Coulomb field of an accelerated charge: physical and mathematical aspects

The Maxwell field equations relative to a uniformly accelerated frame, and the variational principle from which they are obtained, are formulated in terms of the technique of geometrical gauge invariant potentials. They refer to the transverse magnetic (TM) and the transeverse electric (TE) modes. This gauge invariant "2+2" decomposition is used to see how the Coulomb field of a charge, static in an accelerated frame, has properties that suggest features of electromagnetism which are different from those in an inertial frame. In particular, (1) an illustrative calculation shows that the Larmor radiation reaction equals the electrostatic attraction between the accelerated charge and the charge induced on the surface whose history is the event horizon, and (2) a spectral decomposition of the Coulomb potential in the accelerated frame suggests the possibility that the distortive effects of this charge on the Rindler vacuum are akin to those of a charge on a crystal lattice.Comment: 27 pages, PlainTex. Related papers available at http://www.math.ohio-state.edu/~gerlac

Bellows flow-induced vibrations

Results of theoretical and experimental investigations of bellows typical of those found in space shuttle external tanks are presented. Correlation parameters are identified which generalize the alternating stress calculations cited in an earlier study. Alternating stress amplitudes and mean stress levels form the basis of a fatigue analysis incorporating seven ordinate charts for 347 stainless steel, alloy 21 6-9, and Inco 718. A crack propagation model is included with a program for computing bellows fatigue life. Two phase flow and material hardness properties are discussed

The Stern-Gerlach Experiment Revisited

The Stern-Gerlach-Experiment (SGE) of 1922 is a seminal benchmark experiment of quantum physics providing evidence for several fundamental properties of quantum systems. Based on today's knowledge we illustrate the different benchmark results of the SGE for the development of modern quantum physics and chemistry. The SGE provided the first direct experimental evidence for angular momentum quantization in the quantum world and thus also for the existence of directional quantization of all angular momenta in the process of measurement. It measured for the first time a ground state property of an atom, it produced for the first time a `spin-polarized' atomic beam, it almost revealed the electron spin. The SGE was the first fully successful molecular beam experiment with high momentum-resolution by beam measurements in vacuum. This technique provided a new kinematic microscope with which inner atomic or nuclear properties could be investigated. The original SGE is described together with early attempts by Einstein, Ehrenfest, Heisenberg, and others to understand directional quantization in the SGE. Heisenberg's and Einstein's proposals of an improved multi-stage SGE are presented. The first realization of these proposals by Stern, Phipps, Frisch and Segr\`e is described. The set-up suggested by Einstein can be considered an anticipation of a Rabi-apparatus. Recent theoretical work is mentioned in which the directional quantization process and possible interference effects of the two different spin states are investigated. In full agreement with the results of the new quantum theory directional quantization appears as a general and universal feature of quantum measurements. One experimental example for such directional quantization in scattering processes is shown. Last not least, the early history of the `almost' discovery of the electron spin in the SGE is revisited.Comment: 50pp, 17 fig

The profile of an emission line from relativistic outflows around a black hole

Recent observations show strong evidence for the presence of Doppler-shifted emission lines in the spectrum of both black hole candidates and active galactic nuclei. These lines are likely to originate from relativistic outflows (or jets) in the vicinity of the central black hole. Consequently, the profile of such a line should be distorted by strong gravitational effects near the black hole, as well as special relativistic effects. In this paper, we present results from a detailed study on how each process affects the observed line profile. We found that the profile is sensitive to the intrinsic properties of the jets (Lorentz factor, velocity profile, and emissivity law), as well as to the spin of the black hole and the viewing angle (with respect to the axis of the jets). More specifically, in the case of approaching jets, an intrisically narrow line (blue-shifted) is seen as simply broadened at small viewing angles, but it shows a doubly peaked profile at large viewing angles for extreme Kerr black holes (due to the combination of gravitational focusing and Doppler effects); the profile is always singly peaked for Schwarzschild black holes. For receding jets, however, the line profile becomes quite complicated owing to complicated photon trajectories. To facilitate comparison with observations, we searched a large parameter space to derive representative line profiles. We show the results and discuss how to use emission lines as a potential tool for probing the inner region of a black hole jet system.Comment: 16 pages in emulateapj style, 11 figure

Axial perturbations of general spherically symmetric spacetimes

The aim of this paper is to present a governing equation for first order axial metric perturbations of general, not necessarily static, spherically symmetric spacetimes. Under the non-restrictive assumption of axisymmetric perturbations, the governing equation is shown to be a two-dimensional wave equation where the wave function serves as a twist potential for the axisymmetry generating Killing vector. This wave equation can be written in a form which is formally a very simple generalization of the Regge-Wheeler equation governing the axial perturbations of a Schwarzschild black hole, but in general the equation is accompanied by a source term related to matter perturbations. The case of a viscous fluid is studied in particular detail.Comment: 16 pages, no figures, minor correction

On the exciton binding energy in a quantum well

We consider a model describing the one-dimensional confinement of an exciton in a symmetrical, rectangular quantum-well structure and derive upper and lower bounds for the binding energy $E_b$ of the exciton. Based on these bounds, we study the dependence of $E_b$ on the width of the confining potential with a higher accuracy than previous reports. For an infinitely deep potential the binding energy varies as expected from $1 Ry$ at large widths to $4 Ry$ at small widths. For a finite potential, but without consideration of a mass mismatch or a dielectric mismatch, we substantiate earlier results that the binding energy approaches the value $1 Ry$ for both small and large widths, having a characteristic peak for some intermediate size of the slab. Taking the mismatch into account, this result will in general no longer be true. For the specific case of a $Ga_{1-x}Al_{x}As/GaAs/Ga_{1-x}Al_{x}As$ quantum-well structure, however, and in contrast to previous findings, the peak structure is shown to survive.Comment: 32 pages, ReVTeX, including 9 figure

Quantum Geometrodynamics I: Quantum-Driven Many-Fingered Time

The classical theory of gravity predicts its own demise -- singularities. We therefore attempt to quantize gravitation, and present here a new approach to the quantization of gravity wherein the concept of time is derived by imposing the constraints as expectation-value equations over the true dynamical degrees of freedom of the gravitational field -- a representation of the underlying anisotropy of space. This self-consistent approach leads to qualitatively different predictions than the Dirac and the ADM quantizations, and in addition, our theory avoids the interpretational conundrums associated with the problem of time in quantum gravity. We briefly describe the structure of our functional equations, and apply our quantization technique to two examples so as to illustrate the basic ideas of our approach.Comment: 11, (No Figures), (Typeset using RevTeX

Uniformly Accelerated Mirrors. Part 1: Mean Fluxes

The Davies-Fulling model describes the scattering of a massless field by a moving mirror in 1+1 dimensions. When the mirror travels under uniform acceleration, one encounters severe problems which are due to the infinite blue shift effects associated with the horizons. On one hand, the Bogoliubov coefficients are ill-defined and the total energy emitted diverges. On the other hand, the instantaneous mean flux vanishes. To obtained well-defined expressions we introduce an alternative model based on an action principle. The usefulness of this model is to allow to switch on and off the interaction at asymptotically large times. By an appropriate choice of the switching function, we obtain analytical expressions for the scattering amplitudes and the fluxes emitted by the mirror. When the coupling is constant, we recover the vanishing flux. However it is now followed by transients which inevitably become singular when the switching off is performed at late time. Our analysis reveals that the scattering amplitudes (and the Bogoliubov coefficients) should be seen as distributions and not as mere functions. Moreover, our regularized amplitudes can be put in a one to one correspondence with the transition amplitudes of an accelerated detector, thereby unifying the physics of uniformly accelerated systems. In a forthcoming article, we shall use our scattering amplitudes to analyze the quantum correlations amongst emitted particles which are also ill-defined in the Davies-Fulling model in the presence of horizons.Comment: 23 pages, 7 postscript figure

Monitoring SO2 emission at the Soufriere Hills Volcano: implications for changes in erruptive conditions

FLWINinfo:eu-repo/semantics/publishe

Origin of Hawaiian Tholeiites: Trace Element Constraints

We report here geochemical studies of Hawaiian tholeiites and ultramafic xenoliths from Salt Lake Crater, Oahu. We focus attention on tholeiitic basalts that comprise the bulk of Hawaiian volcanoes. When the samples are screened to include only those lying neat the log-MgO (about 7 percent) end of olivine-control lines (Wright, 1971), tholeiites from individual volcanoes are remarkably uniform. On this basis, we show that, for tholeiites from six volcanoes, systematic geochemical differences exist that cannot be attributed to differentiation of these magmas from a common parental magma. Apparently there have been important differences in the processes of magma generation, source composition, or source mineral constitution. Partial melting calculations based on REE contents emphasize these distinctions, but unique melting models are not presented. In these models, relative REE abundances in the source material is a major uncertainty. Nd isotopic studies of Hawaiian basalts require systematic differences in Sm/Nd for the source material of each volcano. Furthermore, the time-integrated Sm/Nd of the sources must be less than that in chondrites. REE analyses of Hawaiian garnet lherzolite xenoliths show that they have chondritic to light REE-enriched relative abundances with absolute contents (for light REE) about 3 to 8 times chondrites. These data obviously conflict with interpretations of the Nd isotopic data. Several possibilities follow: (1) the available xenoliths are not parental to tholeiite, (2) our simple interpretation of the Nd isotopic data is wrong, and (3) the source regions may have been invaded at geologically recent times by a light REE-enriched phase, in which case the xenoliths may represent the course material. If the xenoliths are characteristic of the source, partial melting calculations indicate that the tholeiites may be generated by 15 to 20 percent melting of garnet lherzolite and at the sane tune conform to constraints imposed by the REE and Ni contents and the partitioning of Fe and Mg between melts and residues. We propose that the primary tholeiitic magmas contain no more than about 12 percent MgO, and that erupted magmas probably fractionated less than 10 to 15 percent of olivine during ascent and storage in high-level chambers