Identifying nonlinear wave interactions in plasmas using two-point measurements: a case study of Short Large Amplitude Magnetic Structures (SLAMS)

A framework is described for estimating Linear growth rates and spectral energy transfers in turbulent wave-fields using two-point measurements. This approach, which is based on Volterra series, is applied to dual satellite data gathered in the vicinity of the Earth's bow shock, where Short Large Amplitude Magnetic Structures (SLAMS) supposedly play a leading role. The analysis attests the dynamic evolution of the SLAMS and reveals an energy cascade toward high-frequency waves.Comment: 26 pages, 13 figure

Tomographic inversion using ℓ1\ell_1-norm regularization of wavelet coefficients

We propose the use of $\ell_1$ regularization in a wavelet basis for the solution of linearized seismic tomography problems $Am=d$, allowing for the possibility of sharp discontinuities superimposed on a smoothly varying background. An iterative method is used to find a sparse solution $m$ that contains no more fine-scale structure than is necessary to fit the data $d$ to within its assigned errors.Comment: 19 pages, 14 figures. Submitted to GJI July 2006. This preprint does not use GJI style files (which gives wrong received/accepted dates). Corrected typ

Theory and application of time-frequency analysis to transient phenomena in electric power and other physical systems

textThis dissertation provides a new theoretical scheme of signal processing: cross time-frequency analysis. The proposed cross time-frequency analysis is applied to various types of real-world signals and systems in order to verify the feasibility and applicability of the proposed theory. The application of time-frequency analysis is focused on electric power and other physical systems. Unfortunately, classical Fourier-based methodologies and power quality indices are not directly applicable for the assessment and localization of transient power quality phenomena. Hence, in this dissertation, application of time-frequency analysis is discussed for the assessment and localization of transient power quality events. Through the use of joint time and frequency localized “energy” distributions, a set of time-frequency based transient power quality indices are presented and applied to real-world disturbance signals. Also, a solution for the spatial localization of transient disturbances is presented. It rests upon calculating a time and frequency localized “phase difference” via cross time-frequency analysis. By evaluating the phase difference of voltage and current at the time and frequency of interest and at different spatial points, one can identify the direction of transient disturbance energy flow in order to pinpoint the location of the transient disturbance source. In addition, applications of time-frequency theory have been extended to various types of real-world physical signals and systems. A new reflectometry methodology, time-frequency domain reflectometry, is proposed and demonstrated with experimental results. Also, cross time-frequency analysis has been utilized for the characterization of ocean wave group propagation, and applied to transient postural sway signals to identify the effects of aging and sensory systems on human postural control systems.Electrical and Computer Engineerin

The origin of quasi-periodicities during circular ribbon flares

Solar flares with a fan-spine magnetic topology can form circular ribbons. The previous study based on H\alpha line observations of the solar flares during March 05, 2014 by Xu et al. (2017) revealed uniform and continuous rotation of the magnetic fan-spine. Preliminary analysis of the flare time profiles revealed quasi-periodic pulsations (QPPs) with similar properties in hard X-rays, H\alpha, and microwaves. In this work, we address which process the observed periodicities are related to: periodic acceleration of electrons or plasma heating? QPPs are analysed in the H\alpha emission from the centre of the fan (inner ribbon R1), a circular ribbon (R2), a remote source (R3), and an elongated ribbon (R4) located between R2 and R3. The methods of correlation, Fourier, wavelet, and empirical mode decomposition are used. QPPs in H\alpha emission are compared with those in microwave and X-ray emission. We found multi-wavelength QPPs with periods around 150 s, 125 s, and 190 s. The 150-s period is seen to co-exist in H\alpha, hard X-rays, and microwave emissions, that allowed us to connect it with flare kernels R1 and R2. These kernels spatially coincide with the site of the primary flare energy release. The 125-s period is found in the H\alpha emission of the elongated ribbon R4 and the microwave emission at 5.7 GHz during the decay phase. The 190-s period is present in the emission during all flare phases in the H\alpha emission of both the remote source R3 and the elongated ribbon R4, in soft X-rays, and microwaves at 4--8 GHz. We connected the dominant 150-s QPPs with the slipping reconnection mechanism occurring in the fan. We suggested that the period of 125 s in the elongated ribbon can be caused by a kink oscillation of the outer spine connecting the primary reconnection site with the remote footpoint. The period of 190 s is associated with the 3-min sunspot oscillations.Comment: Accepted for publication in A&