Solution to the Equations of the Moment Expansions

We develop a formula for matching a Taylor series about the origin and an asymptotic exponential expansion for large values of the coordinate. We test it on the expansion of the generating functions for the moments and connected moments of the Hamiltonian operator. In the former case the formula produces the energies and overlaps for the Rayleigh-Ritz method in the Krylov space. We choose the harmonic oscillator and a strongly anharmonic oscillator as illustrative examples for numerical test. Our results reveal some features of the connected-moments expansion that were overlooked in earlier studies and applications of the approach

Three-dimensional Simulations of Disk Accretion to an Inclined Dipole: I. Magnetospheric Flow at Different Theta

We present results of fully three-dimensional MHD simulations of disk accretion to a rotating magnetized star with its dipole moment inclined at an angle Theta to the rotation axis of the disk. We observed that matter accretes from the disk to a star in two or several streams depending on Theta. Streams may precess around the star at small Theta. The inner regions of the disk are warped. The warping is due to the tendency of matter to co-rotate with inclined magnetosphere. The accreting matter brings positive angular momentum to the (slowly rotating) star tending to spin it up. The corresponding torque N_z depends only weakly on Theta. The angular momentum flux to the star is transported predominantly by the magnetic field; the matter component contributes < 1 % of the total flux. Results of simulations are important for understanding the nature of classical T Tauri stars, cataclysmic variables, and X-ray pulsars.Comment: 26 pages, 22 figures, LaTeX, macros: emulapj.sty, avi simulations are available at http://www.astro.cornell.edu/us-rus/inclined.ht

q-Breathers and the Fermi-Pasta-Ulam Problem

The Fermi-Pasta-Ulam (FPU) paradox consists of the nonequipartition of energy among normal modes of a weakly anharmonic atomic chain model. In the harmonic limit each normal mode corresponds to a periodic orbit in phase space and is characterized by its wave number $q$. We continue normal modes from the harmonic limit into the FPU parameter regime and obtain persistence of these periodic orbits, termed here $q$-Breathers (QB). They are characterized by time periodicity, exponential localization in the $q$-space of normal modes and linear stability up to a size-dependent threshold amplitude. Trajectories computed in the original FPU setting are perturbations around these exact QB solutions. The QB concept is applicable to other nonlinear lattices as well.Comment: 4 pages, 4 figure

Properties and nature of Be stars: 29. Orbital and long-term spectral variations of \gamma\ Cassiopei\ae

A detailed analysis of more than 800 electronic high-resolution spectra of gamma Cas, which were obtained during a time interval of over 6000 days (16.84 yrs) at several observatories, documents the smooth variations in the density and/or extend of its circumstellar envelope. We found a clear anticorrelation between the peak intensity and FWHM of the H alpha emission, which seems to agree with recent models of such emission lines. The main result of this study is a confirmation of the binary nature of the object, determination of a reliable linear ephemeris T_{min.RV} = HJD (2452081.9$\pm$0.6) + (203.52$\pm$0.08)*E, and a rather definitive set of orbital elements. We clearly demonstrated that the orbit is circular within the limits of accuracy of our measurements and has a semi-amplitude of radial-velocity curve of 4.30$\pm$0.09 (km/s). No trace of the low-mass secondary was found. The time distribution of our spectra does not allow a reliable investigation of rapid spectral variations, which are undoubtedly present in the spectra. We postpone this investigation for a future study, based on series of dedicated whole-night spectral observations

Multiple stressors: using the honeybee model BEEHAVE to explore how spatial and temporal forage stress affects colony resilience

The causes underlying the increased mortality of honeybee colonies (Apis mellifera) observed over the past decade remain unclear. Since so far the evidence for monocausal explanations is equivocal, involvement of multiple stressors is generally assumed. We here focus on various aspects of forage availability, which have received less attention than other stressors because it is virtually impossible to explore them empirically. We applied the colony model BEEHAVE, which links within-hive dynamics and foraging, to stylized landscape settings to explore how foraging distance, forage supply, and “forage gaps”, i.e. periods in which honeybees cannot find any nectar and pollen, affect colony resilience and the mechanisms behind. We found that colony extinction was mainly driven by foraging distance, but the timing of forage gaps had strongest effects on time to extinction. Sensitivity to forage gaps of 15 days was highest in June or July even if otherwise forage availability was sufficient to survive. Forage availability affected colonies via cascading effects on queen's egg-laying rate, reduction of new-emerging brood stages developing into adult workers, pollen debt, lack of workforce for nursing, and reduced foraging activity. Forage gaps in July led to reduction in egg-laying and increased mortality of brood stages at a time when the queen's seasonal egg-laying rate is at its maximum, leading to colony failure over time. Our results demonstrate that badly timed forage gaps interacting with poor overall forage supply reduce honeybee colony resilience. Existing regulation mechanisms which in principle enable colonies to cope with varying forage supply in a given landscape and year, such as a reduction in egg-laying, have only a certain capacity. Our results are hypothetical, as they are obtained from simplified landscape settings, but they are consistent with existing empirical knowledge. They offer ample opportunities for testing the predicted effects of forage stress in controlled experiments

Reentrant superconductivity in superconductor/ferromagnetic-alloy bilayers

We studied the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) like state establishing due to the proximity effect in superconducting Nb/Cu41Ni59 bilayers. Using a special wedge-type deposition technique, series of 20-35 samples could be fabricated by magnetron sputtering during one run. The layer thickness of only a few nanometers, the composition of the alloy, and the quality of interfaces were controlled by Rutherford backscattering spectrometry, high resolution transmission electron microscopy, and Auger spectroscopy. The magnetic properties of the ferromagnetic alloy layer were characterized with superconducting quantum interference device (SQUID) magnetometry. These studies yield precise information about the thickness, and demonstrate the homogeneity of the alloy composition and magnetic properties along the sample series. The dependencies of the critical temperature on the Nb and Cu41Ni59 layer thickness, Tc(dS) and Tc(dF), were investigated for constant thickness dF of the magnetic alloy layer and dS of the superconducting layer, respectively. All types of non-monotonic behaviors of Tc versus dF predicted by the theory could be realized experimentally: from reentrant superconducting behavior with a broad extinction region to a slight suppression of superconductivity with a shallow minimum. Even a double extinction of superconductivity was observed, giving evidence for the multiple reentrant behavior predicted by theory. All critical temperature curves were fitted with suitable sets of parameters. Then, Tc(dF) diagrams of a hypothetical F/S/F spin-switch core structure were calculated using these parameters. Finally, superconducting spin-switch fabrication issues are discussed in detail in view of the achieved results.Comment: 34 pages, 9 figure

Interdisciplinary design methodology for systems of mechatronic systems focus on highly dynamic environmental applications

This paper discusses a series of research challenges in the design of systems of mechatronic systems. A focus is given to environmental mechatronic applications within the chain “Renewable energy production - Smart grids - Electric vehicles”. For the considered mechatronic systems, the main design targets are formulated, the relations to state and parameter estimation, disturbance observation and rejection as well as control algorithms are highlighted. Finally, the study introduces an interdisciplinary design approach based on the intersectoral transfer of knowledge and collaborative experimental activities

Neural network based automatic limit prediction and avoidance system and method

A method for performance envelope boundary cueing for a vehicle control system comprises the steps of formulating a prediction system for a neural network and training the neural network to predict values of limited parameters as a function of current control positions and current vehicle operating conditions. The method further comprises the steps of applying the neural network to the control system of the vehicle, where the vehicle has capability for measuring current control positions and current vehicle operating conditions. The neural network generates a map of current control positions and vehicle operating conditions versus the limited parameters in a pre-determined vehicle operating condition. The method estimates critical control deflections from the current control positions required to drive the vehicle to a performance envelope boundary. Finally, the method comprises the steps of communicating the critical control deflection to the vehicle control system; and driving the vehicle control system to provide a tactile cue to an operator of the vehicle as the control positions approach the critical control deflections