Nonlinear collective nuclear motion

For each real number $\Lambda$ a Lie algebra of nonlinear vector fields on three dimensional Euclidean space is reported. Although each algebra is mathematically isomorphic to $gl(3,{\bf R})$, only the $\Lambda=0$ vector fields correspond to the usual generators of the general linear group. The $\Lambda < 0$ vector fields integrate to a nonstandard action of the general linear group; the $\Lambda >0$ case integrates to a local Lie semigroup. For each $\Lambda$, a family of surfaces is identified that is invariant with respect to the group or semigroup action. For positive $\Lambda$ the surfaces describe fissioning nuclei with a neck, while negative $\Lambda$ surfaces correspond to exotic bubble nuclei. Collective models for neck and bubble nuclei are given by irreducible unitary representations of a fifteen dimensional semidirect sum spectrum generating algebra $gcm(3)$ spanned by its nonlinear $gl(3,{\bf R})$ subalgebra plus an abelian nonlinear inertia tensor subalgebra.Comment: 13 pages plus two figures(available by fax from authors by request

Algebraic nonlinear collective motion

Finite-dimensional Lie algebras of vector fields determine geometrical collective models in quantum and classical physics. Every set of vector fields on Euclidean space that generates the Lie algebra sl(3, R) and contains the angular momentum algebra so(3) is determined. The subset of divergence-free sl(3, R) vector fields is proven to be indexed by a real number $\Lambda$. The $\Lambda=0$ solution is the linear representation that corresponds to the Riemann ellipsoidal model. The nonlinear group action on Euclidean space transforms a certain family of deformed droplets among themselves. For positive $\Lambda$, the droplets have a neck that becomes more pronounced as $\Lambda$ increases; for negative $\Lambda$, the droplets contain a spherical bubble of radius $|\Lambda|^{{1/3}}$. The nonlinear vector field algebra is extended to the nonlinear general collective motion algebra gcm(3) which includes the inertia tensor. The quantum algebraic models of nonlinear nuclear collective motion are given by irreducible unitary representations of the nonlinear gcm(3) Lie algebra. These representations model fissioning isotopes ($\Lambda>0$) and bubble and two-fluid nuclei ($\Lambda<0$).Comment: 32pages, 4 figures not include

Global Time Distribution via Satellite-Based Sources of Entangled Photons

We propose a satellite-based scheme to perform clock synchronization between ground stations spread across the globe using quantum resources. We refer to this as a quantum clock synchronization (QCS) network. Through detailed numerical simulations, we assess the feasibility and capabilities of a near-term implementation of this scheme. We consider a small constellation of nanosatellites equipped only with modest resources. These include quantum devices such as spontaneous parametric down conversion (SPDC) sources, avalanche photo-detectors (APDs), and moderately stable on-board clocks such as chip scale atomic clocks (CSACs). In our simulations, the various performance parameters describing the hardware have been chosen such that they are either already commercially available, or require only moderate advances. We conclude that with such a scheme establishing a global network of ground based clocks synchronized to sub-nanosecond level (up to a few picoseconds) of precision, would be feasible. Such QCS satellite constellations would form the infrastructure for a future quantum network, able to serve as a globally accessible entanglement resource. At the same time, our clock synchronization protocol, provides the sub-nanosecond level synchronization required for many quantum networking protocols, and thus, can be seen as adding an extra layer of utility to quantum technologies in the space domain designed for other purposes.Comment: 20 pages, 12 figures and 6 tables. Comments are welcom

Automated detection of Karnal bunt teliospores

Karnal bunt is a fungal disease which infects wheat and, when present in wheat crops, yields it unsatisfactory for human consumption. Due to the fact that Karnal bunt (KB) is difficult to detect in the field, samples are taken to laboratories where technicians use microscopes and methodically search for KB teliospores. AlliedSignal Federal Manufacturing and Technologies (FM and T), working with the Kansas Department of Agriculture, created a system which utilizes pattern recognition, feature extraction, and neural networks to prototype an automated detection system for identifying KB teliospores. System hardware consists of a biological compound microscope, motorized stage, CCD camera, frame grabber, and a PC. Integration of the system hardware with custom software comprises the machine vision system. Fundamental processing steps involve capturing an image from the slide, while concurrently processing the previous image. Features extracted from the acquired imagery are then processed by a neural network classifier which has been trained to recognize spore-like objects. Images with spore-like objects are reviewed by trained technicians. Benefits of this system include: (1) reduction of the overall cycle-time; (2) utilization of technicians for intelligent decision making (vs. manual searching); (3) a regulatory standard which is quantifiable and repeatable; (4) guaranteed 100% coverage of the cover slip; and (5) significantly enhanced detection accuracy