Positive Lyapunov exponents for a class of deterministic potentials

LetV() be a smooth, non-constant function on the torus and letT be a hyperbolic toral automorphism. Consider a discrete one dimensional Schrödinger operatorH, whose potential at sitej is given bygV _j =gV(T ^j ). We prove that wheng0 is small andg ^1/2 |E|2–g ^1/2 , the Lyapunov exponent for the cocycle generated byH-E is proportional tog ². The proof relies on a formula of Pastur and Figotin and on symbolic dynamics.     

Generalized hypergeometric functions and rational curves on Calabi-Yau complete intersections in toric varieties

We formulate general conjectures about the relationship between the A-model connection on the cohomology of ad-dimensional Calabi-Yau complete intersectionV ofr hypersurfacesV ₁ ,...,V _r in a toric varietyP and the system of differential operators annihilating the special generalized hypergeometric series ⁰ constructed from the fan . Using this generalized hypergeometric series, we propose conjectural mirrorsV ofV and the canonicalq-coordinates on the moduli spaces of Calabi-Yau manifolds.In the second part of the paper we consider some examples of Calabi-Yau 3-folds having Picard number >1 in products of projective spaces. For conjectural mirrors, using the recurrent relation among coefficients of the restriction of the hypergeometric function ⁰ on a special line in the moduli space, we determine the Picard-Fuchs equation satisfied by periods of this special one-parameter subfamily. This allows to obtain some sequences of integers which can be conjecturally interpreted in terms of Gromov-Witten invariants. Using standard techniques from enumerative geometry, first terms of these sequence of integers are checked to coincide with numbers of rational curves on Calabi-Yau 3-folds.     

Optimization of spin-valve parameters for magnetic bead trapping and manipulation

Magneto-optic Kerr effect (MOKE) and magnetoresistance (MR) measurements were used to measure the switching characteristics of spin-valve (SV) arrays currently being developed to trap and release superparamagnetic beads within a fluid medium. The effect of SV size on switching observed by MOKE showed that a 1 μm×8 μm SV element was found to have optimal switching characteristics. MR measurements on a single 1 μm×8 μm SV switched with either an external applied magnetic field or a local magnetic field generated by an integrated write wire (current density ranging from 10⁶ to 10⁷ A/cm²) confirmed the MOKE findings. The 1 μm×8 μm SV low field switching was observed to be +8 and −2 mT with two stable states at zero field; the high field switching was observed to be −18 mT. The low switching fields and the large magnetic moment of the SV trap along with our observation of minimal magnetostatic effects for dense arrays are necessary design characteristics for high-force, “switchable-magnet,” microfluidic bead trap applications.     

Tracking X‐ray‐derived redox changes in crystals of a methylamine dehydrogenase/amicyanin complex using single‐crystal UV/Vis microspectrophotometry

X‐ray exposure during crystallographic data collection can result in unintended redox changes in proteins containing functionally important redox centers. In order to directly monitor X‐ray‐derived redox changes in trapped oxidative half‐reaction intermediates of Paracoccus denitrificans methylamine dehydrogenase, a commercially available single‐crystal UV/Vis microspectrophotometer was installed on‐line at the BioCARS beamline 14‐BM‐C at the Advanced Photon Source, Argonne, USA. Monitoring the redox state of the intermediates during X‐ray exposure permitted the creation of a general multi‐crystal data collection strategy to generate true structures of each redox intermediate.     

Use of quartz crystal nanobalance to study the binding and stabilization of albumin and doxycycline on a thin layer of hydroxyapatite

This study reports the use of quartz crystal nanobalance (QCN) to study the adsorption of two model molecules namely albumin and doxycycline by hydroxyapatite (HA). The work focuses on the deposition of a stable coating of HA on the quartz crystal, modification of the coating using doxycycline and its subsequent effects on albumin adsorption. The uniformity and thickness of the HA coating has been studied using atomic force microscopy (AFM). The functional groups to ascertain the presence of the selected moieties have been characterized by Raman spectroscopy. The results indicate that the mass of albumin deposited on the surface of the HA coated quartz crystal functionalized with doxycycline shows a substantial increase when compared to the standard HA coated quartz crystal. The adsorbed albumin has also been found to be retained for an enhanced period of time. This surface immobilization of doxycycline and subsequent albumin adsorption seem to be a promising approach to confer biomaterials with antithrombogenic and antibacterial surfaces.     

Surface chemistry and optimization of focused ion beam iodine-enhanced etching of indium phosphide

Focused ion beam physical sputtering and iodine-enhanced etching of indium phosphide (InP) were performed. Up to 15× enhanced etching rates over sputtering were measured at room temperature, due to the addition of iodine to the sputter-process. Reaction mechanisms and products are discussed and characterized. The reaction is limited by the desorption of indium triiodide (InI₃) at room temperature. InI₃ has to be removed by sputtering, which simultaneously amorphizes the underlying substrate. Surface roughness and stoichiometry of InP are compared for sputtering and etching. Gallium-contamination and the damaged zone in InP are significantly reduced by iodine-enhanced etching. Based on the reaction mechanisms, an optimum beam scanning strategy is proposed which allows precise microfabrication in reduced time and minimizes damage to the substrate. The method is also applicable for other halide gas etching processes of III-V semiconductors.     

Solitons in geometric potentials

We show that the geometrically induced potential existing in undulated slab waveguides dramatically affects the properties of solitons. In particular, whereas solitons residing in the potential maxima do not feature power thresholds and are stable, their counterparts residing in the potential minima are unstable and may exhibit a power threshold for their existence. Additionally, the geometric potential is shown to support stable multipole solitons that cannot be supported by straight waveguides. Finally, the geometric potential results in the appearance of the effective barriers that prevent transverse soliton motion.     

Dual-core ytterbium fiber amplifier for high-power 1060 nm swept source multichannel optical coherence tomography imaging

A novel (to our knowledge) dual-core ytterbium (Yb(3+)) doped fiber, as an optically pumped amplifier, boosts the output power from a 1060 nm swept source laser beyond 250 mW, while providing a wavelength tuning range of 93 nm, for optical coherence tomography (OCT) imaging. The design of the dual-core Yb-doped fiber amplifier and its multiple wavelength optical pumping scheme to optimize output bandwidth are discussed. Use of the dual-core fiber amplifier showed no appreciable degradation to the coherence length of the seed laser. The signal intensity improvement of this amplifier is demonstrated on a multichannel in vivo OCT imaging system at 1060 nm.     

A CTRW-based model of time-resolved fluorescence lifetime imaging in a turbid medium

We develop an analytic model of time-resolved fluorescent imaging of photons migrating through a semi-infinite turbid medium bounded by an infinite plane in the presence of a single stationary point fluorophore embedded in the medium. In contrast to earlier models of fluorescent imaging in which photon motion is assumed to be some form of continuous diffusion process, the present analysis is based on a continuous-time random walk (CTRW) on a simple cubic lattice, the objective being to estimate the position and lifetime of the fluorophore. This can provide information related to local variations in pH and temperature with potential medical significance. Aspects of the theory were tested using time-resolved measurements of the fluorescence from small inclusions inside tissue-like phantoms. The experimental results were found to be in good agreement with theoretical predictions provided that the fluorophore was not located too close to the planar boundary, a common problem in many diffusive systems.     

Group Foundations of Quantum and Classical Dynamics : Towards a Globalization and Classification of Some of Their Structures

This paper is devoted to a constructiveand critical analysis of the structure of certain dynamical systems from a group manifold point of view recently developed. This approach is especially suitable for discussing the structure of the quantum theory, the classical limit, the Hamilton-Jacobi theory and other problems such as the definition and globalization of the Poincaré-Cartan form which appears in the variational approach to higher order dynamical systems. At the same time, i t opens a way for the classification of all hamiltonian and lagrangian systems associated with suitably defined dynamical groups. Both classical and quantum dynamics are discussed, and examples of all the different structures appearingin the theory are provided, including a treatment of constrained and generalized higher order dynamical systems.