into the reversal region. Several analogies to magnetotail dynamics are discussed: (1) It is shown that the presence of a localized criticality in the model produces a remarkable stability in the global configuration of the field reversal while simultaneously exciting extraordinarily dynamic internal evolution. (2) Under steady forcing it is shown that a loading-unloading cycle may arise that, as a consequence of the global stability, is quasi-periodic and, therefore, predictable despite the presence of internal turbulence in the field distribution. Indeed, it is shown that the global loading-unloading cycle is a consequence of the internal turbulence. (3) It is shown that under steady, strong forcing the loading-unloading cycle vanishes. Instead, a recovery from a single unloading persists indefinitely. The field reversal is globally very steady while internally it is very dynamic as field annihilation goes on at the rate necessary to match the strong forcing. From this result we speculate that steady magnetospheric convection events result when the plasma sheet has been driven close to criticality over an extended spatial domain. During these events we would expect to find localized reconnection sites distributed over the spatial domain of near criticality, and we would expect to find plasma sheet transport in that domain to be closely related to that of BBF and fast flow events.

Correlation dimension and affinity of AE data and bicolored noise

This paper is concerned with the general question of the dynamics of the magnetosphere. In general, to solve the dynamics of the magnetosphere one has to solve magnetohydrodynamic equations with some appropriate set of boundary conditions. This results in a very complex solution, which gives indications of being chaotic. The question of the chaotic nature of the magnetospheric dynamics has been addressed by various authors by looking at the correlation dimension of the auroral electrojet index. There has been disagreement on the outcome of such experiments, so the authors report on a detailed analysis of the auroral electrojet index time series. They find a correlation dimension of 3.4. For comparison they have generated a bicolored noise signal, and show that it shares many of the characteristics of the auroral electrojet data. They also find that the auroral electrojet time series is self-affine in nature.

Nonlinear energy dissipation in a cellular automaton magnetotail field model

A magnetic field model of the magnetotail current sheet based on cellular automaton (CA) is presented. The present isotropic model is a continuously driven, two-dimensional running CA. The model has a physical interpretation in terms of magnetohydrodynamic (MHD) equations, and features self-organized critical (SOC) behavior with power-law scalings both in durations and sizes of instabilities (avalanches). The model has nonlinear energy dissipation, and shows avalanches with and without an external trigger. Thus the model reproduces some of the statistical features recently observed in the magnetotail.

Characteristic time scale of auroral electrojet data

The structure function of the AE time series shows that the AE time series is self-affine such that the scaling exponent changes at the time scale of approximately 113 (±9) minutes. Autocorrelation function is shown to have scaling properties similar to those of the structure function. From this result it can be deduced that the time scale at which the scaling properties of the AE data change should equal the typical autocorrelation time of these data. We find the typical autocorrelation time of the AE data is 118 (±9) minutes. The characteristic time scale of the AE data appears as a spectral break in their power spectrum at a period of about twice the autocorrelation time.

Comparison of the dynamics of the AU and PC indices

The properties of AU and PC data were analyzed with different methods. It is shown that the dynamical behavior of the AU and PC time series, as analyzed by the structure function (SF), are very similar, while the SF of the AL time series shows different behavior. The SF of the AL data has a slope of 0.5 up to about 2 hours, after which it quickly decreases to about 0.1. On the other hand the slope of the SFs of AU and PC data continuously decreases to about 0.2, and in a longer time scale. It is suggested that the dissipative auroral electrojet currents have a characteristic time scale of 2 hours, and this underlies the AL dynamics. In contrast with this, the nondissipative Hall currents that most influence the AU and PC dynamics, do not seem to have a distinct characteristic time scale. However, the cross-correlation between the PC and AL indices is higher than that of the PC and AU indices, especially during wintertime. This is argued to result from the polar cap currents being more interconnected with the westward electrojets than with the eastward electrojets, in spite of the difference in their dynamic behaviors.

Neural network prediction of AE data

Neural network (NN) models were constructed to study prediction of the AE index. Both solar wind (vBz) and previous observed AE inputs were used to predict AE data for different numbers of time steps ahead. It seems that prediction of the original unsmoothed AE data is possible only for 10 time steps (25 min) ahead. The predicted time series of the AE data for 50 time steps (125 min) ahead was found to be dynamically different from the original time series. It is possible that the NN model cannot reproduce the turbulent part of the power spectrum of the AE data. However, when using smoothed AE data the prediction for 10 time steps ahead gave an NMSE of 0.0438, and a correlation coefficient of 0.98. The predictive ability of the model gradually decreased as the lead time of the predictions was increased, but was quite good up to predictions for 30 time steps (75 min) ahead.

Structure function as a tool in AE and Dst time series analysis

A new method to analyse the structure function (SF) has been constructed and used in the analysis of the AE time series for the years 1978-85 and Dst time series for 1957-84. It is shown that this SF analysis makes a clear distinction between affine and periodicity dominated time series, and it displays the essential periodicities of the series in a range relevant to its characteristic time scale. The AE time series is found to be affine such that the scaling exponent changes at a time scale of 113 (±9) minutes. On the other hand, in the SF function analysis, the Dst data are dominated by the 24-hour and 27-day periods. The 27-day period is modulated by the annual variation.

A coupled‐map model for the magnetotail current sheet

A magnetic field model of the magnetotail current sheet in the form of a coupled-map lattice (CML) is presented. It is a continuously driven and based on the MHD diffusion equation. Solar wind vBs data (solar wind speed multiplied by the southward component of IMF) are used for driving the model, and it is shown to exhibit perturbations (avalanches) with power-law scalings in their distributions of duration and size. Such distributions may indicate self-organized critical (SOC) behavior. Furthermore, it is shown that the power spectra of the model outputs are of bicolor power-law form with different slopes for high and low frequencies. The model parameters determine the frequency of the break points of the spectra, and the slopes of their low and high frequency regimes.

Using the fibre structure of paper to determine authenticity of the documents: Analysis of transmitted light images of stamps and banknotes

A novel method is presented for distinguishing postal stamp forgeries and counterfeit banknotes from genuine samples. The method is based on analyzing differences in paper fibre networks. The main tool is a curvelet-based algorithm for measuring overall fibre orientation distribution and quantifying anisotropy. Using a couple of more appropriate parameters makes it possible to distinguish forgeries from genuine originals as concentrated point clouds in two- or three-dimensional parameter space.

Curvelet-based method for orientation estimation of particles from optical images

Abstract. A method based on the curvelet transform is introduced to estimate the orientation distribution from two-dimensional images of small anisotropic particles. Orientation of fibers in paper is considered as a particular application of the method. Theoretical aspects of the suitability of this method are discussed and its efficiency is demonstrated with simulated and real images of fibrous systems. Comparison is made with two traditionally used methods of orientation analysis, and the new curvelet-based method is shown to perform better than these traditional methods.