Variational Integrators for Almost-Integrable Systems

We construct several variational integrators--integrators based on a discrete variational principle--for systems with Lagrangians of the form L = L_A + epsilon L_B, with epsilon << 1, where L_A describes an integrable system. These integrators exploit that epsilon << 1 to increase their accuracy by constructing discrete Lagrangians based on the assumption that the integrator trajectory is close to that of the integrable system. Several of the integrators we present are equivalent to well-known symplectic integrators for the equivalent perturbed Hamiltonian systems, but their construction and error analysis is significantly simpler in the variational framework. One novel method we present, involving a weighted time-averaging of the perturbing terms, removes all errors from the integration at O(epsilon). This last method is implicit, and involves evaluating a potentially expensive time-integral, but for some systems and some error tolerances it can significantly outperform traditional simulation methods.Comment: 14 pages, 4 figures. Version 2: added informative example; as accepted by Celestial Mechanics and Dynamical Astronom

Discrete Variational Optimal Control

This paper develops numerical methods for optimal control of mechanical systems in the Lagrangian setting. It extends the theory of discrete mechanics to enable the solutions of optimal control problems through the discretization of variational principles. The key point is to solve the optimal control problem as a variational integrator of a specially constructed higher-dimensional system. The developed framework applies to systems on tangent bundles, Lie groups, underactuated and nonholonomic systems with symmetries, and can approximate either smooth or discontinuous control inputs. The resulting methods inherit the preservation properties of variational integrators and result in numerically robust and easily implementable algorithms. Several theoretical and a practical examples, e.g. the control of an underwater vehicle, will illustrate the application of the proposed approach.Comment: 30 pages, 6 figure

An evaluation of combined geophysical and geotechnical methods to characterize beach thickness

Beaches provide sediment stores and have an important role in the development of the coastline in response to climate change. Quantification of beach thickness and volume is required to assess coastal sediment transport budgets. Therefore, portable, rapid, non-invasive techniques are required to evaluate thickness where environmental sensitivities exclude invasive methods. Site methods and data are described for a toolbox of electrical, electromagnetic, seismic and mechanical based techniques that were evaluated at a coastal site at Easington, Yorkshire. Geophysical and geotechnical properties are shown to be dependent upon moisture content, porosity and lithology of the beach and the morphology of the beach–platform interface. Thickness interpretation, using an inexpensive geographic information system to integrate data, allowed these controls and relationships to be understood. Guidelines for efficient site practices, based upon this case history including procedures and techniques, are presented using a systematic approach. Field results indicated that a mixed sand and gravel beach is highly variable and cannot be represented in models as a homogeneous layer of variable thickness overlying a bedrock half-space

Atomic position localization via dual measurement

We study localization of atomic position when a three-level atom interacts with a quantized standing-wave field in the Ramsey interferometer setup. Both the field quadrature amplitude and the atomic internal state are measured to obtain the atomic position information. It is found that this dual measurement scheme produces an interference pattern superimposed on a diffraction-like pattern in the atomic position distribution, where the former pattern originates from the state-selective measurement and the latter from the field measurement. The present scheme results in a better resolution in the position localization than the field-alone measurement schemes. We also discuss the measurement-correlated mechanical action of the standing-wave field on the atom in the light of Popper's test.Comment: 6.5 pages and 5 figure

Sericin Promotes Fibroin Silk I Stabilization Across a Phase-Separation.

Natural silk spinning offers several advantages over the synthetic fiber spinning, although the underlying mechanisms of this process are yet to be fully elucidated. Silkworm silks, specifically B. mori, comprise two main proteins: fibroin, which forms the fiber, and sericin, a coextruded coating that acts as a matrix in the resulting nonwoven composite cocoon. To date, most studies have focused on fibroin's self-assembly and gelation, with the influence of sericin during spinning receiving little to no attention. This study investigates sericin's effects on the self-assembly of fibroin via their natural phase-separation. Through changes in sample opacity, FTIR, and XRD, we report that increasing sericin concentration retards the time to gelation and β-sheet formation of fibroin, causing it to adopt a Silk I conformation. Such findings have important implications for both the natural silk spinning process and any future industrial applications, suggesting that sericin may be able to induce long-range conformational and stability control in silk fibroin, while being in a separate phase, a factor that would facilitate long-term storage or silk feedstocks

Geometry, Scaling and Universality in the Mass Distributions in Heavy Ion Collisions

Various features of the mass yields in heavy ion collisions are studied. The mass yields are discussed in terms of iterative one dimensional discrete maps. These maps are shown to produce orbits for a monomer or for a nucleus which generate the mass yields and the distribution of cluster sizes. Simple Malthusian dynamics and non-linear Verhulst dynamics are used to illustrate the approach. Nuclear cobwebbing, attractors of the dynamics, and Lyapanov exponents are discussed for the mass distribution. The self-similar property of the Malthusian orbit offers a new variable for the study of scale invariance using power moments of the mass distribution. Correlation lengths, exponents and dimensions associated with scaling relations are developed. Fourier transforms of the mass distribution are used to obtain power spectra which are investigated for a $1/f^{\beta}$ behavior.Comment: 29 pages in REVTEX, 9 figures (available from the authors), RU-92-0

The Liquid-Gas Phase Transitions in a Multicomponent Nuclear System with Coulomb and Surface Effects

The liquid-gas phase transition is studied in a multi-component nuclear system using a local Skyrme interaction with Coulomb and surface effects. Some features are qualitatively the same as the results of Muller and Serot which uses relativistic mean field without Coulomb and surface effects. Surface tension brings the coexistance binodal surface to lower pressure. The Coulomb interaction makes the binodal surface smaller and cause another pair of binodal points at low pressure and large proton fraction with less protons in liquid phase and more protons in gas phase.Comment: 20 pages including 7 postscript figure

Quantification of bioactive compound content in advanced fenugreek lines selected in Alberta: levels of galactomannan

Non-Peer ReviewedFenugreek (Trigonella foenum-graecum L.) was initially introduced to Alberta as a spice and forage crop. Numerous animal and clinical studies have associated the medicinal properties of the plant with galactomannan, diosgenin and 4-hydroxyisoleucine, the three major bioactive compounds found in fenugreek seed. These bioactive molecules have been demonstrated to regulate plasma cholesterol levels, reduce plasma triglyceride concentrations and stimulate insulin secretion for blood glucose metabolism. Fourteen advanced lines grown satisfactorily in southern Alberta were selected for quantification of these compounds over two harvest seasons. These lines were grown at three locations (Brooks, Bow Island and Lethbridge) in southern Alberta under two growing conditions (rain-fed or irrigated). In this study we report on five different seed lines which possessed a high galactomannan yield during the study; i.e., seed lines F75, L3312, CDC Quatro, F80 and L3308. Seed line F75 was the only line that performed well across all locations and growing conditions. It was observed that seed yield had a greater influence on galactomannan yield compared to seed galactomannan content. This suggests that cultivation of fenugreek plants for neutraceutical purposes should emphasize lines with high seed yield, as galactomannan content does not vary significantly among lines. An understanding of the interaction of bioactive compound content with respective ecotypes will assist in the selection of lines for their economic potential in the functional food and natural health product industry

Chasing the identification of ASCA Galactic Objects (ChIcAGO): An X-ray survey of unidentified sources in the galactic plane. I : Source sample and initial results

We present the Chasing the Identification of ASCA Galactic Objects (ChIcAGO) survey, which is designed to identify the unknown X-ray sources discovered during the ASCA Galactic Plane Survey (AGPS). Little is known about most of the AGPS sources, especially those that emit primarily in hard X-rays (2-10 keV) within the Fx 10-13 to 10-11 erg cm -2 s-1 X-ray flux range. In ChIcAGO, the subarcsecond localization capabilities of Chandra have been combined with a detailed multiwavelength follow-up program, with the ultimate goal of classifying the >100 unidentified sources in the AGPS. Overall to date, 93 unidentified AGPS sources have been observed with Chandra as part of the ChIcAGO survey. A total of 253 X-ray point sources have been detected in these Chandra observations within 3′ of the original ASCA positions. We have identified infrared and optical counterparts to the majority of these sources, using both new observations and catalogs from existing Galactic plane surveys. X-ray and infrared population statistics for the X-ray point sources detected in the Chandra observations reveal that the primary populations of Galactic plane X-ray sources that emit in the Fx 10-13 to 10-11 erg cm -2 s-1 flux range are active stellar coronae, massive stars with strong stellar winds that are possibly in colliding wind binaries, X-ray binaries, and magnetars. There is also another primary population that is still unidentified but, on the basis of its X-ray and infrared properties, likely comprises partly Galactic sources and partly active galactic nuclei.Peer reviewedSubmitted Versio