Local Minimizers of the Ginzburg-Landau Energy with Magnetic Field in Three Dimensions

We establish the existence of locally minimizing vortex solutions to the full Ginzburg-Landau energy in three dimensional simply-connected domains with or without the presence of an applied magnetic field. The approach is based upon the theory of weak Jacobians and applies to nonconvex sample geometries for which there exists a configuration of locally shortest line segments with endpoints on the boundary.Research partially supported by NSERC grant number 261955     

Kinetics of polarization reversal in irradiated thin PZT films

The effect of irradiation with electrons and neutrons and of exposure to synchrotron radiation on cyclic switching of polarization in thin films of lead zirconate titanate Pb(Zr,Ti)O₃ (PZT) was studied. It is shown that variations in the shape of switching currents are due to the generation of a spatially nonuniform bound internal field with account for an increase in the rate of bulk screening caused by irradiation. A correlation between structural variations and the evolution of the switching current measured during and after irradiation is established.     

The Angle Defect for Odd-Dimensional Simplicial Manifolds

In a 1967 paper, Banchoff stated that a certain type of polyhedral curvature, that applies to all finite polyhedra, was zero at all vertices of an odd-dimensional polyhedral manifold; one then obtains an elementary proof that odd-dimensional manifolds have zero Euler characteristic. In a previous paper, the author defined a different approach to curvature for arbitrary simplicial complexes, based upon a direct generalization of the angle defect. The generalized angle defect is not zero at the simplices of every odd-dimensional manifold. In this paper we use a sequence based upon the Bernoulli numbers to define a variant of the angle defect for finite simplicial complexes that still satisfies a Gauss-Bonnet-type theorem, but is also zero at any simplex of an odd-dimensional simplicial complex K (of dimension at least 3), such that χ(link(ηⁱ, K)) = 2 for all i-simplices ηⁱ of K, where i is an even integer such that 0 ≤ i ≤ n – 1. As a corollary, an elementary proof is given that any such simplicial complex has Euler characteristic zero.     

On the local structure of doubly laced crystals

Let g be a Lie algebra all of whose regular subalgebras of rank 2 are type A₁×A₁, A₂, or C₂, and let B be a crystal graph corresponding to a representation of g. We explicitly describe the local structure of B, confirming a conjecture of Stembridge.     

On a theorem of Shchepin and Repovš concerning the smoothness of compacta

We show that a theorem of Shchepin and Repovš concerning the smoothness of compacta follows from the theory of semicontinuous relations.     

Gas chromatography for in situ analysis of a cometary nucleus. II. Analysis of permanent gases and light hydrocarbons with a carbon molecular sieve porous layer open tubular column

Considering the severe constraints of space instrumentation, a great improvement for the in situ gas chromatographic (GC) determination of permanent and noble gases in a cometary nucleus is the use of a new carbon molecular sieve porous layer open tubular (PLOT) column called Carbobond. No exhaustive data dealing with this column being available, studies were carried out to entirely characterize its analytical performances, especially when used under the operating conditions of the cometary sampling and composition (COSAC) experiment of the European Space Agency (ESA) Rosetta space mission to be launched in 2003 for a rendezvous with comet 46 P/Wirtanen in 2011. The high efficiency and speed of analysis of this column at both atmospheric and vacuum outlet column pressure is demonstrated, and the kinetic mass transfer contribution of this carbon molecular sieve adsorbent is calculated. Besides, differential adsorption enthalpies of several gases and light hydrocarbons were determined from the variation of retention volume with temperature. The data indicate close adsorption behaviors on the Carbobond porous layer adsorbent and on the carbon molecular sieve Carboxen support used to prepare the packed columns. Moreover, taking into account the in situ operating conditions of the experiment, a study of two columns with different porous layer thicknesses allowed one to optimize the separation of the target components and to select the column parameters compatible with the instrument constraints. Comparison with columns of similar selectivity shows that these capillary columns are the first ones able to perform the same work as the packed and micro-packed columns dedicated to the separation of this range of compounds in GC space exploration.     

Immanant positivity for Catalan-Stieltjes matrices

We give some sufficient conditions for the nonnegativity of immanants of square submatrices of Catalan-Stieltjes matrices and their corresponding Hankel matrices. To obtain these sufficient conditions, we construct new planar networks with a recursive nature for Catalan-Stieltjes matrices. As applications, we provide a unified way to produce inequalities for many combinatorial polynomials, such as the Eulerian polynomials, Schröder polynomials, and Narayana polynomials.     

Evidence for a two-step mechanism in electronically selective single-walled carbon nanotube reactions

Covalent and noncovalent chemistries that are selective to single-walled carbon nanotubes of a particular electronic type have become increasingly important for electronic structure separation and on-chip modification of nanoelectronic devices. By monitoring transient Raman spectroscopy and photoluminescence (PL) during a reaction with 4-chlorobenzene diazonium in aqueous solution, evidence for a characteristic two-step mechanism with two distinct time constants is uncovered. A long-lived intermediate selectively and noncovalently binds and partially dopes the nanotube surface (tau = 2.4 min). A slower, covalent reaction is tracked using the time-dependent increase in the disorder mode in Raman (tau = 73 min). The transient Raman and PL data are well described using a series of two first-order reactions. The covalent bonding step can be deactivated by changing the structure of the surfactant adsorbed phase, further supporting the mechanism.