Exact solutions and transformation properties of nonlinear partial differential equations from general relativity

Various families of exact solutions to the Einstein and Einstein-Maxwell field equations of General Relativity are treated for situations of sufficient symmetry that only two independent variables arise. The mathematical problem then reduces to consideration of sets of two coupled nonlinear differential equations.

The physical situations in which such equations arise include: a) the external gravitational field of an axisymmetric, uncharged steadily rotating body, b) cylindrical gravitational waves with two degrees of freedom, c) colliding plane gravitational waves, d) the external gravitational and electromagnetic fields of a static, charged axisymmetric body, and e) colliding plane electromagnetic and gravitational waves. Through the introduction of suitable potentials and coordinate transformations, a formalism is presented which treats all these problems simultaneously. These transformations and potentials may be used to generate new solutions to the Einstein-Maxwell equations from solutions to the vacuum Einstein equations, and vice-versa.

The calculus of differential forms is used as a tool for generation of similarity solutions and generalized similarity solutions. It is further used to find the invariance group of the equations; this in turn leads to various finite transformations that give new, physically distinct solutions from old. Some of the above results are then generalized to the case of three independent variables.

Legal dimensions of the Chinese experience in Los Angeles, 1860-1880

On October 24, 1871, a massacre of eighteen Chinese in Los Angeles brought the small southern California settlement into the national spotlight. Within a few days, news of this “night of horrors” was reported in newspapers across the country. This massacre has been cited in Asian American narratives as the first documented outbreak of ethnic violence against a Chinese community in the United States. This is ironic because Los Angeles’ small population has generally placed it on the periphery in historical studies of the California anti-Chinese movement. Because the massacre predated Los Angeles’ organized Chinese exclusion movements of the late 1870s, it has often been erroneously dismissed as an aberration in the history of the city.

The violence of 1871 was an outburst highlighting existing community tensions that would become part of public debate by decade’s close. The purpose of this study is to insert the massacre into a broader context of anti-Chinese sentiments, legal discrimination, and dehumanization in nineteenth century Los Angeles. While a second incident of widespread anti-Chinese violence never occurred, brutal attacks directed at Chinese small businessmen and others highlighted continued community conflict. Similarly, economic rivalries and concerns over Chinese prostitution that underlay the 1871 massacre were manifest in later campaigns of economic discrimination and vice suppression that sought to minimize Chinese influence within municipal limits. An analysis of the massacre in terms of anti-Chinese legal, social and economic strategies in nineteenth-century Los Angeles will elucidate these important continuities.

A study of a new electromechanical energy conversion process using superconducting frequency modulated resonators

Experimental demonstrations and theoretical analyses of a new electromechanical energy conversion process which is made feasible only by the unique properties of superconductors are presented in this dissertation. This energy conversion process is characterized by a highly efficient direct energy transformation from microwave energy into mechanical energy or vice versa and can be achieved at high power level. It is an application of a well established physical principle known as the adiabatic theorem (Boltzmann-Ehrenfest theorem) and in this case time dependent superconducting boundaries provide the necessary interface between the microwave energy on one hand and the mechanical work on the other. The mechanism which brings about the conversion is another known phenomenon - the Doppler effect. The resonant frequency of a superconducting resonator undergoes continuous infinitesimal shifts when the resonator boundaries are adiabatically changed in time by an external mechanical mechanism. These small frequency shifts can accumulate coherently over an extended period of time to produce a macroscopic shift when the resonator remains resonantly excited throughout this process. In addition, the electromagnetic energy in s ide the resonator which is proportional to the oscillation frequency is al so accordingly changed so that a direct conversion between electromagnetic and mechanical energies takes place. The intrinsically high efficiency of this process is due to the electromechanical interactions involved in the conversion rather than a process of thermodynamic nature and therefore is not limited by the thermodynamic value.

A highly reentrant superconducting resonator resonating in the range of 90 to 160 MHz was used for demonstrating this new conversion technique. The resonant frequency was mechanically modulated at a rate of two kilohertz. Experimental results showed that the time evolution of the electromagnetic energy inside this frequency modulated (FM) superconducting resonator indeed behaved as predicted and thus demonstrated the unique features of this process. A proposed usage of FM superconducting resonators as electromechanical energy conversion devices is given along with some practical design considerations. This device seems to be very promising in producing high power (~10W/cm^3) microwave energy at 10 - 30 GHz.

Weakly coupled FM resonator system is also analytically studied for its potential applications. This system shows an interesting switching characteristic with which the spatial distribution of microwave energies can be manipulated by external means. It was found that if the modulation was properly applied, a high degree (>95%) of unidirectional energy transfer from one resonator to the other could be accomplished. Applications of this characteristic to fabricate high efficiency energy switching devices and high power microwave pulse generators are also found feasible with present superconducting technology.

From lakes to lungs : assessing microbial activity in diverse environments

All major geochemical cycles on the Earth’s surface are mediated by microorganisms. Our understanding of how these microbes have interacted with their environments (and vice versa) throughout Earth's history, and how they will respond to changes in the future, is primarily based on studying their activity in different environments today. The overarching questions that motivate the research presented in the two parts of this thesis -- how do microorganisms shape their environment (and vice versa)? and how can we best study microbial activity in situ? -- have arisen from the ultimate goal of being able to predict microbial activity in response to changes within their environments both past and future.

Part one focuses on work related to microbial processes in iron-rich Lake Matano and, more broadly, microbial interactions with the biogeochemical cycling of iron. Primarily, we find that the chelation of ferrous iron by organic ligands can affect the role of iron in anoxic environmental systems, enabling photomixotrophic growth of anoxygenic microorganisms with ferrous iron, as well as catalyzing the oxidation of ferrous iron by denitrification intermediates. These results imply that the ability to grow photomixotrophically on ferrous iron might be more widespread than previously assumed, and that the co-occurrence of chemical and biological processes involved in the coupled biogeochemical cycling of iron and nitrogen likely dominate organic-rich environmental systems.

Part two switches focus to in situ measurements of growth activity and comprises work related to microbial processes in the Cystic Fibrosis lung, and more broadly, the physiology of slow growth. We introduce stable isotope labeling of microbial membrane fatty acids and whole cells with heavy water as a new technique to measure microbial activity in a wide range of environments, demonstrate its application in continuous culture in the laboratory at the population and single cell level, and apply the tool to measure the in situ activity of the opportunistic pathogen Staphylococcus aureus within the environment of expectorated mucus from cystic fibrosis patients. We find that the average in situ growth rates of S. aureus fall into a range of generation times between ~12 hours and ~4 days, with substantial heterogeneity at the single-cell level. These data illustrate the use of heavy water as a universal environmental tracer for microbial activity, and highlight the crucial importance of studying the physiology of slow growth in representative laboratory systems in order to understand the role of these microorganisms in their native environments.