Constant Q-curvature metrics in arbitrary dimension

Working in a given conformal class, we prove existence of constant Q-curvature metrics on compact manifolds of arbitrary dimension under generic assumptions. The problem is equivalent to solving a nth-order non-linear elliptic differential (or integral) equation with variational structure, where n is the dimension of the manifold. Since the corresponding Euler functional is in general unbounded from above and below, we use critical point theory, jointly with a compactness result for the above equation.     

Dependence of calculated electron effective attenuation lengths on transport mean free paths obtained from two atomic potentials

We report changes in electron effective attenuation lengths (EALs) resulting from use of transport mean free paths (TMFPs) obtained from the Dirac–Hartree–Fock (DHF) potential instead of the Thomas–Fermi–Dirac (TFD) potential in an algorithm used in the National Institute of Standards and Technology (NIST) Electron Effective‐Attenuation‐Length Database (SRD 82). TMFPs from the former potential are believed to be more reliable than those obtained from the latter potential. We investigated changes in the EALs for selected photoelectron and Auger‐electron lines in four elemental solids (Si, Cu, Ag, and W), for Si 2p photoelectrons of varying energy in SiO₂, and for photoelectrons excited by Al Kα X rays in four candidate gate‐dielectric materials (HfO₂, ZrO₂, HfSiO₄, and ZrSiO₄). For each material, we computed the change in the average EAL for a range of overlayer‐film thicknesses from zero to a maximum value corresponding to attenuation of the substrate signal to 10% of its original value. This EAL change was a maximum for electrons emitted normally from the surface and decreased monotonically with increasing emission angle. The maximum EAL change varied between ?4.4% and 2.6% for the three groups of materials. We found that the maximum EAL change correlated mainly with the TMFP change. We found that TMFP changes in other solids could generally lead to maximum EAL changes between ?2.6% and 1.9% for electron energies between 500 and 2000 eV. For lower energies, the maximum EAL changes could be larger for some solids. Our revised EALs for Si 2p photoelectrons in SiO₂ excited by Mg and Al Kα X rays agree within 0.5% with values reported by Seah and Spencer from a detailed analysis of SiO₂ film‐thickness measurements by XPS and other techniques. Copyright © 2006 John Wiley & Sons, Ltd.     

On the Snider equation

We study the physical content of the Snider quantum transport equation and the origin of a puzzling feature of this equation, which implies contradictory values for the one-particle density operator. We discuss in detail why the two values are in fact not very different provided that the studied particles have sufficiently large wave packets and only a small interaction probability, a condition which puts a limit on the validity of the Snider equation. In order to improve its range of application, we propose a reinterpretation of the equation as a mixed equation relating the real one-particle distribution function (on the left-hand side of the equation) to the free distribution (on the right-hand side), which we have introduced in a recent contribution. In its original form, the Snider equation is valid only when used to generate Boltzmann-type equations where collisions are treated as point processes in space and time (no range, no duration); in this approximation, virial corrections are not included, so that the real and free distributions coincide. If the equation is used beyond this approximation to generate nonlocal and density corrections, we conclude that the results are not necessarily correct.     

Current distribution on a three-dimensional,bond-diluted,random-resistor network at the percolation threshold

Current and logarithm-current distributions on a three-dimensional random-bond percolation cubic network were studied at the percolation threshold by computer simulations. Predictions of a hierarchical model that combine fractal structure and randomness agree with our numerical simulations. In the thermodynamic limit the logarithm-current distribution exhibits ann(ln(i))i ^1/3 dependence below some characteristic currenti _c. This distribution may scale with lni/lnL, but the data are insufficient to make this a definite conclusion. Due to the small range of lnL considered, a study of the moments does not reveal this behavior and a study of the distribution itself is required.     

A new quantum statistical evaluation method for time correlation functions

Considering a system ofN identical interacting particles, which obey Fermi-Dirac or Bose-Einstein statistics, we derive new formulas for correlation functions of the type (whereB _j is diagonal in the free-particle states) in the thermodynamic limit. Thereby we apply and extend a superoperator formalism, recently developed for the derivation of long-time tails in semiclassical systems. As an illustrative application, the Boltzmann equation value of the time-integrated correlation functionC(t) is derived in a straightforward manner. Due to exchange effects, the obtained t-matrix and the resulting scattering cross section, which occurs in the Boltzmann collision operator, are now functionals of the Fermi-Dirac or Bose-Einstein distribution.     

New Method to Calculate Thermodynamic and Transport Properties of a Multi-Temperature Plasma: Application to N2 Plasma

Multi-temperature thermal plasmas have often to be considered to account for the nonequilibrium effects. Recently André et al. have developed the calculation of concentrations in a multi-temperature plasma by artificially separating the partition functions into a product by assuming that the excitation energies are those of the lower levels (electronic, vibration, and rotation). However, at equilibrium, differences, increasing with temperature, can be observed between partition functions calculated rigorously and with their method. This paper presents a modified method where it has been assumed that the preponderant rotational energy is that of the vibrational level v=0 of the ground electronic state and the preponderant vibrational energy is that of the ground electronic state. The internal partition function can then be expressed as a product of series expressions. At equilibrium for N ₂ and N ₂ ⁺ partition functions the values calculated with our method differ by less than 0.1% from those calculated rigorously. The calculation has been limited to three temperatures: heavy species T_h , electrons T_e , and vibrational T _v temperatures. The plasma composition has been calculated by minimizing the Gibbs free enthalpy with the steepest descent numerical technique. The nonequilibrium properties have been calculated using the method of Devoto, modified by Bonnefoi and Aubreton. The ratio =T_e/T_h was varied between 1 and 2 as well as the ratio _v =T _v /T _h for a nitrogen plasma. At equilibrium the corresponding equilibrium transport properties of Ar and N ₂ are in good agreement with those of Devoto and Murphy except for T>10,000 K where we used a different interaction potential for N–N ⁺ . The effects of _v and _e on thermodynamic and transport properties of N ₂ are then discussed.     

有机金属络合物用于高分子富氧膜的研究进展

本文介绍了能够可逆吸附分子氧的有机金属络合物用于高分子富氧膜的研究进展，以及以双重吸附理论进行的膜的促进输送机理。     

TiO(2) porous electrodes with hierarchical branched inner channels for charge transport in viscous electrolytes.

Titanium dioxide (TiO(2)) photoelectrodes with micro/nano hierarchical branched inner channels have been prepared by an electrohydrodynamic (EHD) technique and assembled to form dye-sensitized solar cells (DSSCs). Excellent penetration of ionic-liquid electrolytes and enhanced light harvesting in the longer wavelength region are realized within the composite-structure electrode, thus a better fill factor (ff) of 75.3 % and higher conversion efficiency (eta) of 7.1 % are obtained for viscous ionic-liquid electrolytes compared to pure nanostructured films. Hierarchical branched channels in the photoanodes can efficiently improve the transport properties of redox-active species in viscous electrolytes, which is demonstrated by electrical impedance spectroscopy (EIS). The incident monochromatic photon-to-electron conversion efficiency (IPCE) shows that enhanced light scattering in the composite film is of benefit for light harvesting and thus for solar energy conversion efficiency.     

Multifunctional Calix[4]arenes Containing Pendant Amide and Phosphoryl Groups: Their Use as Extracting Agents and Carriers for Alkali Cations

The complexing, extracting and mobile carrier properties of the tetra(phosphine oxide)-calix[4]arene 1 and the hybrid diamide-di(phosphine oxide)-calix[4]arene 2 were studied. Both ligands give 1 : 1 complexes with alkali cations in THF as shown by the picrate method. 1H NMR experiments were run to follow encapsulation of sodium and potassium cations. The corresponding spectra indicate C2-symmetrical structure. The observed extraction orders of the alkali picrates were as follows K+>Rb+>Li+>Cs+>Na+ for 1 and Li+>Na+>K+>Rb++ for 2. Transport kinetics was analysed by means of a model which assumes pure diffusion and which allows the evaluation of mass transfer coefficients in all systems. These coefficients and their influences on the transport rate are discussed in terms of size of the transporting species in the liquid membrane.     

Synthesis of Molecular Wires of Linear and Branched Bis(terpyridine)‐Complex Oligomers and Electrochemical Observation of Through‐Bond Redox Conduction

Films of linear and branched oligomer wires of Fe(tpy)₂ (tpy=2,2′:6′,2′′‐terpyridine) were constructed on a gold‐electrode surface by the interfacial stepwise coordination method, in which a surface‐anchoring ligand, (tpy? C₆H₄N?NC₆H₄? S)₂ ( 1 ), two bridging ligands, 1,4‐(tpy)₂C₆H₄ ( 3 ) and 1,3,5‐(C?C? tpy)₃C₆H₃ ( 4 ), and metal ions were used. The quantitative complexation of the ligands and Fe^II ions was monitored by electrochemical measurements in up to eight complexation cycles for linear oligomers of 3 and in up to four cycles for branched oligomers of 4 . STM observation of branched oligomers at low surface coverage showed an even distribution of nanodots of uniform size and shape, which suggests the quantitative formation of dendritic structures. The electron‐transport mechanism and kinetics for the redox reaction of the films of linear and branched oligomer wires were analyzed by potential‐step chronoamperometry (PSCA). The unique current‐versus‐time behavior observed under all conditions indicates that electron conduction occurs not by diffusional motion but by successive electron hopping between neighboring redox sites within a molecular wire. Redox conduction in a single molecular wire in a redox‐polymer film has not been reported previously. The analysis provided the rate constant for electron transfer between the electrode and the nearest redox‐complex moiety, k₁ (s^?1), as well as that for intrawire electron transfer between neighboring redox‐complex moieties, k₂ (cm² mol^?1 s^?1). The strong effect of the electrolyte concentration on both k₁ and k₂ indicates that the counterion motion limits the electron‐hopping rate at lower electrolyte concentrations. Analysis of the dependence of k₁ and k₂ on the potential gave intrinsic kinetic parameters without overpotential effects: k₁⁰=110 s^?1, k₂⁰=2.6×10¹² cm² mol^?1 s^?1 for [n Fe 3 ], and k₁⁰=100 s^?1, k₂⁰=4.1×10¹¹ cm² mol^?1 s^?1 for [n Fe 4 ] (n=number of complexation cycles).