Response to "Comment on 'Finding finite-time invariant manifolds in two-dimensional velocity fields' " [Chaos 11, 427 (2001)

Lapeyre, Hua, and Legras have recently suggested that the detection of finite-time invariant manifolds in two-dimensional fluid flows, as described by Haller and Haller and Yuan, can be substantially improved. In particular, they suggested (a) a change of coordinates to strain basis before the application of Theorem 1 of Haller and (b) the use of a nondimensionalized time computed from Theorem 1. Here we discuss why these proposed steps will not result in a significant overall improvement. We verify our arguments in a more detailed computation of the example analyzed in Lapeyre, Hau, and Legras (the Kida ellipse), as well as in a two-dimensional barotropic turbulence simulation. While in both of these examples the techniques suggested by Lapeyre, Hau, and Legras reveal additional thin regions of hyperbolicity near vortex cores, they also lead to an overall loss of detail in the global computation of finite-time invariant manifolds. (c) 2001 American Institute of Physics.     

Nickel(II)-catalyzed highly enantioselective hydrophosphination of methacrylonitrile

The dicationic Ni(II) complex [Ni(Pigiphos)(THF)](ClO4)2, [1](ClO4)2 ((R)-(S)-Pigiphos = bis-{(R)-1-[(S)-2-(diphenylphosphino)ferrocenyl]ethyl}cyclohexylphosphine), catalyzes the addition of bulky aliphatic secondary phosphines to methaacrylonitrile. This hydrophosphination reaction reaches TON = 900 and enantioselectivities up to 94%. A catalytic cycle involving 1,4-conjugate addition of R2PH to methacrylonitrile is supported by the isolation and characterization of a catalytically active N-coordinated, methacrylonitrile Ni complex.     

Sulfated poly-amido-saccharides (sulPASs) are anticoagulants in vitro and in vivo

Anticoagulant therapeutics are a mainstay of modern surgery and of clotting disorder management such as venous thrombosis, yet performance and supply limitations exist for the most widely used agent – heparin. Herein we report the first synthesis, characterization, and performance of sulfated poly-amido-saccharides (sulPASs) as heparin mimetics. sulPASs inhibit the intrinsic pathway of coagulation, specifically FXa and FXIa, as revealed by ex vivo human plasma clotting assays and serine protease inhibition assays. sulPASs activity positively correlates with molecular weight and degree of sulfation. Importantly, sulPASs are not degraded by heparanases and are non-hemolytic. In addition, their activity is reversed by protamine sulfate, unlike small molecule anticoagulants. In an in vivo murine model, sulPASs extend clotting time in a dose dependent manner with bleeding risk comparable to heparin. These findings support continued development of synthetic anticoagulants to address the clinical risks and shortages associated with heparin.

Heparin mimicking sulfated poly-amido-saccharides (sulPASs) are anticoagulants resistant to heparanases and reversed by protamine sulfate. In an in vivo murine model, sulPASs extend clotting time without the increased risk of bleeding.     

N-pulse homoclinic orbits in perturbations of resonant hamiltonian systems

In this paper we develop an analytical method to detect orbits doubly asymptotic to slow manifolds in perturbations of integrable, two-degree-of-freedom resonant Hamiltonian systems. Our energy-phase method applies to both Hamiltonian and dissipative perturbations and reveals families of multi-pulse solutions which are not amenable to Melnikov-type methods. As an example, we study a two-mode approximation of the nonlinear, nonplanar oscillations of a parametrically forced inextensional beam. In this problem we find unusually complicated mechanisms for chaotic motions and verify their existence numerically.     

Global dynamics of an autoparametric spring–mass–pendulum system

In this paper, a study of the global dynamics of an autoparametric four degree-of-freedom (DOF) spring–mass–pendulum system with a rigid body mode is presented. Following a modal decoupling procedure, typical approximate periodic solutions are obtained for the autoparametrically coupled modes in 1:2 internal resonance. A novel technique based on forward-time solutions for finite-time Lyapunov exponent is used to establish global convergence and domains of attraction of different solutions. The results are compared to numerically constructed domains of attraction in the plane of initial position and initial velocity for the pendulum. Simulations are also provided for a few interesting cases of interest near critical values of parameters. Results also shed some light on the role played by other modes present in a multi-DOF system in shaping the overall system response.     

Observation of two-neutrino double-beta decay in 136Xe with the EXO-200 detector

We report the observation of two-neutrino double-beta decay in (136)Xe with T(1/2) = 2.11 ± 0.04(stat) ± 0.21(syst) × 10(21) yr. This second-order process, predicted by the standard model, has been observed for several nuclei but not for (136)Xe. The observed decay rate provides new input to matrix element calculations and to the search for the more interesting neutrinoless double-beta decay, the most sensitive probe for the existence of Majorana particles and the measurement of the neutrino mass scale.     

Three-body correlation functions and recombination rates for bosons in three dimensions and one dimension

We investigate local three-body correlations for bosonic particles in three dimensions and one dimension as a function of the interaction strength. The three-body correlation function g(3) is determined by measuring the three-body recombination rate in an ultracold gas of Cs atoms. In three dimensions, we measure the dependence of g(3) on the gas parameter in a BEC, finding good agreement with the theoretical prediction accounting for beyond-mean-field effects. In one dimension, we observe a reduction of g(3) by several orders of magnitude upon increasing interactions from the weakly interacting BEC to the strongly interacting Tonks-Girardeau regime, in good agreement with predictions from the Lieb-Liniger model for all strengths of interaction.     

Probing Transient Conformational States of Proteins by Solid‐State R1ρ Relaxation‐Dispersion NMR Spectroscopy

The function of proteins depends on their ability to sample a variety of states differing in structure and free energy. Deciphering how the various thermally accessible conformations are connected, and understanding their structures and relative energies is crucial in rationalizing protein function. Many biomolecular reactions take place within microseconds to milliseconds, and this timescale is therefore of central functional importance. Here we show that R_1ρ relaxation dispersion experiments in magic‐angle‐spinning solid‐state NMR spectroscopy make it possible to investigate the thermodynamics and kinetics of such exchange process, and gain insight into structural features of short‐lived states.     

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Quantum gauge equivalence in QED

We discuss gauge transformations in QED coupled to a charged spinor field, and examine whether we can gauge-transform the entire formulation of the theory from one gauge to another, so that not only the gauge and spinor fields, but also the forms of the operator-valued Hamiltonians are transformed. The discussion includes the covariant gauge, in which the gauge condition and Gauss's law are not primary constraints on operator-valued quantities; it also includes the Coulomb gauge, and the spatial axial gauge, in which the constraints are imposed on operator-valued fields by applying the Dirac-Bergmann procedure. We show how to transform the covariant, Coulomb, and spatial axial gauges to what we call “common form,” in which all particle excitation modes have identical properties. We also show that, once that common form has been reached, QED in different gauges has a common time-evolution operator that defines time-translation for states that represent systems of electrons and photons. By combining gauge transformations with changes of representation from standard to common form, the entire apparatus of a gauge theory can be transformed from one gauge to another.