Postprocessing of Non-Conservative Flux for Compatibility with Transport in Heterogeneous Media

A conservative flux postprocessing algorithm is presented for both steady-state and dynamic flow models. The postprocessed flux is shown to have the same convergence order as the original flux. An arbitrary flux approximation is projected into a conservative subspace by adding a piecewise constant correction that is minimized in a weighted $L^2$ norm. The application of a weighted norm appears to yield better results for heterogeneous media than the standard $L^2$ norm which has been considered in earlier works. We also study the effect of different flux calculations on the domain boundary. In particular we consider the continuous Galerkin finite element method for solving Darcy flow and couple it with a discontinuous Galerkin finite element method for an advective transport problem.Comment: 34 pages, 17 figures, 11 table

Gravitational Geons Revisited

A careful analysis of the gravitational geon solution found by Brill and Hartle is made. The gravitational wave expansion they used is shown to be consistent and to result in a gauge invariant wave equation. It also results in a gauge invariant effective stress-energy tensor for the gravitational waves provided that a generalized definition of a gauge transformation is used. To leading order this gauge transformation is the same as the usual one for gravitational waves. It is shown that the geon solution is a self-consistent solution to Einstein's equations and that, to leading order, the equations describing the geometry of the gravitational geon are identical to those derived by Wheeler for the electromagnetic geon. An appendix provides an existence proof for geon solutions to these equations.Comment: 18 pages, ReVTeX. To appear in Physical Review D. Significant changes include more details in the derivations of certain key equations and the addition of an appendix containing a proof of the existence of a geon solution to the equations derived by Wheeler. Also a reference has been added and various minor changes have been mad

The Fermionic Projector, Entanglement, and the Collapse of the Wave Function

After a brief introduction to the fermionic projector approach, we review how entanglement and second quantized bosonic and fermionic fields can be described in this framework. The constructions are discussed with regard to decoherence phenomena and the measurement problem. We propose a mechanism leading to the collapse of the wave function in the quantum mechanical measurement process.Comment: 17 pages, LaTeX, 2 figures, minor changes (published version

Probing spacetime foam with extragalactic sources

Due to quantum fluctuations, spacetime is probably ``foamy'' on very small scales. We propose to detect this texture of spacetime foam by looking for core-halo structures in the images of distant quasars. We find that the Very Large Telescope interferometer will be on the verge of being able to probe the fabric of spacetime when it reaches its design performance. Our method also allows us to use spacetime foam physics and physics of computation to infer the existence of dark energy/matter, independent of the evidence from recent cosmological observations.Comment: LaTeX, 11 pages, 1 figure; version submitted to PRL; several references added; very useful comments and suggestions by Eric Perlman incorporate

Dynamics of Inflationary Universes with Positive Spatial Curvature

If the spatial curvature of the universe is positive, then the curvature term will always dominate at early enough times in a slow-rolling inflationary epoch. This enhances inflationary effects and hence puts limits on the possible number of e-foldings that can have occurred, independently of what happened before inflation began and in particular without regard for what may have happened in the Planck era. We use a simple multi-stage model to examine this limit as a function of the present density parameter $\Omega_0$ and the epoch when inflation ends.Comment: 9 Pages RevTex4. Revised and update

Non locality and causal evolution in QFT

Non locality appearing in QFT during the free evolution of localized field states and in the Feynman propagator function is analyzed. It is shown to be connected to the initial non local properties present at the level of quantum states and then it does not imply a violation of Einstein's causality. Then it is investigated a simple QFT system with interaction, consisting of a classical source coupled linearly to a quantum scalar field, that is exactly solved. The expression for the time evolution of the state describing the system is given. The expectation value of any arbitrary ``good'' local observable, expressed as a function of the field operator and its space and time derivatives, is obtained explicitly at all order in the field-matter coupling constant. These expectation values have a source dependent part that is shown to be always causally retarded, while the non local contributions are source independent and related to the non local properties of zero point vacuum fluctuations.Comment: Submitted to Journal of Physics B: 16 pages: 1 figur

Decoherence in a double-slit quantum eraser

We study and experimentally implement a double-slit quantum eraser in the presence of a controlled decoherence mechanism. A two-photon state, produced in a spontaneous parametric down conversion process, is prepared in a maximally entangled polarization state. A birefringent double-slit is illuminated by one of the down-converted photons, and it acts as a single-photon two-qubits controlled not gate that couples the polarization with the transversal momentum of these photons. The other photon, that acts as a which-path marker, is sent through a Mach-Zehnder-like interferometer. When the interferometer is partially unbalanced, it behaves as a controlled source of decoherence for polarization states of down-converted photons. We show the transition from wave-like to particle-like behavior of the signal photons crossing the double-slit as a function of the decoherence parameter, which depends on the length path difference at the interferometer.Comment: Accepted in Physical Review

A Scalable System Architecture for High-Performance Fault Tolerant Machine Drives

When targeting mission critical applications, the design of the electronic actuation systems needs to consider many requirements and constraints not typical in standard industrial applications. One of these is tolerance to faults, as the unplanned shutdown of a critical subsystem, if not handled correctly, could lead to financial harm, environmental disaster, or even loss of life. One way this can be avoided is through the design of an electric drive systems based on multi-phase machines that can keep operating, albeit with degraded performance, in a partial configuration under fault conditions. Distributed architectures are uniquely suited to meet these challenges, by providing a large degree of isolation between the various components. This paper presents a system architecture suitable for scalable and high-performance fault tolerant machine drive systems. the effectiveness of this system is demonstrated through theoretical analysis and experimental verification on a six-phase machine

Pre-Existing Superbubbles as the Sites of Gamma-Ray Bursts

According to recent models, gamma-ray bursts apparently explode in a wide variety of ambient densities ranging from ~ 10^{-3} to 30 cm^{-3}. The lowest density environments seem, at first sight, to be incompatible with bursts in or near molecular clouds or with dense stellar winds and hence with the association of gamma-ray bursts with massive stars. We argue that low ambient density regions naturally exist in areas of active star formation as the interiors of superbubbles. The evolution of the interior bubble density as a function of time for different assumptions about the evaporative or hydrodynamical mass loading of the bubble interior is discussed. We present a number of reasons why there should exist a large range of inferred afterglow ambient densities whether gamma-ray bursts arise in massive stars or some version of compact star coalescence. We predict that many gamma-ray bursts will be identified with X-ray bright regions of galaxies, corresponding to superbubbles, rather than with blue localized regions of star formation. Massive star progenitors are expected to have their own circumstellar winds. The lack of evidence for individual stellar winds associated with the progenitor stars for the cases with afterglows in especially low density environments may imply low wind densities and hence low mass loss rates combined with high velocities. If gamma-ray bursts are associated with massive stars, this combination might be expected for compact progenitors with atmospheres dominated by carbon, oxygen or heavier elements, that is, progenitors resembling Type Ic supernovae.Comment: 14 pages, no figures, submitted to The Astrophysical Journa