Abraham C.-L. Chian

Alfvén Intermittent Turbulence Driven by Temporal Chaos

The temporal evolution of Alfven intermittent turbulence in cosmic plasmas is studied. The chaotic dynamics of a driven-dissipative Alfven system is determined by numerically solving the derivative nonlinear Schrodinger equation in the low-dimensional limit. Two types of Alfven intermittent turbulence are identified: Pomeau-Manneville intermittency and crisis-induced intermittency. The significance of this theory for Alfvenic intermittent turbulence observed in the solar wind is discussed.

Analysis of chaotic saddles in high-dimensional dynamical systems: The Kuramoto–Sivashinsky equation

This paper presents a methodology to study the role played by nonattracting chaotic sets called chaotic saddles in chaotic transitions of high-dimensional dynamical systems. Our methodology is applied to the Kuramoto-Sivashinsky equation, a reaction-diffusion partial differential equation. The paper describes a novel technique that uses the stable manifold of a chaotic saddle to characterize the homoclinic tangency responsible for an interior crisis, a chaotic transition that results in the enlargement of a chaotic attractor. The numerical techniques explained here are important to improve the understanding of the connection between low-dimensional chaotic systems and spatiotemporal systems which exhibit temporal chaos and spatial coherence.

Detection of Current Sheets and Magnetic Reconnections at the Turbulent Leading Edge of an Interplanetary Coronal Mass Ejection

The relation between current sheets, turbulence, and magnetic reconnections at the leading edge of an interplanetary coronal mass ejection detected by four Cluster spacecraft on 2005 January 21 is studied. We report the observational evidence of two magnetically reconnected current sheets in the vicinity of a front magnetic cloud boundary layer with the following characteristics: (1) a Kolmogorov power spectrum in the inertial subrange of the magnetic turbulence, (2) the scaling exponent of structure functions of magnetic fluctuations exhibiting multi-fractal scaling predicted by the She-Leveque magnetohydrodynamic model, and (3) bifurcated current sheets with the current density computed by both single-spacecraft and multi-spacecraft techniques.

Nonlinear generation of the fundamental radiation of interplanetary type III radio bursts

A new generation mechanism of interplanetary type III radio bursts at the fundamental electron plasma frequency is discussed. It is shown that the electromagnetic oscillating two-stream instability, driven by two oppositely propagating Langmuir waves, can account for the experimental observations. In particular, the major difficulties encountered by the previously considered electromagnetic decay instability are removed. 19 references.

Nonlinear excitation of kinetic Alfvén waves and whistler waves by electron beam-driven Langmuir waves in the solar corona

We study a new nonlinear excitation mechanism of kinetic Alfven waves (KAWs) and whistler waves (Ws) by elec- tron beam-driven Langmuir waves (Ls). The generation conditions for the parametric decay instability L W+ KAW are determined and the growth rate is calculated. We show that the resonant pairs of KAWs and whistler waves are nonlinearly coupled to the pump Langmuir waves and their amplitudes undergo exponential growth from the thermal level. The perpen- dicular dispersion of KAWs strongly increases the coupling due to the nonlinear current parallel to the ambient magnetic field. Our study suggests that the nonlinear coupling of Langmuir wave energy into KAWs and whistlers can provide an ecient sink for weakly dispersive Langmuir waves excited by fast electron beams in the solar corona when the electron plasma frequency is lower than the electron gyrofrequency. This condition can be satisfied in the low-density magnetic filaments that are rooted in the depleted patches at the coronal base and extend to the high corona. At the same time, the Langmuir-driven KAWs and whistlers give rise to scattering and/or thin structures of radio emission penetrating through, or generated in these regions. Since the decay into sunward propagating KAWs is strongest, the nonlinearly driven KAWs can be easily distinguished from the waves generated at the coronal base and propagating away from the Sun. Our results may be used in the analysis of solar radio data and for remote probing of the coronal plasma, magnetic fields, and waves.

Turbulence in the interstellar medium

Turbulence is ubiquitous in the insterstellar medium and plays a major role in several processes such as the formation of dense structures and stars, the stability of molecular clouds, the amplification of magnetic fields, and the re-acceleration and diffusion of cosmic rays. De- spite its importance, interstellar turbulence, like turbulence in general, is far from being fully understood. In this review we present the basics of turbulence physics, focusing on the statistics of its structure and energy cascade. We explore the physics of compressible and incompressible turbulent flows, as well as magnetised cases. The most relevant observational techniques that provide quantitative insights into interstel- lar turbulence are also presented. We also discuss the main difficulties in developing a three-dimensional view of inter- stellar turbulence from these observations. Finally, we briefly present what the main sources of turbulence in the interstellar medium could be.

Coherent structures and the saturation of a nonlinear dynamo

Eulerian and Lagrangian tools are used to detect coherent structures in the velocity and magnetic fields of a mean-field dynamo, produced by direct numerical simulations of the three-dimensional compressible magnetohydrodynamic equations with an isotropic helical forcing and moderate Reynolds number. Two distinct stages of the dynamo are studied: the kinematic stage, where a seed magnetic field undergoes exponential growth; and the saturated regime. It is shown that the Lagrangian analysis detects structures with greater detail, in addition to providing information on the chaotic mixing properties of the flow and the magnetic fields. The traditional way of detecting Lagrangian coherent structures using finite-time Lyapunov exponents is compared with a recently developed method called function M. The latter is shown to produce clearer pictures which readily permit the identification of hyperbolic regions in the magnetic field, where chaotic transport/dispersion of magnetic field lines is highly enhanced.

DETECTION OF COHERENT STRUCTURES IN PHOTOSPHERIC TURBULENT FLOWS

We study coherent structures in solar photospheric flows in a plage in the vicinity of the active region AR 10930 using the horizontal velocity data derived from Hinode/Solar Optical Telescope magnetograms. Eulerian and Lagrangian coherent structures (LCSs) are detected by computing the Q-criterion and the finite-time Lyapunov exponents of the velocity field, respectively. Our analysis indicates that, on average, the deformation Eulerian coherent structures dominate over the vortical Eulerian coherent structures in the plage region. We demonstrate the correspondence of the network of high magnetic flux concentration to the attracting Lagrangian coherent structures (aLCSs) in the photospheric velocity based on both observations and numerical simulations. In addition, the computation of aLCS provides a measure of the local rate of contraction/expansion of the flow.

Hamiltonian chaos in two coupled three-wave parametric interactions with quadratic nonlinearity

Abstract The nonlinear dynamical behavior of parametric wave-wave interactions is studied. The temporal dynamics of the model equations describing resonant coupling of two wave triplets in quadratic nonlinear medium is analyzed. This Hamiltonian system is shown to undergo transition from regular to chaotic states via the route of quasiperiodicity. Application to nonlinear optics in plasmas is exemplified.

Crisis-induced intermittency in non-linear economic cycles

A new type of economic intermittency is found in non-linear business cycles. Following a merging crisis, a complex economic system has the ability to retain memory of its weakly chaotic dynamics prior to crisis. The resulting time series exhibits episodic regime switching between periods of weakly and strongly chaotic fluctuations of economic variables. The characteristic intermittency time, useful for forecasting the average duration of contractionary phases and the turning point to the expansionary phase of business cycles, is computed from the simulated time series.