Bessel-Zernike Discrete Variable Representation Basis

The connection between the Bessel discrete variable basis expansion and a specific form of an orthogonal set of Jacobi polynomials is demonstrated. These so-called Zernike polynomials provide alternative series expansions of suitable functions over the unit interval. Expressing a Bessel function in a Zernike expansion provides a straightforward method of generating series identities. Furthermore, the Zernike polynomials may also be used to efficiently evaluate the Hankel transform for rapidly decaying functions or functions with finite support

Closed-form solutions of the Schroedinger equation for a class of smoothed Coulomb potentials

An infinite family of closed-form solutions is exhibited for the Schroedinger equation for the potential $V(r) = -Z/\sqrt{|r|^{2} + a^{2}}$. Evidence is presented for an approximate dynamical symmetry for large values of the angular momentum $l$.Comment: 13 pages LaTeX, uses included Institute of Physics style files, 3 PostScript figures. In press at J. Phys. B: At. Mol. Opt. Phys. (1997

Failure Modes and Diagnostic Signatures Working Group - Ignition Diagnostics Requirements Update

We have performed an initial assessment of the sensitivity of various expected ignition diagnostic signatures to ignition failure modes using one and two-dimensional hydrodynamics simulations and post-processed simulated diagnostic output. As a result of this assessment, we recommend several changes to the current requirements for the ignition diagnostic suite. These recommendations are summarized in Table 1

Traveling through potential energy landscapes of disordered materials: the activation-relaxation technique

A detailed description of the activation-relaxation technique (ART) is presented. This method defines events in the configurational energy landscape of disordered materials, such as a-Si, glasses and polymers, in a two-step process: first, a configuration is activated from a local minimum to a nearby saddle-point; next, the configuration is relaxed to a new minimum; this allows for jumps over energy barriers much higher than what can be reached with standard techniques. Such events can serve as basic steps in equilibrium and kinetic Monte Carlo schemes.Comment: 7 pages, 2 postscript figure

High yield Cu-Co CPP GMR multilayer sensors

We have fabricated and tested GMR magnetic flux sensors that operate in the CPP mode. This work is a continuation of the ultra-high density magnetic sensor research introduced at INTERMAG 96. We have made two significant modifications to the process sequence. First, contact to the sensor is made through a metal conduit deposited in situ with the multilayers. This deposition replaces electroplating. This configuration ensures a good electrical interface between the top of multilayer stack and the top contact, and a continuous, conductive current path to the sensor. The consequences of this modification are an increase in yield of operational devices to {ge}90% per wafer and a significant reduction of the device resistance to {le}560 milliohms and of the uniformity of the device resistance to {le}3%. Second, the as-deposited multilayer structure has been changed from [Cu 30 {angstrom}/Co 20 {angstrom}]{sub 18} (third peak) to [Cu 20.5 {angstrom}/Co 12 {angstrom}]{sub 30} (second peak) to increase the CPP and CIP responses. The sheet film second peak CIP GMR response is 18% and the sensitivity is 0.08 %/Oe. The sheet film third peak CIP GMR response is 8% and the sensitivity is 0. 05 %/Oe. The second peak CPP GMR response averaged over twenty devices on a four inch silicon substrate is 28% {+-} 6%. The response decreases radially from the substrate center. The average response at the center of the substrate is 33% {+-} 4%. The average second peak CPP sensitivity is 0.09 %/Oe {+-} 0.02 %/Oe. The best second peak CPP response from a single device is 39%. The sensitivity of that device is 0.13 %/Oe. The third peak CPP GMR response is approximately 14 %. The third peak CPP response sensitivity is 0.07 %/Oe. 6 refs., 3 figs

Flux penetration and expulsion in thin superconducting disks

Using an expansion of the order parameter over the eigenfunctions of the linearized first Ginzburg-Landau (GL) equation, we obtain numerically the saddle points of the free energy separating the stable states with different number of vortices. In contrast to known surface and geometrical barrier models, we find that in a wide range of magnetic fields below the penetration field, the saddle point state for flux penetration into a disk does not correspond to a vortex located nearby the sample boundary, but to a region of suppressed superconductivity at the disk edge with no winding of the current, and which is {\it a nucleus} for the following vortex creation. The height of this {\it nucleation barrier}, which determines the time of flux penetration, is calculated for different disk radii and magnetic fields.Comment: Accepted for publication in Physical Review Letter

Chaos in Static Axisymmetric Spacetimes I : Vacuum Case

We study the motion of test particle in static axisymmetric vacuum spacetimes and discuss two criteria for strong chaos to occur: (1) a local instability measured by the Weyl curvature, and (2) a tangle of a homoclinic orbit, which is closely related to an unstable periodic orbit in general relativity. We analyze several static axisymmetric spacetimes and find that the first criterion is a sufficient condition for chaos, at least qualitatively. Although some test particles which do not satisfy the first criterion show chaotic behavior in some spacetimes, these can be accounted for the second criterion.Comment: More comments for the quantitative estimation of chaos are added, and some inappropriate terms are changed. This will appear on Class. Quant. Gra

Spontaneous emission of non-dispersive Rydberg wave packets

Non dispersive electronic Rydberg wave packets may be created in atoms illuminated by a microwave field of circular polarization. We discuss the spontaneous emission from such states and show that the elastic incoherent component (occuring at the frequency of the driving field) dominates the spectrum in the semiclassical limit, contrary to earlier predictions. We calculate the frequencies of single photon emissions and the associated rates in the "harmonic approximation", i.e. when the wave packet has approximately a Gaussian shape. The results agree well with exact quantum mechanical calculations, which validates the analytical approach.Comment: 14 pages, 4 figure

Assessing the Prospects for Achieving Double-Shell Ignition on the National Ignition Facility Using Vacuum Hohlraums

The goal of demonstrating ignition on the National Ignition Facility (NIF) has motivated a revisit of double-shell (DS) targets as a complementary path to the cryogenic baseline approach. Expected benefits of DS ignition targets include non-cryogenic deuterium-tritium (DT) fuel preparation, minimal hohlraum-plasma mediated laser backscatter, low threshold ignition temperatures ({approx} 4 keV) for relaxed hohlraum x-ray flux asymmetry tolerances, and minimal (two-) shock timing requirements. On the other hand, DS ignition presents several formidable challenges, encompassing room-temperature containment of high-pressure DT ({approx} 790 atm) in the inner shell, strict concentricity requirements on the two shells (< 3 {micro}m), development of nano-porous (<100 nm) low-density (<100 mg/cc) metallic foams for structural support of the inner shell and hydrodynamic instability mitigation, and effective control of hydrodynamic instabilities on the high-Atwood number interface between the DT fuel and the high-Z inner shell. Recent progress in DS ignition designs and required materials-science advances at the nanoscale are described herein. Two new ignition designs that use rugby-shaped vacuum hohlraums are presented which utilize either 1 MJ or 2 MJ of laser energy at 3{omega}. The capability of the NIF to generate the requested reverse-ramp pulse shape for DS ignition is expected to be comparable to the planned high-contrast ({approx}100) pulse-shape at 1.8 MJ for the baseline cryogenic target. Nano-crystalline, high-strength, Au-Cu alloy inner shells are under development using electrochemical deposition over a glass mandrel, exhibiting tensile strengths well in excess of 790 atm. Novel, low-density (85 mg/cc) copper foams have recently been demonstrated using 10 mg/cc SiO{sub 2} nano-porous aerogels with suspended Cu particles. A prototype demonstration of an ignition DS is planned for 2008, incorporating the needed novel nano-materials science developments and the required fabrication tolerances for a realistic ignition attempt after 2010