The Petrocarb pneumatic feeding system: A proven method for feeding particulate solids at controlled rates

An outline of the principal features of the Petrocarb Pneumatic Feeding System is given. Early development and various commercial applications are included. It is concluded that the Petrocarb Injection System is capable of feeding dry solids into most of the processes being developed for utilizing coal

"Regularity Singularities" and the Scattering of Gravity Waves in Approximate Locally Inertial Frames

It is an open question whether solutions of the Einstein-Euler equations are smooth enough to admit locally inertial coordinates at points of shock wave interaction, or whether "regularity singularities" can exist at such points. The term {\it regularity singularity} was proposed by the authors as a point in spacetime where the gravitational metric tensor is Lipschitz continuous ($C^{0,1}$), but no smoother, in any coordinate system of the $C^{1,1}$ atlas. An existence theory for shock wave solutions in $C^{0,1}$ admitting arbitrary interactions has been proven for the Einstein-Euler equations in spherically symmetric spacetimes, but $C^{1,1}$ is the requisite smoothness required for space-time to be locally flat. Thus the open problem of regularity singularities is the problem as to whether locally inertial coordinate systems exist at shock waves within the larger $C^{1,1}$ atlas. To clarify this open problem, we identify new "Coriolis type" effects in the geometry of $C^{0,1}$ shock wave metrics and prove they are essential in the sense that they can never be made to vanish within the atlas of {\it smooth} coordinate transformations, the atlas usually assumed in classical differential geometry. Thus the problem of existence of regularity singularities is equivalent to the question as to whether or not these Coriolis type effects are essentially non-removable and `real', or merely coordinate effects that can be removed, (in analogy to classical Coriolis forces), by going to the less regular atlas of $C^{1,1}$ transformations. If essentially non-removable, it would argue strongly for a `real' new physical effect for General Relativity, providing a physical context to the open problem of regularity singularities.Comment: 29 pages. Version 2: Corrections of some typographical errors and improvements of wording. Results are unchange

A Non-Perturbative Construction of the Fermionic Projector on Globally Hyperbolic Manifolds II - Space-Times of Infinite Lifetime

The previous functional analytic construction of the fermionic projector on globally hyperbolic Lorentzian manifolds is extended to space-times of infinite lifetime. The construction is based on an analysis of families of solutions of the Dirac equation with a varying mass parameter. It makes use of the so-called mass oscillation property which implies that integrating over the mass parameter generates decay of the Dirac wave functions at infinity. We obtain a canonical decomposition of the solution space of the massive Dirac equation into two subspaces, independent of observers or the choice of coordinates. The constructions are illustrated in the examples of ultrastatic space-times and de Sitter space-time.Comment: 29 pages, LaTeX, minor improvements (published version

Channelization architecture for wide-band slow light in atomic vapors

We propose a ``channelization'' architecture to achieve wide-band electromagnetically induced transparency (EIT) and ultra-slow light propagation in atomic Rb-87 vapors. EIT and slow light are achieved by shining a strong, resonant ``pump'' laser on the atomic medium, which allows slow and unattenuated propagation of a weaker ``signal'' beam, but only when a two-photon resonance condition is satisfied. Our wideband architecture is accomplished by dispersing a wideband signal spatially, transverse to the propagation direction, prior to entering the atomic cell. When particular Zeeman sub-levels are used in the EIT system, then one can introduce a magnetic field with a linear gradient such that the two-photon resonance condition is satisfied for each individual frequency component. Because slow light is a group velocity effect, utilizing differential phase shifts across the spectrum of a light pulse, one must then introduce a slight mismatch from perfect resonance to induce a delay. We present a model which accounts for diffusion of the atoms in the varying magnetic field as well as interaction with levels outside the ideal three-level system on which EIT is based. We find the maximum delay-bandwidth product decreases with bandwidth, and that delay-bandwidth product ~1 should be achievable with bandwidth ~50 MHz (~5 ns delay). This is a large improvement over the ~1 MHz bandwidths in conventional slow light systems and could be of use in signal processing applications.Comment: Published in SPIE Proceedings, Photonics West 2005 (San Jose, CA, Jan. 22-27, 2005