Study of magnetic helicity in solar active regions and its relationship with solar eruptions

It is generally believed that eruptive phenomena in the solar atmosphere such as solar flares and coronal mass ejections (CMEs) occur in solar active regions with complex magnetic structures. The magnetic complexity is quantified in terms of twists, kinks, and interlinkages of magnetic field lines. Magnetic helicity has been recognized as a useful measure for these properties of a given magnetic field system. Magnetic helicity studies have been naturally directed to the energy buildup and instability leading to solar eruptions. However, in spite of many years of study, detailed aspects of initiation mechanisms of eruptive events are still not well understood. The objective of this dissertation is to understand a long-term (a few days) variation of magnetic helicity in active regions and its relationship with flares and CMEs. The research presented in this dissertation benefited significantly from the comprehensive data now available, including SOHO/MDI full-disk longitudinal magnetograms, Hinode/SOT/SP vector magnetograms, and GOES soft X-ray data. In addition, several advanced data analysis tools were utilized such as local correlation tracking, differential affine velocity estimator, Stokes inversion, 180° ambiguity resolution, and nonlinear force-free magnetic field extrapolation. Statistical studies of flare productivity and magnetic helicity injection in ~400 active regions were carried out. The time profile of the coronal magnetic helicity in the active region NOAA 10930 was also investigated to find its characteristic variation related to the X3.4 flare on 2006 December 13. In addition, the temporal varia tion of magnetic helicity injected through the photosphere of active regions was examined related to 46 CMEs and two active-region coronal arcades building up to CMEs. The main findings in this dissertation are as follows: (1) the study of magnetic helicity for active regions producing major flares and CMEs indicates that there is always a significant helicity injection of 1042–1043 Mx2 through the active-region photosphere over a long period of ~0.5–a few days before the flares and CMEs; (2) the study of the 2006 December 13 X3.4 flare shows that the flare is preceded by not only a large increase of negative helicity in the corona over ~1.5 days but also a noticeable injection of oppositelysigned helicity though the photospheric surface around the flaring magnetic polarity inversion line; (3) the gradual inflation stage of the two arcades is temporally associated with helicity injection from the active-region photosphere; and (4) for the 30 CMEs under investigation, it is found that there is a fairly good correlation (linear correlation coefficient of 0.71) between the average helicity injection in the CME-productive active regions and the CME speed. Beside the scientific contribution, a major broader impact of this dissertation is the observational discovery of a characteristic variation of the pattern of magnetic helicity injection in flare/CME-productive active regions, which can be used for the improvement of solar eruption forecasting. An early warning sign of flare-CME occurrence could be implemented based on tracking of a period of monotonically increasing helicity because there was always a significant amount of helicity accumulation in active regions a few days before the major flares and CMEs under investigation

NONINVASIVE IMAGING OF BRAIN VASCULATURE WITH HIGH RESOLUTION BLOOD OXYGENATION LEVEL-DEPENDENT VENOGRAPHY IN MAGNETIC RESONANCE IMAGING: APPLICATIONS TO FUNCTIONAL AND CLINICAL STUDIES

BOLD techniques have been used in a vast range of applications including functional MRI (fMRI) and clinical MR venography of brain vasculature. Despite the immense success of BOLD fMRI applications, our understanding of complex neuronal and hemodynamic processes associated with BOLD techniques is limited. An experimental investigation with BOLD MR venography may allow us to expand our knowledge in hemodynamic process involved in BOLD fMRI. BOLD techniques are also clinically useful. In clinical brain imaging studies, imaging both time-of-flight (TOF) MR angiogram (MRA) and BOLD MR venogram (MRV) is often desirable, because they complement the depiction of vascular pathologies. Nevertheless, MRV is usually not acquired to minimize the image acquisition time. It will be highly beneficial if we can acquire MRV while imaging MRA without increasing scan time. Thus, the objective of our study was to develop and assess BOLD MRV techniques for both functional and clinical applications. For the experimental evaluation of BOLD MRV, we used a rat brain model at 9.4T. The scan condition for BOLD MRV was optimized and the venous origin of hypointense vasculature was investigated with modulation of oxygenation. Detailed venules of ˜16-30μm diameter were detected in the resulting in vivo images with 78μm isotropic scan resolution, verified with in vivo two-photon microscopy and computer simulation data. Activation foci of high-resolution BOLD fMRI maps were correlated with relatively large intracortical veins detected with high-resolution BOLD MRV, indicating that detectability of conventional BOLD fMRI is limited by density of these intracortical veins (˜1.5 vessels/mm²). For the clinical application of BOLD MRV, we developed and tested a compatible dual-echo arteriovenography (CODEA) technique for simultaneous acquisition of TOF MRA and BOLD MRV at a 3T human system. Image quality of the CODEA technique acquired in a single session was comparable to conventional TOF MRA and BOLD MRV separately acquired in two sessions. The CODEA technique was applied to chronic stroke studies. Detailed vascular structures including arterial occlusions and venous abnormalities were depicted. The CODEA technique appears valuable to other clinical applications, particularly for those requiring efficient MRA/MRV imaging with limited scan time such as acute stroke studies

Simultaneous detection of the nonlinear restoring and excitation of a forced nonlinear oscillation: an integral approach

We address in this article, how to calculate the restoring characteristic and the excitation of a nonlinear forced oscillating system. Under the assumption that the forced nonlinear oscillator has a periodic solution with period, we constructed a system of linear equations by introducing time-dependent multipliers. The periodicity assumption helps simplify the system of linear equations. The stability and uniqueness are also presented for the inverse problem. Numerical testing is conducted to show the effectiveness of our presented methodology.Peer ReviewedPostprint (author's final draft