The Stability of Magnetic VorticesRID="*"ID="*"Research on this paper was supported by NSERC under grant N7901

We study the linearized stability of n-vortex (n∈ℤ) solutions of the magnetic Ginzburg–Landau (or Abelian Higgs) equations. We prove that the fundamental vortices (n = ± 1) are stable for all values of the coupling constant, λ, and we prove that the higher-degree vortices (|n|≥ 2) are stable for λ < 1, and unstable for λ > 1. This resolves a long-standing conjecture (see, eg, [JT]). Received: 16 November 1998 / Accepted: 3 January 2000 RID="*" ID="*"Research on this paper was supported by NSERC under grant N7901 RID="**" ID="**"Present address: Courant Institute, 251 Mercer St., New York, NY 10012, USA.&para;E-mail: gustaf&commat;cims.nyu.edu     

$$L^p$$-Fourier asymptotics,Hardy-type inequality and fractal measures

Suppose \(\mu \) is an \(\alpha \)-dimensional fractal measure for some \(0<\alpha <n\). Inspired by the results proved by Strichartz (J Funct Anal 89:154–187, 1990), we discuss the \(L^p\)-asymptotics of the Fourier transform of \(fd\mu \) by estimating bounds of

$$\begin{aligned} \underset{L\rightarrow \infty }{\liminf }\ \frac{1}{L^k} \int _{|\xi |\le L}\ |\widehat{fd\mu }(\xi )|^pd\xi , \end{aligned}$$

for \(f\in L^p(d\mu )\) and \(2<p<2n/\alpha \). In a different direction, we prove a Hardy type inequality, that is,

$$\begin{aligned} \int \frac{|f(x)|^p}{(\mu (E_x))^{2-p}}d\mu (x)\le C\ \underset{L\rightarrow \infty }{\liminf }\frac{1}{L^{n-\alpha }} \int _{B_L(0)}|\widehat{fd\mu }(\xi )|^pd\xi \end{aligned}$$

where \(1\le p\le 2\) and \(E_x=E\cap (-\infty ,x_1]\times (-\infty ,x_2]\ldots (-\infty ,x_n]\) for \(x=(x_1,\ldots x_n)\in {\mathbb R}^n\) generalizing the one dimensional results by Hudson and Leckband (J Funct Anal 108:133–160, 1992).

     

CdO as the archetypical transparent conducting oxide. Systematics of dopant ionic radius and electronic structure effects on charge transport and band structure

A series of yttrium-doped CdO (CYO) thin films have been grown on both amorphous glass and single-crystal MgO(100) substrates at 410 degrees C by metal-organic chemical vapor deposition (MOCVD), and their phase structure, microstructure, electrical, and optical properties have been investigated. XRD data reveal that all as-deposited CYO thin films are phase-pure and polycrystalline, with features assignable to a cubic CdO-type crystal structure. Epitaxial films grown on single-crystal MgO(100) exhibit biaxial, highly textured microstructures. These as-deposited CYO thin films exhibit excellent optical transparency, with an average transmittance of >80% in the visible range. Y doping widens the optical band gap from 2.86 to 3.27 eV via a Burstein-Moss shift. Room temperature thin film conductivities of 8,540 and 17,800 S/cm on glass and MgO(100), respectively, are obtained at an optimum Y doping level of 1.2-1.3%. Finally, electronic band structure calculations are carried out to systematically compare the structural, electronic, and optical properties of the In-, Sc-, and Y-doped CdO systems. Both experimental and theoretical results reveal that dopant ionic radius and electronic structure have a significant influence on the CdO-based TCO crystal and band structure: (1) lattice parameters contract as a function of dopant ionic radii in the order Y (1.09 A) < In (0.94 A) < Sc (0.89 A); (2) the carrier mobilities and doping efficiencies decrease in the order In > Y > Sc; (3) the dopant d state has substantial influence on the position and width of the s-based conduction band, which ultimately determines the intrinsic charge transport characteristics.     

The facile reduction of methoxyethoxymethyl esters with lithium triethylborohydride

The use of a methoxyethylmethyl (MEM) ester has been shown to facilitate the selective reduction of that ester function in the presence of other reduceable esters.     

Heat Transfer and Flow Investigation of a Multi-spoke Flameholder for an Annular Combustor

This paper details the experimental techniques and numerical analysis used to investigate the flow field established by a multi-spoke, annular flameholder. The results from this work were used to maximise the Sustained Hypersonic Flight Experiment (SHyFE) ramjet combustion efficiency whilst ensuring that the vehicle wall temperature limits would not be exceeded. Through an overview of flameholder combustion enhancement the reasoning behind the use of pressure loss, three-dimensional air velocity and turbulence intensity profile measurements in conjunction with CFD analysis to optimise the flameholder is explained. The assessment of three flameholder designs within the paper allows a clearer representation of the processing techniques and allows the influence of spoke size and blockage ratio on mixing capability to be presented. The high resolution liquid crystal thermography technique used to investigate the influence of flameholder design on the SHyFE wall heat loads is also detailed and example results presented.     

Interpreting early land management through compound specific stable isotope analyses of archaeological soils

Compound specific stable isotope analyses of managed soils using isotope ratio mass spectrometry have been undertaken as a means of determining early land use practices. delta (15)N amino acid signals demonstrate differences between manured grassland, unmanured grassland and continuous cereal cultivation under long-term experimental land use control conditions, with delta (15)N in hydrophobic amino acids providing the most distinctive signals. Analysis of early modern/medieval and of Bronze age anthropogenic soils from Orkney demonstrates that such signals are retained in archaeological contexts. delta (13)C analyses of n- alkanoic acid components of the fossil, Bronze Age, anthropogenic soils suggest a major terrestrial input to these soils, with uniform composition of formation materials. Surficial soils demonstrate the assimilation of isotopically lighter carbon, providing a means of assessing the mobility of the n- alkanoic acids within soils and sediments. Copyright 1999 John Wiley & Sons, Ltd.     

Sliding Presentation of the Jeux de Taquin for Classical Lie Groups

The simple \(GL(n,\mathbb {C})\)-modules are described by using semistandard Young tableaux. Any semistandard skew tableau can be transformed into a well defined semistandard tableau by a combinatorial operation, the Schützenberger jeu de taquin. Associated to the classical Lie groups \(SP(2n,\mathbb {C})\), \(SO(2n+1,\mathbb {C})\), there are other notions of semistandard Young tableaux and jeux de taquin. In this paper, we study these various jeux de taquin, proving that each of them has a simple and explicit formulation as a step-by-step sliding. Any of these jeux de taquin is the restriction of the orthogonal one, associated to \(SO(2n+1,\mathbb {C})\).     

Dynamic particle-surface tribocharging: The role of shape and contact mode

Triboelectric particle charging features in many industrial processes. Dynamic particle-surface contact is the key charging mechanism in many types of particle tribocharger. Models of dynamic charging have tended to assume that the particle is spherical, but experiments have shown that particle shape can strongly influence the charging behaviour. We review some experimental work, then present a simple two-dimensional model of the dynamic contact charging of an elliptical particle, of varying roundness ratio, with a flat surface. A rich variety of contact modes (sliding, rolling, tumbling) are captured, each producing distinctive charging behaviour.