Γ-Convergence of 2D Ginzburg-Landau functionals with vortex concentration along curves

We study the variational convergence of a family of twodimensional Ginzburg-Landau functionals arising in the study of superfluidity or thin-film superconductivity as the Ginzburg-Landau parameter ε tends to 0. In this regime and for large enough applied rotations (for superfluids) or magnetic fields (for superconductors), the minimizers acquire quantized point singularities (vortices). We focus on situations in which an unbounded number of vortices accumulate along a prescribed Jordan curve or a simple arc in the domain. This is known to occur in a circular annulus under uniform rotation, or in a simply connected domain with an appropriately chosen rotational vector field. We prove that if suitably normalized, the energy functionals Γ-converge to a classical energy from potential theory. Applied to global minimizers, our results describe the limiting distribution of vortices along the curve in terms of Green equilibrium measures.     

Absolute fixed point sets for continuum-valued maps

The notion of an absolute fixed point set in the setting of continuum-valued maps will be defined and characterized.

     

Frequency-domain statistics of the chaotic optical field of a high-gain, self-amplified free-electron laser and its correlation to the time-domain statistics

Recently, the temporal evolution of the amplitude and phase of the chaotic output from a self-amplified free-electron laser was determined. In this letter, we characterize the frequency dependence of the amplitude and phase of the output radiation and discuss the relationship between the characteristics of the spiky intensity structures observed in both the time and the frequency domains. The distribution of the rms time–bandwidth products for an ensemble of output pulses is presented. Experimental results are compared with simulation and theory. PACS 41.60.Cr; 42.50.Ar; 05.40.-a; 42.55.Vc     

An Extended Model for Establishing Dominance in Multiattribute Decisionmaking

This paper is concerned with the use of incomplete information about utilities and weights in multiattribute decisionmaking. Because of time pressure and/or lack of knowledge, a decision maker may only be able to provide incomplete information which might be expressed as a set of linear inequalities. If the decision maker's information on both weights and utilities is imprecisely identified, then the model for establishing pairwise dominance becomes a non-linear program. A method for obtaining non-dominated alternatives without solving the non-linear program is proposed using a simple weighted-additive function.     

SU(5) Higgs problem with adjoint + vector representations

Recently Kim has given a general method, using group-invariant orbit parameters, for determining the energy and residual symmetry of the Higgs potential minimum. In this paper we illustrate the method by working out the case of a quartic SU(5) Higgs potential with $\text{5}$ and $\text{24}$ higgsons. In this method the Gell-Mann-Slansky conjecture concerning possible little groups of the potential minimum takes a geometric form, which is verified for our case. The results are used to discuss the hierarchical symmetry breaking of SU(5) grand unification theory. We generalize our results to the SU(N) adjoint + vector models, which are all closely related.     

Nitrogen isotope enrichment via infrared laser induced isomerization of methyl and ethyl isocyanide

Methyl and ethyl isocyanide undergo isomerization to the corresponding nitriles when irradiated with the focused output of a CO₂ TEA laser. This process is shown to be isotopically selective for nitrogen isotopes when operating pressures are on the order of 1 to 2 torr. At higher pressures thermal isomerization becomes dominant.     

Biflavone glucosides from Ginkgo biloba yellow leaves

Phytochemical investigation of Ginkgo biloba (Ginkgoaceae) has resulted in the isolation of two new biflavone glucosides, ginkgetin 7'-O-beta-D-glucopyranoside (1) and isoginkgetin 7-O-beta-D-glucopyranoside (2). The structures were determined on the basis of chemical and spectroscopic evidences.     

Simulations on the thermal decomposition of a poly(dimethylsiloxane) polymer using the ReaxFF reactive force field

To investigate the failure of the poly(dimethylsiloxane) polymer (PDMS) at high temperatures and pressures and in the presence of various additives, we have expanded the ReaxFF reactive force field to describe carbon-silicon systems. From molecular dynamics (MD) simulations using ReaxFF we find initial thermal decomposition products of PDMS to be CH(3) radical and the associated polymer radical, indicating that decomposition and subsequent cross-linking of the polymer is initiated by Si-C bond cleavage, in agreement with experimental observations. Secondary reactions involving these CH(3) radicals lead primarily to formation of methane. We studied temperature and pressure dependence of PDMS decomposition by following the rate of production of methane in the ReaxFF MD simulations. We tracked the temperature dependency of the methane production to extract Arrhenius parameters for the failure modes of PDMS. Furthermore, we found that at increased pressures the rate of PDMS decomposition drops considerably, leading to the formation of fewer CH(3) radicals and methane molecules. Finally, we studied the influence of various additives on PDMS stability. We found that the addition of water or a SiO(2) slab has no direct effect on the short-term stability of PDMS, but addition of reactive species such as ozone leads to significantly lower PDMS decomposition temperature. The addition of nitrogen monoxide does not significantly alter the degradation temperature but does retard the initial production of methane and C(2) hydrocarbons until the nitrogen monoxide is depleted. These results, and their good agreement with available experimental data, demonstrate that ReaxFF provides a useful computational tool for studying the chemical stability of polymers.