Hamiltonians for curves

We examine the equilibrium conditions of a curve in space when a local energy penalty is associated with its extrinsic geometrical state characterized by its curvature and torsion. To do this we tailor the theory of deformations to the Frenet-Serret frame of the curve. The Euler-Lagrange equations describing equilibrium are obtained; Noether's theorem is exploited to identify the constants of integration of these equations as the Casimirs of the euclidean group in three dimensions. While this system appears not to be integrable in general, it {\it is} in various limits of interest. Let the energy density be given as some function of the curvature and torsion, $f(\kappa,\tau)$. If $f$ is a linear function of either of its arguments but otherwise arbitrary, we claim that the first integral associated with rotational invariance permits the torsion $\tau$ to be expressed as the solution of an algebraic equation in terms of the bending curvature, $\kappa$. The first integral associated with translational invariance can then be cast as a quadrature for $\kappa$ or for $\tau$.Comment: 17 page

Low angular momentum accretion in the collapsar: how long can a long GRB be?

The collapsar model is the most promising scenario to explain the huge release of energy associated with long duration gamma-ray-bursts (GRBs). Within this scenario GRBs are believed to be powered by accretion through a rotationally support torus or by fast rotation of a compact object. In both cases then, rotation of the progenitor star is one of the key properties because it must be high enough for the torus to form, the compact object to rotate very fast, or both. Here, we check what rotational properties a progenitor star must have in order to sustain torus accretion over relatively long activity periods as observed in most GRBs. We show that simple, often cited, estimates of the total mass available for torus formation and consequently the duration of a GRB are only upper limits. We revise these estimates by taking into account the long term effect that as the compact object accretes the minimum specific angular momentum needed for torus formation increases. This in turn leads to a smaller fraction of the stellar envelope that can form a torus. We demostrate that this effect can lead to a significant, an order of magnidute, reduction of the total energy and overall duration of a GRB event. This of course can be mitigated by assuming that the progenitor star rotates faster then we assumed. However, our assumed rotation is already high compared to observational and theoretical constraints. We also discuss implications of our result.Comment: 29 pages, 10 figures, including 1 color fig., revised version accepted by Ap

Localized induction equation and pseudospherical surfaces

We describe a close connection between the localized induction equation hierarchy of integrable evolution equations on space curves, and surfaces of constant negative Gauss curvature.Comment: 21 pages, AMSTeX file. To appear in Journal of Physics A: Mathematical and Genera

Atomic oxygen beam source for erosion simulation

A device for the production of low energy (3 to 10 eV) neutral atomic beams for surface modification studies is described that reproduces the flux of atomic oxygen in low Earth orbit. The beam is produced by the acceleration of plasma ions onto a negatively biased plate of high-Z metal; the ions are neutralized and reflected by the surface, retaining some fraction of their incident kinetic energy, forming a beam of atoms. The plasma is generated by a coaxial RF exciter which produces a magnetically-confined (4 kG) plasma column. At the end of the column, ions fall through the sheath to the plate, whose bias relative to the plasma can be varied to adjust the beam energy. The source provides a neutral flux approximately equal to 5 x 10(exp 16)/sq cm at a distance of 9 cm and a fluence approximately equal to 10(exp 20)/sq cm in five hours. The composition and energy of inert gas beams was diagnosed using a mass spectometer/energy analyzer. The energy spectra of the beams demonstrate energies in the range 5 to 15 eV, and qualitatively show expected dependences upon incident and reflecting atom species and potential drop. Samples of carbon film, carbon-based paint, Kapton, mylar, and teflon exposed to atomic O beams show erosion quite similar to that observed in orbit on the space shuttle

Morphology of Polyanhydride Microsphere Delivery Systems

Scanning electron microscopy (SEM) was used to elucidate the mechanism of polymer degradation and drug release in polyanhydride microspheres. Three different fabrication methods — solvent removal, solvent evaporation, and hot melt microencapsulation — were used to prepare polyanhydride microspheres containing a variety of drugs. The morphology of these microspheres releasing drug in vitro and in vivo was studied by SEM and compared with degradation and release data measured by conventional methods. Microspheres prepared by the three techniques were shown to have distinctive morphological characteristics induced by the nature of the fabrication method. In addition, SEM analysis could be used to explain the drug release profiles and polymer degradation behavior seen in vitro as well as the in vivo effects of insulin-loaded microspheres on diabetic rats. This study has shown SEM to be an important and powerful tool for analyzing the effects of microsphere fabrication method on drug release

Flux penetration in slab shaped Type-I superconductors

We study the problem of flux penetration into type--I superconductors with high demagnetization factor (slab geometry).Assuming that the interface between the normal and superconducting regions is sharp, that flux diffuses rapidly in the normal regions, and that thermal effects are negligible, we analyze the process by which flux invades the sample as the applied field is increased slowly from zero.We find that flux does not penetrate gradually.Rather there is an instability in the process and the flux penetrates from the boundary in a series of bursts, accompanied by the formation of isolated droplets of the normal phase, leading to a multiply connected flux domain structure similar to that seen in experiments.Comment: 4 pages, 2 figures, Fig 2.(b) available upon request from the authors, email - [email protected]

Randomized Benchmarking of Quantum Gates

A key requirement for scalable quantum computing is that elementary quantum gates can be implemented with sufficiently low error. One method for determining the error behavior of a gate implementation is to perform process tomography. However, standard process tomography is limited by errors in state preparation, measurement and one-qubit gates. It suffers from inefficient scaling with number of qubits and does not detect adverse error-compounding when gates are composed in long sequences. An additional problem is due to the fact that desirable error probabilities for scalable quantum computing are of the order of 0.0001 or lower. Experimentally proving such low errors is challenging. We describe a randomized benchmarking method that yields estimates of the computationally relevant errors without relying on accurate state preparation and measurement. Since it involves long sequences of randomly chosen gates, it also verifies that error behavior is stable when used in long computations. We implemented randomized benchmarking on trapped atomic ion qubits, establishing a one-qubit error probability per randomized pi/2 pulse of 0.00482(17) in a particular experiment. We expect this error probability to be readily improved with straightforward technical modifications.Comment: 13 page