Shilnikov Lemma for a nondegenerate critical manifold of a Hamiltonian system

We prove an analog of Shilnikov Lemma for a normally hyperbolic symplectic critical manifold $M\subset H^{-1}(0)$ of a Hamiltonian system. Using this result, trajectories with small energy $H=\mu>0$ shadowing chains of homoclinic orbits to $M$ are represented as extremals of a discrete variational problem, and their existence is proved. This paper is motivated by applications to the Poincar\'e second species solutions of the 3 body problem with 2 masses small of order $\mu$. As $\mu\to 0$, double collisions of small bodies correspond to a symplectic critical manifold of the regularized Hamiltonian system

Distributed computing system with dual independent communications paths between computers and employing split tokens

This is a distributed computing system providing flexible fault tolerance; ease of software design and concurrency specification; and dynamic balance of the loads. The system comprises a plurality of computers each having a first input/output interface and a second input/output interface for interfacing to communications networks each second input/output interface including a bypass for bypassing the associated computer. A global communications network interconnects the first input/output interfaces for providing each computer the ability to broadcast messages simultaneously to the remainder of the computers. A meshwork communications network interconnects the second input/output interfaces providing each computer with the ability to establish a communications link with another of the computers bypassing the remainder of computers. Each computer is controlled by a resident copy of a common operating system. Communications between respective ones of computers is by means of split tokens each having a moving first portion which is sent from computer to computer and a resident second portion which is disposed in the memory of at least one of computer and wherein the location of the second portion is part of the first portion. The split tokens represent both functions to be executed by the computers and data to be employed in the execution of the functions. The first input/output interfaces each include logic for detecting a collision between messages and for terminating the broadcasting of a message whereby collisions between messages are detected and avoided

Anisotropic magnetoresistance in nanocontacts

We present ab initio calculations of the evolution of anisotropic magnetoresistance (AMR) in Ni nanocontacts from the ballistic to the tunnel regime. We find an extraordinary enhancement of AMR, compared to bulk, in two scenarios. In systems without localized states, like chemically pure break junctions, large AMR only occurs if the orbital polarization of the current is large, regardless of the anisotropy of the density of states. In systems that display localized states close to the Fermi energy, like a single electron transistor with ferromagnetic electrodes, large AMR is related to the variation of the Fermi energy as a function of the magnetization direction.Comment: 7 pages, 4 figures; revised for publication, new figures in greyscal

Symbolic dynamics for the NN-centre problem at negative energies

We consider the planar $N$-centre problem, with homogeneous potentials of degree -\a<0, \a \in [1,2). We prove the existence of infinitely many collisions-free periodic solutions with negative and small energy, for any distribution of the centres inside a compact set. The proof is based upon topological, variational and geometric arguments. The existence result allows to characterize the associated dynamical system with a symbolic dynamics, where the symbols are the partitions of the $N$ centres in two non-empty sets

Photoresponse of PbS nanoparticles-quaterthiophene films prepared by gaseous deposition as probed by XPS

Cataloged from PDF version of article.Semiconducting lead sulfide (PbS) nanoparticles were cluster beam deposited into evaporated quaterthiophene (4T) organic films, which in some cases were additionally modified by simultaneous 50 eV acetylene ion bombardment. Surface chemistry of these nanocomposite films was first examined using standard x-ray photoelectron spectroscopy (XPS). XPS was also used to probe photoinduced shifts in peak binding energies upon illumination with a continuous wave green laser and the magnitudes of these peak shifts were interpreted as changes in relative photoconductivity. The four types of films examined all displayed photoconductivity: 4T only, 4T with acetylene ions, 4T with PbS nanoparticles, and 4T with both PbS nanoparticles and acetylene ions. Furthermore, the ion-modified films displayed higher photoconductivity, which was consistent with enhanced bonding within the 4T organic matrix and between 4T and PbS nanoparticles. PbS nanoparticles displayed higher photoconductivity than the 4T component, regardless of ion modification. (C) 2012 American Vacuum Society

How close can one approach the Dirac point in graphene experimentally?

The above question is frequently asked by theorists who are interested in graphene as a model system, especially in context of relativistic quantum physics. We offer an experimental answer by describing electron transport in suspended devices with carrier mobilities of several 10^6 cm^2V^-1s^-1 and with the onset of Landau quantization occurring in fields below 5 mT. The observed charge inhomogeneity is as low as \approx10^8 cm^-2, allowing a neutral state with a few charge carriers per entire micron-scale device. Above liquid helium temperatures, the electronic properties of such devices are intrinsic, being governed by thermal excitations only. This yields that the Dirac point can be approached within 1 meV, a limit currently set by the remaining charge inhomogeneity. No sign of an insulating state is observed down to 1 K, which establishes the upper limit on a possible bandgap

The Non-Trapping Degree of Scattering

We consider classical potential scattering. If no orbit is trapped at energy E, the Hamiltonian dynamics defines an integer-valued topological degree. This can be calculated explicitly and be used for symbolic dynamics of multi-obstacle scattering. If the potential is bounded, then in the non-trapping case the boundary of Hill's Region is empty or homeomorphic to a sphere. We consider classical potential scattering. If at energy E no orbit is trapped, the Hamiltonian dynamics defines an integer-valued topological degree deg(E) < 2. This is calculated explicitly for all potentials, and exactly the integers < 2 are shown to occur for suitable potentials. The non-trapping condition is restrictive in the sense that for a bounded potential it is shown to imply that the boundary of Hill's Region in configuration space is either empty or homeomorphic to a sphere. However, in many situations one can decompose a potential into a sum of non-trapping potentials with non-trivial degree and embed symbolic dynamics of multi-obstacle scattering. This comprises a large number of earlier results, obtained by different authors on multi-obstacle scattering.Comment: 25 pages, 1 figure Revised and enlarged version, containing more detailed proofs and remark

VLBI-derived troposphere parameters during CONT08

Time-series of zenith wet and total troposphere delays as well as north and east gradients are compared, and zenith total delays (ZTD) are combined on the level of parameter estimates. Input data sets are provided by ten Analysis Centers (ACs) of the International VLBI Service for Geodesy and Astrometry (IVS) for the CONT08 campaign (12-26 August 2008). The inconsistent usage of meteorological data and models, such as mapping functions, causes systematics among the ACs, and differing parameterizations and constraints add noise to the troposphere parameter estimates. The empirical standard deviation of ZTD among the ACs with regard to an unweighted mean is 4.6 mm. The ratio of the analysis noise to the observation noise assessed by the operator/software impact (OSI) model is about 2.5. These and other effects have to be accounted for to improve the intra-technique combination of VLBI-derived troposphere parameters. While the largest systematics caused by inconsistent usage of meteorological data can be avoided and the application of different mapping functions can be considered by applying empirical corrections, the noise has to be modeled in the stochastic model of intra-technique combination. The application of different stochastic models shows no significant effects on the combined parameters but results in different mean formal errors: the mean formal errors of the combined ZTD are 2.3 mm (unweighted), 4.4 mm (diagonal), 8.6 mm [variance component (VC) estimation], and 8.6 mm (operator/software impact, OSI). On the one hand, the OSI model, i.e. the inclusion of off-diagonal elements in the cofactor-matrix, considers the reapplication of observations yielding a factor of about two for mean formal errors as compared to the diagonal approach. On the other hand, the combination based on VC estimation shows large differences among the VCs and exhibits a comparable scaling of formal errors. Thus, for the combination of troposphere parameters a combination of the two extensions of the stochastic model is recommended

Electronic structure, magnetic and optical properties of intermetallic compounds R2Fe17 (R=Pr,Gd)

In this paper we report comprehensive experimental and theoretical investigation of magnetic and electronic properties of the intermetallic compounds Pr2Fe17 and Gd2Fe17. For the first time electronic structure of these two systems was probed by optical measurements in the spectral range of 0.22-15 micrometers. On top of that charge carriers parameters (plasma frequency and relaxation frequency) and optical conductivity s(w) were determined. Self-consistent spin-resolved bandstructure calculations within the conventional LSDA+U method were performed. Theoretical interpetation of the experimental s(w) dispersions indicates transitions between 3d and 4p states of Fe ions to be the biggest ones. Qualitatively the line shape of the theoretical optical conductivity coincides well with our experimental data. Calculated by LSDA+U method magnetic moments per formula unit are found to be in good agreement with observed experimental values of saturation magnetization.Comment: 16 pages, 5 figures, 1 tabl