SURPHEX (tm): New dry photopolymers for replication of surface relief diffractive optics

High efficiency, deep groove, surface relief Diffractive Optical Elements (DOE) with various optical functions can be recorded in a photoresist using conventional interferometric holographic and computer generated photolithographic recording techniques. While photoresist recording media are satisfactory for recording individual surface relief DOE, a reliable and precise method is needed to replicate these diffractive microstructures to maintain the high aspect ratio in each replicated DOE. The term 'high aspect ratio' means that the depth of a groove is substantially greater, i.e. 2, 3, or more times greater, than the width of the groove. A new family of dry photopolymers SURPHEX was developed recently at Du Pont to replicate such highly efficient, deep groove DOE's. SURPHEX photopolymers are being utilized in Du Pont's proprietary Dry Photopolymer Embossing (DPE) technology to replicate with very high degree of precision almost any type of surface relief DOE. Surfaces relief microstructures with width/depth aspect ratio of 1:20 (0.1 micron/2.0 micron) were faithfully replicated by DPE technology. Several types of plastic and glass/quartz optical substrates can be used for economical replication of DOE

Applications of vortex gas models to tornadogenesis and maintenance

Processes related to the production of vorticity in the forward and rear flank downdrafts and their interaction with the boundary layer are thought to play a role in tornadogenesis. We argue that an inverse energy cascade is a plausible mechanism for tornadogenesis and tornado maintenance and provide supporting evidence which is both numerical and observational. We apply a three-dimensional vortex gas model to supercritical vortices produced at the surface boundary layer possibly due to interactions of vortices brought to the surface by the rear flank downdraft and also to those related to the forward flank downdraft. Two-dimensional and three-dimensional vortex gas models are discussed, and the three-dimensional vortex gas model of Chorin, developed further by Flandoli and Gubinelli, is proposed as a model for intense small- scale subvortices found in tornadoes and in recent numerical studies by Orf et al. In this paper, the smaller scales are represented by intense, supercritical vortices, which transfer energy to the larger-scale tornadic flows (inverse energy cascade). We address the formation of these vortices as a result of the interaction of the flow with the surface and a boundary layer.Comment: 20 pages, 6 figure

Vacuum Breakdown near a Black Hole Charged by Hypercritical Accretion

We consider a black hole accreting spherically from the surrounding medium. If accretion produces a luminosity close to the Eddington limit the hole acquires a net charge so that electrons and ions can fall with the same velocity. The condition for the electrostatic field to be large enough to break the vacuum near the hole horizon translates into an upper limit for the hole mass, $M\sim 6.6\times 10^{20} {\rm g}.$ The astrophysical conditions under which this phaenomenon can take place are rather extreme, but in principle they could be met by a mini black hole residing at the center of a star.Comment: 6 pages, accepted for publication in the Astrophysical Journa

Fractal powers in Serrin\u27s swirling vortex solutions

We consider a modification of the fluid flow model for a tornado-like swirling vortex developed by Serrin [Phil. Trans. Roy. Soc. London, Series A, Math & Phys. Sci. 271(1214) (1972), 325–360], where velocity decreases as the reciprocal of the distance from the vortex axis. Recent studies, based on radar data of selected severe weather events [Mon. Wea. Rev. 133(9) (2005), 2535–2551; Mon. Wea. Rev. 128(7) (2000), 2135–2164; Mon. Wea. Rev. 133(1) (2005), 97–119], indicate that the angular momentum in a tornado may not be constant with the radius, and thus suggest a different scaling of the velocity/radial distance dependence. Motivated by this suggestion, we consider Serrin\u27s approach with the assumption that the velocity decreases as the reciprocal of the distance from the vortex axis to the power b with a general b\u3e0. This leads to a boundary-value problem for a system of nonlinear differential equations. We analyze this problem for particular cases, both with nonzero and zero viscosity, discuss the question of existence of solutions, and use numerical techniques to describe those solutions that we cannot obtain analytically

Ultra-high energy cosmic rays from Quark Novae

We explore acceleration of ions in the Quark Nova (QN) scenario, where a neutron star experiences an explosive phase transition into a quark star (born in the propeller regime). In this picture, two cosmic ray components are isolated: one related to the randomized pulsar wind and the other to the propelled wind, both boosted by the ultra-relativistic Quark Nova shock. The latter component acquires energies $10^{15} {\rm eV}<E<10^{18} {\rm eV}$ while the former, boosted pulsar wind, achieves ultra-high energies $E> 10^{18.6}$ eV. The composition is dominated by ions present in the pulsar wind in the energy range above $10^{18.6}$ eV, while at energies below $10^{18}$ eV the propelled ejecta, consisting of the fall-back neutron star crust material from the explosion, is the dominant one. Added to these two components, the propeller injects relativistic particles with Lorentz factors $\Gamma_{\rm prop.} \sim 1-1000$, later to be accelerated by galactic supernova shocks. The QN model appears to be able to account for the extragalactic cosmic rays above the ankle and to contribute a few percent of the galactic cosmic rays below the ankle. We predict few hundred ultra-high energy cosmic ray events above $10^{19}$ eV for the Pierre Auger detector per distant QN, while some thousands are predicted for the proposed EUSO and OWL detectors.Comment: 20 pages, 1 figure. Major revisions in the text. Accepted for publication in the Astrophysical Journa

Prospect for relic neutrino searches

Unlike the relic photons, relic neutrinos have not so far been observed. The Cosmic Neutrino Background (C$\nu$B) is the oldest relic from the Big Bang, produced a few seconds after the Bang itself. Due to their impact in cosmology, relic neutrinos may be revealed indireclty in the near future through cosmological observations. In this talk we concentrate on other proposals, made in the last 30 years, to try to detect the C$\nu$B directly, either in laboratory searches (through tiny accelerations they produce on macroscopic targets) or through astrophysical observations (looking for absorption dips in the flux of Ultra-High Energy neutrinos, due to the annihilation of these neutrinos with relic neutrinos at the Z-resonance). We concentrate mainly on the first of these two possibilities.Comment: Talk given at the Nobel Symposium on Neutrino Physics, Enkoping, Sweden, Augus 19-24, 2004; 16 page

On the axisymmetric steady incompressible Beltrami flows

In this paper, Beltrami vector fields in several orthogonal coordinate systems are obtained analytically and numerically. Specifically, axisymmetric incompressible inviscid steady state Beltrami (Trkalian) fluid flows are obtained with the motivation to model flows that have been hypothesized to occur in tornadic flows. The studied coordinate systems include those that appear amenable to modeling such flows: the cylindrical, spherical, paraboloidal, and prolate and oblate spheroidal systems. The usual Euler equations are reformulated using the Bragg-Hawthorne equation for the stream function of the flow, which is solved analytically or numerically in each coordinate system under the assumption of separability of variables. Many of the obtained flows are visualized via contour plots of their stream functions in the rz-plane. Finally, the results are combined to provide a qualitative quasi-static model for a progression of tornado-like flows that develop as swirl increases. The results in this paper are equally applicable in electromagnetics, where the equivalent concept is that of a force-free magnetic field