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.

Effects of anode temperature on working characteristics and performance of a low power arcjet thruster

An arc-heated thruster of 130–800 W input power is tested in a vacuum chamber at pressures lower than 20 Pa with argon or H2–N2 gas mixture as propellant. The time-dependent arc voltage-current curve, outside-surface temperature of the anode nozzle and the produced thrust of the firing arcjet thruster are measured in situ simultaneously, in order to analyze and evaluate the dependence of thruster working characteristics and output properties, such as specific impulse and thrust efficiency, on nozzle temperature.

Nucleon structure functions from ν_µ-Fe interactions and a study of the valence quark distribution

Data were taken in 1979-80 by the CCFRR high energy neutrino experiment at Fermilab. A total of 150,000 neutrino and 23,000 antineutrino charged current events in the approximate energy range 25 < E_v < 250GeV are measured and analyzed. The structure functions F2 and xF_3 are extracted for three assumptions about σ_L/σ_T:R=0., R=0.1 and R= a QCD based expression. Systematic errors are estimated and their significance is discussed. Comparisons or the X and Q^2 behaviour or the structure functions with results from other experiments are made.

We find that statistical errors currently dominate our knowledge of the valence quark distribution, which is studied in this thesis. xF_3 from different experiments has, within errors and apart from level differences, the same dependence on x and Q^2, except for the HPWF results. The CDHS F_2 shows a clear fall-off at low-x from the CCFRR and EMC results, again apart from level differences which are calculable from cross-sections.

The result for the the GLS rule is found to be 2.83±.15±.09±.10 where the first error is statistical, the second is an overall level error and the third covers the rest of the systematic errors. QCD studies of xF_3 to leading and second order have been done. The QCD evolution of xF_3, which is independent of R and the strange sea, does not depend on the gluon distribution and fits yield

ʌ_(LO) = 88^(+163)_(-78) ^(+113)_(-70) MeV

The systematic errors are smaller than the statistical errors. Second order fits give somewhat different values of ʌ, although α_s (at Q^2_0 = 12.6 GeV^2) is not so different.

A fit using the better determined F_2 in place of xF_3 for x > 0.4 i.e., assuming q = 0 in that region, gives

ʌ_(LO) = 266^(+114)_(-104) ^(+85)_(-79) MeV

Again, the statistical errors are larger than the systematic errors. An attempt to measure R was made and the measurements are described. Utilizing the inequality q(x)≥0 we find that in the region x > .4 R is less than 0.55 at the 90% confidence level.

Photon-photon scattering in a plasma channel

The Heisenberg-Euler correction due to photon-photon scattering, a still unverified quantum electrodynamics effect, on electromagnetic wave interaction inside a plasma channel is investigated theoretically. From a signal laser beam in the relativistic overdense plasma channel, photon-photon scattering can produce a detectable output beam of different frequency and polarization. (C) 2003 American Institute of Physics.

Two-body photodisintegration of the deuteron at intermediate energy

We have measured the differential cross section for two-body deuteron photodisintegration at center-of-mass angles of 90°, 53° and 37° with photon energies from 1.6 Ge V to 2.8 Ge V. Additional data were taken at θ* = 37° and E_γ = 4.2 GeV. Invariant cross sections at θ* =90° and 53° appear to follow a simple scaling law predicted by constituent counting rules of perturbative QCD, while the cross section at θ* = 37° shows a slower fall-off with photon energy. Angular distributions show increasing forward peaking at higher energies. Agreement with various theoretical predictions based on pQCD and meson-exchange models is discussed.

Mechanistic and kinetic studies of the surface chemistry of iridium and ruthenium

Quantitative investigations of the mechanisms and the kinetics of the surface-catalyzed activation of C-H, N-H, C-C, and C-N bonds on the close-packed surfaces of Ir(111) and Ru(001) have been performed. The interaction of CH_3NH_2 with Ru(001) was investigated in ultrahigh vacuum with the techniques of high-resolution electron energy loss spectroscopy and thermal desorption mass spectrometry. Activation of the central C-N bond is observed, but it is less favored than the competing channel of complete dehydrogenation, by a ratio between 2:1 to 3:1. The decomposition mechanism has been characterized with several surface intermediates and gas-phase products identified. A pronounced preference for the activation of C-H over N-H and C-N bonds has been established. Additionally, the kinetics of the initial dissociation of short chain alkanes on Ir(111) has been examined, and the rate parameters of the activation of C-C bonds and primary, secondary, and tertiary C-H bonds have been determined. The formation of primary alkyl products is favored, over most of the experimental temperature range, despite the thermodynamic preference for the activation of individual secondary and tertiary C-H bonds in comparison to individual primary C-H bonds. At higher surface temperatures, the activation of C-C bonds occurs at competitive rates to the C-H reaction channel. The measured deuterium kinetic isotope effect implicates substantial deformation of the terminal methyl group in the transition state of C-C bond cleavage. Finally, the surface structure sensitivity of C-H bond cleavage has been quantified for smooth (111) and corrugated (110) surfaces of iridium and platinum, as well as for step edge defect sites on Ir(111).

Black holes in the early universe, in compact binaries, and as energy sources inside solar-type stars

This thesis consists of three separate studies of roles that black holes might play in our universe.

In the first part we formulate a statistical method for inferring the cosmological parameters of our universe from LIGO/VIRGO measurements of the gravitational waves produced by coalescing black-hole/neutron-star binaries. This method is based on the cosmological distance-redshift relation, with "luminosity distances" determined directly, and redshifts indirectly, from the gravitational waveforms. Using the current estimates of binary coalescence rates and projected "advanced" LIGO noise spectra, we conclude that by our method the Hubble constant should be measurable to within an error of a few percent. The errors for the mean density of the universe and the cosmological constant will depend strongly on the size of the universe, varying from about 10% for a "small" universe up to and beyond 100% for a "large" universe. We further study the effects of random gravitational lensing and find that it may strongly impair the determination of the cosmological constant.

In the second part of this thesis we disprove a conjecture that black holes cannot form in an early, inflationary era of our universe, because of a quantum-field-theory induced instability of the black-hole horizon. This instability was supposed to arise from the difference in temperatures of any black-hole horizon and the inflationary cosmological horizon; it was thought that this temperature difference would make every quantum state that is regular at the cosmological horizon be singular at the black-hole horizon. We disprove this conjecture by explicitly constructing a quantum vacuum state that is everywhere regular for a massless scalar field. We further show that this quantum state has all the nice thermal properties that one has come to expect of "good" vacuum states, both at the black-hole horizon and at the cosmological horizon.

In the third part of the thesis we study the evolution and implications of a hypothetical primordial black hole that might have found its way into the center of the Sun or any other solar-type star. As a foundation for our analysis, we generalize the mixing-length theory of convection to an optically thick, spherically symmetric accretion flow (and find in passing that the radial stretching of the inflowing fluid elements leads to a modification of the standard Schwarzschild criterion for convection). When the accretion is that of solar matter onto the primordial hole, the rotation of the Sun causes centrifugal hangup of the inflow near the hole, resulting in an "accretion torus" which produces an enhanced outflow of heat. We find, however, that the turbulent viscosity, which accompanies the convective transport of this heat, extracts angular momentum from the inflowing gas, thereby buffering the torus into a lower luminosity than one might have expected. As a result, the solar surface will not be influenced noticeably by the torus's luminosity until at most three days before the Sun is finally devoured by the black hole. As a simple consequence, accretion onto a black hole inside the Sun cannot be an answer to the solar neutrino puzzle.

Search for color transparency in A(e,e'p) at high momentum transfer

Rates for A(e, e'p) on the nuclei ^2H, C, Fe, and Au have been measured at momentum transfers Q^2 = 1, 3, 5, and 6.8 (GeV fc)^2 . We extract the nuclear transparency T, a measure of the importance of final state interactions (FSI) between the outgoing proton and the recoil nucleus. Some calculations based on perturbative QCD predict an increase in T with momentum transfer, a phenomenon known as Color Transparency. No statistically significant rise is seen in the present experiment.

Physical investigations of small particles : (I) aerosol particle charging and flux enhancement and (II) whispering gallery mode sensing

Part I

Particles are a key feature of planetary atmospheres. On Earth they represent the greatest source of uncertainty in the global energy budget. This uncertainty can be addressed by making more measurement, by improving the theoretical analysis of measurements, and by better modeling basic particle nucleation and initial particle growth within an atmosphere. This work will focus on the latter two methods of improvement.

Uncertainty in measurements is largely due to particle charging. Accurate descriptions of particle charging are challenging because one deals with particles in a gas as opposed to a vacuum, so different length scales come into play. Previous studies have considered the effects of transition between the continuum and kinetic regime and the effects of two and three body interactions within the kinetic regime. These studies, however, use questionable assumptions about the charging process which resulted in skewed observations, and bias in the proposed dynamics of aerosol particles. These assumptions affect both the ions and particles in the system. Ions are assumed to be point monopoles that have a single characteristic speed rather than follow a distribution. Particles are assumed to be perfect conductors that have up to five elementary charges on them. The effects of three body interaction, ion-molecule-particle, are also overestimated. By revising this theory so that the basic physical attributes of both ions and particles and their interactions are better represented, we are able to make more accurate predictions of particle charging in both the kinetic and continuum regimes.

The same revised theory that was used above to model ion charging can also be applied to the flux of neutral vapor phase molecules to a particle or initial cluster. Using these results we can model the vapor flux to a neutral or charged particle due to diffusion and electromagnetic interactions. In many classical theories currently applied to these models, the finite size of the molecule and the electromagnetic interaction between the molecule and particle, especially for the neutral particle case, are completely ignored, or, as is often the case for a permanent dipole vapor species, strongly underestimated. Comparing our model to these classical models we determine an “enhancement factor” to characterize how important the addition of these physical parameters and processes is to the understanding of particle nucleation and growth.

Part II

Whispering gallery mode (WGM) optical biosensors are capable of extraordinarily sensitive specific and non-specific detection of species suspended in a gas or fluid. Recent experimental results suggest that these devices may attain single-molecule sensitivity to protein solutions in the form of stepwise shifts in their resonance wavelength, \lambda_{R}, but present sensor models predict much smaller steps than were reported. This study examines the physical interaction between a WGM sensor and a molecule adsorbed to its surface, exploring assumptions made in previous efforts to model WGM sensor behavior, and describing computational schemes that model the experiments for which single protein sensitivity was reported. The resulting model is used to simulate sensor performance, within constraints imposed by the limited material property data. On this basis, we conclude that nonlinear optical effects would be needed to attain the reported sensitivity, and that, in the experiments for which extreme sensitivity was reported, a bound protein experiences optical energy fluxes too high for such effects to be ignored.

Phase dependence of electron acceleration in a tightly focused laser beam

Electron acceleration using a tightly focused ultraintensity laser beam is investigated numerically and strong phase dependence is found. The acceleration is periodic to the variety of the initial laser field phase, and the accelerated electrons are emitted in pulses of which the full width is the half period of the laser field. When a 10 PW intense laser beam is used, the electron with energy less than 1 Mev can be accelerated up to energies about 1.4 GeV. The optimal initial condition for electron acceleration is found. (C) 2005 American Institute of Physics.

Characterization of exoplanet atmospheres : spectral retrieval and chemistry

The study of exoplanets is rapidly evolving into an important and exciting field of its own. My investigations over the past half-decade have focused on understanding just a small sliver of what they are trying to tell us. That small sliver is their atmospheres. Atmospheres are the buffer between the bulk planet and the vacuum of space. The atmosphere is an important component of a planet as it is the most readily observable and contains the most information about the physical processes that can occur in a planet. I have focused on two aspects of exoplanetary atmospheres. First, I aimed to understand the chemical mechanisms that control the atmospheric abundances. Second, I focused on interpreting exoplanet atmospheric spectra and what they tell us about the temperatures and compositions through inverse modeling. Finally, I interpreted the retrieved temperature and abundances from inverse modeling in the context of chemical disequilibrium in the planetary atmospheres.

Charged pion contribution to the anomalous magnetic moment of the muon

The model dependence inherent in hadronic calculations is one of the dominant sources of uncertainty in the theoretical prediction of the anomalous magnetic moment of the muon. In this thesis, we focus on the charged pion contribution and turn a critical eye on the models employed in the few previous calculations of $a_\mu^{\pi^+\pi^-}$. Chiral perturbation theory provides a check on these models at low energies, and we therefore calculate the charged pion contribution to light-by-light (LBL) scattering to $\mathcal{O}(p^6)$. We show that the dominant corrections to the leading order (LO) result come from two low energy constants which show up in the form factors for the $\gamma\pi\pi$ and $\gamma\gamma\pi\pi$ vertices. Comparison with the existing models reveal a potentially significant omission - none include the pion polarizability corrections associated with the $\gamma\gamma\pi\pi$ vertex. We next consider alternative models where the pion polarizability is produced through exchange of the $a_1$ axial vector meson. These have poor UV behavior, however, making them unsuited for the $a_\mu^{\pi^+\pi^-}$ calculation. We turn to a simpler form factor modeling approach, generating two distinct models which reproduce the pion polarizability corrections at low energies, have the correct QCD scaling at high energies, and generate finite contributions to $a_\mu^{\pi^+\pi^-}$. With these two models, we calculate the charged pion contribution to the anomalous magnetic moment of the muon, finding values larger than those previously reported: $a_\mu^\mathrm{I} = -1.779(4)\times10^{-10}\,,\,a_\mu^\mathrm{II} = -4.892(3)\times10^{-10}$.

紧聚焦的超短超强激光脉冲在真空中加速斜入射的相对论电子

研究了紧聚焦的线偏振飞秒超强高斯激光脉冲俘获并剧烈加速斜入射低能相对论电子的效应，发现被俘获的电子在激光脉冲纵向有质动力的强大加速作用下，可以获得GeV量级的能量，并详细研究了入射电子的初能量、斜入射角、电子与激光脉冲的相对延迟时间和激光脉冲宽度等条件对电子能量增益的影响，发现当激光脉宽超过10λ时，脉宽对电子能量增益影响不大．