Heteroclinic connections between periodic orbits and resonance transitions in celestial mechanics

In this paper we apply dynamical systems techniques to the problem of heteroclinic connections and resonance transitions in the planar circular restricted three-body problem. These related phenomena have been of concern for some time in topics such as the capture of comets and asteroids and with the design of trajectories for space missions such as the Genesis Discovery Mission. The main new technical result in this paper is the numerical demonstration of the existence of a heteroclinic connection between pairs of periodic orbits: one around the libration point L(1) and the other around L(2), with the two periodic orbits having the same energy. This result is applied to the resonance transition problem and to the explicit numerical construction of interesting orbits with prescribed itineraries. The point of view developed in this paper is that the invariant manifold structures associated to L(1) and L(2) as well as the aforementioned heteroclinic connection are fundamental tools that can aid in understanding dynamical channels throughout the solar system as well as transport between the "interior" and "exterior" Hill's regions and other resonant phenomena. (c) 2000 American Institute of Physics.     

Maps preserving the nilpotency of products of operators

Let B(X) be the algebra of all bounded linear operators on the Banach space X, and let N(X) be the set of nilpotent operators in B(X). Suppose ?:B(X)→B(X) is a surjective map such that A,B∈B(X) satisfy AB∈N(X) if and only if ?(A)?(B)∈N(X). If X is infinite dimensional, then there exists a map f:B(X)→C?{0} such that one of the following holds:

(a)

There is a bijective bounded linear or conjugate-linear operator S:X→X such that ? has the form A?S[f(A)A]S^-1.

(b)

The space X is reflexive, and there exists a bijective bounded linear or conjugate-linear operator S : X′ → X such that ? has the form A ? S[f(A)A′]S⁻¹.

If X has dimension n with 3 ? n < ∞, and B(X) is identified with the algebra M_n of n × n complex matrices, then there exist a map f:M_n→C?{0}, a field automorphism ξ:C→C, and an invertible S ∈ M_n such that ? has one of the following forms:

     

Separation of polar mushroom toxins by mixed-mode hydrophilic and ionic interaction liquid chromatography-electrospray ionization-mass spectrometry

Reversed-phase liquid chromatography (RPLC) is commonly used to analyze nonvolatile contaminants and naturally occurring toxins in foods. However, polar compounds, such as hydrophilic polypeptides and quaternary ammonium salts, are often not satisfactorily separated by RPLC and present a challenge for analytical scientists. In this study, hydrophilic interaction liquid chromatography (HILIC), on an amide-based stationary phase in combination with electrospray ionization (ESI) tandem mass spectrometry (MS-MS), is successfully employed to simultaneously separate polar mushroom toxins, including amanitins and phallotoxins, which are cyclic oligopeptides and muscarine, a quaternary ammonium compound, in mushrooms. The sensitivity of different ionization modes is studied, and the positive ionization mode is found to provide a more sensitive and effective tool for the unambiguous identification of the concerned polar toxins because of their characteristic fragmentation patterns. The properties of the mobile phase are also found to have significant impacts on the separation. At a high acetonitrile (ACN) concentration, hydrophilic interaction dominates, and all analytes under study demonstrate a much higher affinity with the stationary phase. The addition of methanol (MeOH) as a modifier could further enhance the HILIC separation for amanitins, phallotoxins, and muscarine. Valley-to-valley separation is achieved upon the optimatizatiqn of the mobile phase (comprising of ACN, MeOH, and ammonium formate buffer at pH approximately 3.5) and the solvent gradient. HILIC coupled with ESI-MS-MS is demonstrated to be a novel technique for the simultaneous separation and confirmatory analysis of the concerned polar toxins by providing an environment of solubility and retention that could not be achieved through the use of RPLC.     

A new route for fast synthesis of copper nanowires and application on flexible transparent conductive films

Journal of Nanoparticle Research - The magnetically assembled chain-like structures of magnetic nanoparticles attract great attention due to their unique properties. In this paper, we studied the...     

Surface-initiated atom transfer radical polymerization on poly(vinylidene fluoride) membrane for antibacterial ability

Surface-active microporous membranes were prepared from the poly(vinylidene fluoride)-graft-poly(2-(2-bromoisobutyryloxy)ethyl acrylate) copolymer (PVDF-g-PBIEA copolymer) by phase inversion in water. The PBIEA side chains could function as initiators for the atom transfer radical polymerization (ATRP) of 2-(N,N-dimethylamino)ethyl methacrylate on the membrane surfaces to give rise to the PVDF-g-PBIEA-ar-PDMAEMA membranes. N-alkylation with hexyl bromide and nitromethane gave rise to the quanternized PVDF-g-PBIEA-ar-QPDMAEMA membranes with polycation chains chemically tethered on the membrane surface, including the pore surfaces. The changes in the surface morphology and the surface chemical composition were confirmed by scanning electron microscopy and X-ray photoelectron spectroscopy. The scanning electron microscopy revealed that, in comparison to the pristine PVDF-g-PBIEA membranes, not only could the PVDF-g-PBIEA-ar-QPDMAEMA membranes remove the Gram-negative bacterium Escherichia coli but also inhibited the bacterial reproduction on the membranes to a significant extent.     

以优化方法求解布料无摩擦接触变形问题

利用作者所提出的布料质点模型,用罚函数法解除布料和其它物体之间的接触约束,把接触约束条件下的极值问题转化为无约束极值问题,用F-R共轭梯度法求解,并用三次插值方法进行一维搜索.计算了有缝摺和裁剪开口的布料与球形物体的接触变形问题,得到的结果符合人们的日常实际观察.     

Normally transparent smart window with haze enhancement via inhomogeneous alignment surface

Smart windows which switch between transparent and scattering states can be used not only as privacy window in buildings and cars, but also as information displays, and motorcycle helmet visors. Here, we have proposed a reverse mode polymer-stabilised liquid crystals (PSLCs) smart window based on inhomogeneous alignment surface, which greatly enhances the haze by 42% when compared to device without inhomogeneity treatment. A 100-cm² window that switches between the power-off clear state (~4% haze) and a power-on scattering state (64% haze at 15 V) in less than 3.5 ms is demonstrated. Since no high-temperature treatment (< 80°C) is involved in device fabrication, further development on plastic films is feasible.     

Push–Pull archetype of reduced graphene oxide functionalized with polyfluorene for nonvolatile rewritable memory

A solution‐processable PFTPA‐convalently grafted reduced graphene oxide (RGO‐PFTPA) was synthesized by the 1,3‐dipolar cycloaddition of azomethine ylide. Bistable electrical switching and nonvolatile rewritable memory effects were demonstrated in a sandwich structure of indium tin oxide/RGO‐PFTPA/Al. The switch‐on voltage of the as‐fabricated device was around ?1.4 V, and the ON/OFF‐state current ratio was more than 10³. The ON–OFF transition process is reversible because the application of a high enough positive voltage can induce the reverse transfer of electrons, reducing the conductivity back to its initial OFF state. Both the OFF and ON states are accessible and very stable under a constant voltage stress of ?1 V for up to 3 h, or under a pulse voltage stress of ?1 V for up to 10⁸ continuous read cycles (pulse period = 2 μs, pulse width = 1 μs). © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

A generic approach for preparing core-shell carbon-metal oxide nanofibers: morphological evolution and its mechanism

Carbon-SnO(2) core-shell hybrid nanofibers were prepared via single-spinneret electrospinning and subsequent heat treatment. The Kirkendall effect during the heat treatment is found to be responsible for the formation of core-shell morphology. The route is proven to be generic for fabrication of carbon-metal oxide or carbon-metal core-shell nanofibers, and corresponding nanotubes.