Ion Velocity Distributions in Inhomogeneous and Time-dependent Auroral Situations

Aurorae often break down into elongated filaments parallel to the geomagnetic field lines (B) with cylindrically symmetric structures. The object of this thesis is to study the ion distribution function and transport properties in response to the sudden introduction of a radial electric field (E) in such a cylindrical geometry. Both collision-free and collisional situations are considered. The thesis starts by solving a collision-free problem where the electric field is constant in time but increases linearly with radius, while the initial ion density is uniform in space. The attendant Boltzmann equation is solved by tracking the ions back in time, thereby using the temporal link between the initial position and velocity of an ion and its position and velocity at an arbitrary time and place. Complete analytical solutions show that the ion distribution function is a pulsating Maxwellian in time, and all transport parameters (e.g., bulk speed, temperature, etc.) oscillate in time but independent of radius. If the ion-neutral collisions are taken into account by employing a simple relaxation model, analytical solutions are also obtained. In this case, the ion distribution function can be driven to horseshoe shapes which are symmetric with respect to the ExB direction. The bulk parameters evolve in a transition period of the order of one collision time as they go from oscillating to the non-oscillating steady state. In more realistic electric field structures which are spatially inhomogeneous but still constant in time, a generalized semi-numerical code is developed under collision-free conditions. This code uses a backmapping approach to calculate the ion velocity distribution and bulk parameters. With arbitrarily selected electric field rofiles, calculations reveal various shapes of ion velocity distribution functions (e.g., tear-drop, core-halo, ear-donut, etc). The associated transport properties are also obtained and discussed. Under both collision-free and collisional conditions, the effect of the density inhomogeneities at the initial time is studied in an electric field which is proportional to radius and constant in time. With two profiles of the initial ion density for the collision-free case, and one profile for the collisional case, complete analytical solutions are obtained. The results reveal that the distribution function and the bulk properties are now strongly dependent on radial position. If the radial electric field is unable to stay constant with time but modulated by in-coming charged particles, a fluid formalism is used to study the excitation of several plasma waves under different kinds of initial conditions. These identified waves include the ion cyclotron oscillation, the ion and electron upper-hybrid oscillations, and the lower-hybrid oscillation. The results of this thesis are expected to be applicable to high-resolution observations. Future work should also include the mirror effect and the formation of conics in velocity space. Finally, the velocity distributions obtained in this thesis could trigger various plasma instabilities, and this topic should also be looked at in the future

Decorrelation of Neutral Vector Variables: Theory and Applications

In this paper, we propose novel strategies for neutral vector variable decorrelation. Two fundamental invertible transformations, namely serial nonlinear transformation and parallel nonlinear transformation, are proposed to carry out the decorrelation. For a neutral vector variable, which is not multivariate Gaussian distributed, the conventional principal component analysis (PCA) cannot yield mutually independent scalar variables. With the two proposed transformations, a highly negatively correlated neutral vector can be transformed to a set of mutually independent scalar variables with the same degrees of freedom. We also evaluate the decorrelation performances for the vectors generated from a single Dirichlet distribution and a mixture of Dirichlet distributions. The mutual independence is verified with the distance correlation measurement. The advantages of the proposed decorrelation strategies are intensively studied and demonstrated with synthesized data and practical application evaluations

Energy Spectrum Theory of Incommensurate Systems

Due to the lack of the translational symmetry, calculating the energy spectrum of an incommensurate system has always been a theoretical challenge. Here, we propose a natural approach to generalize the energy band theory to the incommensurate systems without reliance on the commensurate approximation, thus providing a comprehensive energy spectrum theory of the incommensurate systems. Except for a truncation dependent weighting factor, the formulae of this theory are formally almost identical to that of the Bloch electrons, making it particularly suitable for complex incommensurate structures. To illustrate the application of this theory, we give three typical examples: one-dimensional bichromatic and trichromatic incommensurate potential model, as well as a moir\'{e} quasicrystal. Our theory establishes a fundamental framework for understanding the incommensurate systems.Comment: 7 pages, 3 figure

The width-flux relation of the broad iron line during the state transition of the black hole X-ray binaries

The observation of varying broad iron lines during the state transition of the black hole X-ray binaries (BHXBs) have been accumulating.In this work, the relation between the normalized intensity and the width of iron lines is investigated, in order to understand better the variation of iron lines and possibly its connection to state transition. Considering the uncertainties due to ionization and illuminating X-rays, only the effects of geometry and gravity are taken into account. Three scenarios were studied, i.e., the continuous disk model, innermost annulus model, and the cloud model. As shown by our calculations, at given iron width, the line flux of the cloud model is smaller than that of the continuous disk model; while for the innermost annulus model, the width is almost unrelated with the flux. The range of the line strength depends on both the BH spin and the inclination of the disk. We then apply to the observation of MAXI J1631-479 by NuSTAR during its decay from the soft state to the intermediate state. We estimated the relative line strength and width according to the spectral fitting results by Xu et al.(2020), and then compared with our theoretical width-flux relation. It was found that the cloud model was more favored. We further modeled the iron line profiles, and found that the cloud model can explain both the line profile and its variation with reasonable parameters.Comment: 7 figures, 12 pages, accepted for publication in RA

catena-Poly[[[tetra­aqua­samarium(III)]-di-μ-isonicotinato-κ4 O:O′] chloride]

In the structure of the title compound, {[Sm(C6H4NO2)2(H2O)4]Cl}n, the unique SmIII atom lies on a crystallographic twofold axis and is eight-coordinated by four O atoms from four isonicotinate ligands and four water mol­ecules in a slightly distorted square-anti­prismatic coodination environment. The SmIII atoms are bridged by two carboxyl­ate groups of two isonicotinate ligands, forming an extended chain along the c-axis direction. These chains are cross-linked through hydrogen bonds, forming a three-dimensional framework, with channels which accommodate the chloride anions

Dynamic Cerebral Autoregulation Remains Stable During the Daytime (8 a.m. to 8 p.m.) in Healthy Adults

Many functions of the human body possess a daily rhythm, disruptions of which often lead to disease. Dynamic cerebral autoregulation (dCA) stabilizes the cerebral blood flow to prompt normal neural function. However, whether dCA is stable across the day remains unknown. This study aimed to investigate the daily rhythm of dCA. Fifty-one healthy adults (38.294 ± 13.279 years, 40 females) were recruited and received six dCA measurements per individual that were conducted at predefined time points: 8:00, 9:00, 11:00, 14:00, 17:00, and 20:00. Although the blood pressure fluctuated significantly, there was no statistical difference in phase difference and gain (autoregulatory parameters) across the six time points. This study demonstrates that dCA remains stable during the interval from 8 a.m. to 8 p.m. and underscores the importance of stable dCA in maintaining cerebral blood flow and neural function