Deterministic dynamics of the magnetosphere: results of the 0–1 test

A test for deterministic dynamics in a time series data, namely the 0–1 test (Gottawald and Melbourne, 2004, 2005), is used to study the magnetospheric dynamics. The data, corresponding to the same time period, of the auroral electrojet index <i>AL</i> and the magnetic field component <i>B<sub>z</sub></i> of the solar wind magnetic field measured at 1 AU are used to compute the parameter <i>K</i>, which is zero for non-chaotic and unity for chaotic systems. For the magnetosphere and also for the turbulent solar wind, <i>K</i> has values corresponding to a nonlinear dynamical system with chaotic behaviour. This result is consistent with the Lyapunov exponents computed from the same time series data

Magnetospheric Multiscale Mission:Cross-scale Exploration of Complexity in the Magnetosphere

The physical processes in the magnetosphere span a wide range of space and time scales and due to the strong cross-scale coupling among them the fundamental processes at the smallest scales are critical to the large scale processes. For example, many key features of magnetic reconnection and particle acceleration are initiated at the smallest scales, typically the ion gyro-radii, and then couples to meso-scale and macro-scale processes, such as plasmoid formation. The Magnetospheric Muliscale (MMS) mission is a multi spacecraft mission dedicated to the study of plasma physics at the smallest scales and their cross-scale coupling to global processes. Driven by the turbulent solar wind, the magnetosphere is far from equilibrium and exhibits complex behavior over many scales. The processes underlying the multi-scale and intermittent features in the magnetosphere are fundamental to sun-earth connection. Recent results from the four spacecraft Cluster and earlier missions have provided new insights into magnetospheric physics and will form the basis for comprehensive studies of the multi-dimensional properties of the plasma processes and their inter-relationships. MMS mission will focus on the boundary layers connecting the magnetospheric regions and provide detailed spatio-temporal data of processes such as magnetic reconnection, thin current sheets, turbulence and particle acceleration. The cross-scale exploration by MMS mission will target the microphysics that will enable the discovery of the chain of processes underlying sun-earth connection.National Science Foundation: ATM-0119196, ATM-0318629, DMS-0417800 National Aeronautics and Space Administration: NNG04E37

Brief Communication: Breeding vectors in the phase space reconstructed from time series data

Bred vectors characterize the nonlinear instability of dynamical systems and so far have been computed only for systems with known evolution equations. In this article, bred vectors are computed from a single time series data using time-delay embedding, with a new technique, nearest-neighbor breeding. Since the dynamical properties of the standard and nearest-neighbor breeding are shown to be similar, this provides a new and novel way to model and predict sudden transitions in systems represented by time series data alone

Data driven approach to study the transition from dispersive to dissipative systems through dimensionality reduction techniques

Complexity is often exhibited in dynamical systems, where certain parameters evolve with time in a strange and chaotic nature. These systems lack predictability and are common in the physical world. Dissipative systems are one of such systems where the volume of the phase space contracts with time. On the other hand, we employ dimensionality reduction techniques to study complicated and complex data, which are tough to analyse. The Principal Component Analysis (PCA) is a dimensionality reduction technique used as a means to study complex data. Through PCA, we studied the reduced dimensional features of the numerical data generated by a nonlinear partial differential equation called the Korteweg de Vries (KdV) equation, which is a nonlinear dispersive system, where solitary waves travel along a specific direction with finite amplitude. Dissipative nature, specific to that of the Lorenz system, were observed in the dimensionally reduced data, which implies a transition from a dispersive system to a dissipative system

Nonequilibrium Phenomena in the Magnetosphere: Phase Transition, Self-organized Criticality and Turbulence

The magnetosphere is a large scale natural system powered by the solar wind that exhibits many nonequilibrium phenomena. A wide range of these phenomena are driven directly by the solar wind or arise from the storage-release processes internal to the magnetosphere. Under the influnce by the turbulent solar wind, the magnetosphere during geomagnetically active periods is far from equilibrium and storms and substorms are essentially non-equilibrium phenomena. In spite of the distributed nature of the physical processes and the apparent irregular behavior, there is a remarkable coherence in the magnetospheric response during substorms and the entire magnetosphere behaves as a global dynamical system. Alongwith the global features, the magnetosphere exhibits many multi-scale and intermittent characteristics. These features of the magnetosphere have been studied in terms of phase transitions, self-organized criticality and turbulence. In the phase transition scenario the global features are modeled as first-order transitions and the multi-scale behavior is interpreted as a manifestation of the scale-free nature of criticality in second order phase transitions. In the self-organized criticality framework substorms are considered as avalanches in the system when criticality is reached. Many features of the magnetosphere, in particular the power law dependence of scale sizes, can be viewed as a feature of a turbulent system.The common theme underlying these approaches is the recognition that the nonequilibrium phenomena in the magnetosphere could be understood in terms of processes generic to such systems. In many cases the power-law behavior of the magnetosphere seen in many observations is the starting point for these studies. This chapter is an overview of the recent understanding achieved using these different approaches, and identifies the common issues and differences.National Science Foundation: ATM-0119196, ATM-0318629, DMS-0417800 National Aeronautics and Space Administration: NNG04E37

Realization of SOC behavior in a dc glow discharge plasma

Experimental observations consistent with Self Organized Criticality (SOC) have been obtained in the electrostatic floating potential fluctuations of a dc glow discharge plasma. Power spectrum exhibits a power law which is compatible with the requirement for SOC systems. Also the estimated value of the Hurst exponent (self similarity parameter), H being greater than 0.5, along with an algebraic decay of the autocorrelation function, indicate the presence of temporal long-range correlations, as may be expected from SOC dynamics. This type of observations in our opinion has been reported for the first time in a glow discharge system.Comment: Key Words: Glow discharge; Self Organized Criticality; Hurst exponent; R/S technique; Power spectrum; Autocorrelation function; Nongaussian probability distribution function. Phys Lett A (article in Press

Ensemble Oscillation Correction (EnOC): leveraging oscillatory modes to improve forecasts of chaotic systems

Oscillatory modes of the climate system are among its most predictable features, especially at intraseasonal time scales. These oscillations can be predicted well with data-driven methods, often with better skill than dynamical models. However, since the oscillations only represent a portion of the total variance, a method for beneficially combining oscillation forecasts with dynamical forecasts of the full system was not previously known. We introduce Ensemble Oscillation Correction (EnOC), a general method to correct oscillatory modes in ensemble forecasts from dynamical models. We compute the ensemble mean—or the ensemble probability distribution—with only the best ensemble members, as determined by their discrepancy from a data-driven forecast of the oscillatory modes. We also present an alternate method that uses ensemble data assimilation to combine the oscillation forecasts with an ensemble of dynamical forecasts of the system (EnOC-DA). The oscillatory modes are extracted with a time series analysis method called multichannel singular spectrum analysis (M-SSA), and forecast using an analog method. We test these two methods using chaotic toy models with significant oscillatory components and show that they robustly reduce error compared to the uncorrected ensemble. We discuss the applications of this method to improve prediction of monsoons as well as other parts of the climate system. We also discuss possible extensions of the method to other data-driven forecasts, including machine learning

Nonequilibrium Phenomena in Plasmas

The complexity of plasmas arises mainly from their inherent nonlinearity and far from equilibrium nature. The nonequilibrium behavior of plasmas is evident in the natural settings, for example, in the Earth's magnetosphere. Similarly, laboratory plasmas such as fusion bottles also have their fair share of complex behavior. Nonequilibrium phenomena are intimately connected with statistical dynamics and form one of the growing research areas in modern nonlinear physics. These studies encompass the ideas of self-organization, phase transition, critical phenomena, self-organized criticality and turbulence. This book presents studies of complexity in the context of nonequilibrium phenomena using theory, modeling, simulations, and experiments, both in the laboratory and in nature

Non-local theory of the resistive hose instability of beams with the Bennett profile

The resistive hose instability of nonrelativistic counter-streaming electron and ion beams propagating through a background plasma with finite conductivity is analyzed by a non-local kinetic theory. The beam as well as the plasma have the Bennett profile and the dominant orbit of the beam particles is taken to be betatron orbits. The eigenmodes are expressed in terms of the zeroes of a Bessel function, and the non-local effects are taken into account by this integral formulation of the stability analysis. In general the eigenvalues of the resistive hose mode are numerically computed from a matrix dispersion relation. A reduced dispersion relation is derived from the general case and this may be solved analytically in the long wavelength limit. The new physical effect considered in this paper is the Landau damping due to the spread in the axial velocity. Thi effect has significant stabilizing influence on the hose eigenmode