Special Lagrangian Submanifolds with Isolated Conical Singularities. II. Moduli spaces

This is the second in a series of five papers studying special Lagrangiansubmanifolds (SLV m-folds) X in (almost) Calabi–Yau m-folds M with singularities x ₁ , ..., x _n locally modelled on specialLagrangian cones C ₁, ..., C _n in ^m with isolated singularities at 0.Readers are advised to begin with Paper V.This paper studies the deformation theory of compact SL m-folds X in Mwith conical singularities. We define the moduli space _X of deformations of X in M, and construct a natural topology on it. Then we show that _X is locally homeomorphic to the zeroes of a smooth map : _{X X} between finite-dimensional vector spaces.Here the infinitesimal deformation space _X depends only on the topology of X, and the obstruction space _X only on the cones C ₁, ..., C _n at x ₁, ..., x _n . If the cones C _i are stable then _X is zero, and _X is a smooth manifold. We also extend our results to families of almost Calabi–Yau structures on M.     

Evolution Equations for Special Lagrangian 3-Folds in C3

This is the third in a series of papers constructing explicit examples of special Lagrangian submanifolds in C ^m . The previous paper (Math. Ann. 320 (2001), 757–797), defined the idea of evolution data, which includes an (m – 1)-submanifold P in R ⁿ , and constructed a family of special Lagrangian m-folds N in C ^m , which are swept out by the image of P under a 1-parameter family of affine maps _t : R ⁿ C ^m , satisfying a first-order o.d.e. in t. In this paper we use the same idea to construct special Lagrangian 3-folds in C³. We find a one-to-one correspondence between sets of evolution data with m = 3 and homogeneous symplectic 2-manifolds P. This enables us to write down several interesting sets of evolution data, and so to construct corresponding families of special Lagrangian 3-folds in C³.Our main results are a number of new families of special Lagrangian 3-foldsin C³, which we write very explicitly in parametric form. Generically these are nonsingular as immersed 3-submanifolds, and diffeomorphic to R³ or ¹× R². Some of the 3-folds are singular, and we describe their singularities, which we believe are of a new kind.We hope these 3-folds will be helpful in understanding singularities ofcompact special Lagrangian 3-folds in Calabi–Yau 3-folds. This will beimportant in resolving the SYZ conjecture in Mirror Symmetry.     

Stability and fragmentation of organic silicon functionalizations studied by laser desorption mass spectrometry

A method is introduced to investigate organic functionalizations on silicon by laser-induced thermal desorption (LITD), where well-ordered Si(1 1 1)-(1 × 1):H(D) surfaces are used to determine the desorption temperature as a function of laser fluence. To demonstrate the potential of this technique silicon surfaces with ultrathin oxide layers were functionalized with organic end groups. The species desorbed with focused XeCl laser pulses were monitored at an oblique angle and their time-of-flight (TOF) distributions were measured with a quadrupole mass analyzer after electron impact ionization. By assuming a negligible contribution of the oxide and organic layers to the heating effect, the TOF temperatures measured for Si(1 1 1)-(1 × 1):H(D) could be used to determine the mass of the desorbed species. Detailed results are presented for dimethylsilyl (DMS), bromomethyldimethylsilyl (BMDMS), and chloromethyldimethylsilyl (CMDMS) terminated surfaces which were prepared by silanization with suitable chloro and disilazane compounds. While for the DMS termination dimethylsilanol (76 u) is desorbed as a single species, clearly identifying the terminating group, in the case of BMDMS and CMDMS further fragmentation of the end group occurs at the surface.     

A high-throughput search for direct methanol fuel cell anode electrocatalysts of type PtxBiyPbz

We used a high-throughput method to screen for direct methanol fuel cell anode electrocatalysts in the Pt-Bi-Pb system. Previous studies showed that PtBi and PtPb (both NiAs structure type) were active electrocatalysts for the oxidation of formic acid, but only PtPb was active in oxidizing methanol. We synthesized thin films with continuous composition spreads of the three elements by magnetron sputtering at deposition temperatures from ambient to 510 °C. A fluorescence method was then used to identify compositions that were active toward methanol oxidation. Only films deposited between temperatures of 160 and 400 °C showed electrocatalytic activity. The areas that were active for methanol oxidation showed predominantly the NiAs structure type according to XRD, with optimal activity for compositions near PtBi_0.01Pb_0.53.     

trans‐Decahydronaphthalene (decalin) from powder diffraction data

The title compound, C₁₀H₁₈, a decalin stereoisomer, crystallizes with Z′ = 0.5 in the space group P2₁/n. The trans‐decalin molecule is located on an inversion centre with both rings in a chair conformation, making for a quasi‐flat overall shape. Despite the absence of hydrogen bonds, it crystallizes easily. In this work the unknown crystal structure of trans‐decalin has been solved and refined using X‐ray powder diffraction data.     

osp(N, 2) AKNS equations

The osp(N, 2) extension of the AKNS scheme is reconsidered. It leads to a general class of integrable nonlinear evolution equations for 2+N(N–1)/2 commuting and 2N anticommuting fields. by reduction, various osp(N, 2) versions of the Korteweg-de Vries equation can be obtained. One of these is shown to be bi-Hamiltonian and its second Hamiltonian structure corresponds to the classical limit of the so(N) superconformal algebra. The nonlinear Schrödinger and modified Korteweg-de Vries reductions are also briefly discussed.Work supported by NSerc and FCAR.     

Synthesis and characterization of BaZrO3-doped YBa2Cu3O7−δ microtapes with improved critical current densities

We have recently demonstrated that through a sol–gel route, superconductor crystallization in the presence of simple biopolymers results in a drastic alteration of morphology, producing technologically useful nanowires and porous architectures. Morphological control is of the utmost importance to bulk high-temperature superconductors, as grain boundaries act as weak links in limiting the achievable critical current density (J_c). Here we show that, as expected, the incorporation of nanoparticulate barium zirconate (BaZrO₃) species into a biopolymer-mediated synthetic protocol for YBa₂Cu₃O_7?δ (Y123) leads to a significantly improved in-field J_c compared to that observed in a sample without BaZrO₃ additions. To ameliorate degradation of the BaZrO₃ species in this protocol, we demonstrate that by drawing the precursor sol into fibers, a microtape architecture is able to be formed, leading to lengthy, anisotropic structures having enhanced J_c through the retention of the BaZrO₃ species.