Symmetry Reduction in Symplectic and Poisson Geometry

We present a quick review of several reduction techniques for symplectic and Poisson manifolds using local and global symmetries compatible with these structures. Reduction based on the standard momentum map (symplectic or Marsden–Weinstein reduction) and on generalized distributions (the optimal momentum map and optimal reduction) is emphasized. Reduction of Poisson brackets is also discussed and it is shown how it defines induced Poisson structures on cosymplectic and coisotropic submanifolds.     

Bloch wave homogenization of a non-homogeneous Neumann problem

In this paper, we use the Bloch wave method to study the asymptotic behavior of the solution of the Laplace equation in a periodically perforated domain, under a non-homogeneous Neumann condition on the boundary of the holes, as the size of the holes goes to zero more rapidly than the domain period. This method allows to prove that, when the hole size exceeds a given threshold, the non-homogeneous boundary condition generates an additional term in the homogenized problem, commonly referred to as “the strange term” in the literature.     

Self-assembled tin-doped ZnO nanowire and nanoplate structures grown by thermal treatment of ZnS powder

Sintering of a ZnS–SnO₂ mixture under argon flow leads to the growth of columnar nanoplate arrays as well as arrays of nanowires, nanorods and nanoplates with six-fold symmetry. The six-fold nanoplate structures correspond to a more advanced stage of growth than the nanowire structures. Cathodoluminescence (CL) in the scanning electron microscope (SEM) shows that the structures contain Sn, but the amount of this element is normally under the detection limit of X-ray energy-dispersive spectroscopy (EDS). The formation of branches in the hierarchical structures depends on the presence of Sn and on defects in the mixture powder.     

Pulsed laser deposition of Co and growth of CoSi2 on Si(111)

Monolayers of Co were prepared by pulsed laser deposition (PLD) and thermal deposition (TD) on Si(111) substrates. The surface structure and morphology were studied as a function of annealing temperature with scanning tunneling microscopy and low-energy electron diffraction (LEED). Comparing PLD to TD in the monolayer regime, we find surface phases with lower Co content in the top layer for annealing temperatures below 500 °C, indicating an implantation of Co into the Si substrate. The implanted Co leads to an increased intermixing of Co and Si and a higher density of nucleation centers for Co multilayers produced by PLD compared to TD. Multilayer PLD films therefore show an improved film quality, which is detected by an increased intensity of the LEED reflectivity. PACS 68.37.Ef; 61.14.Hg; 68.55.-a     

A Symplectic Slice Theorem

We provide a model for an open invariant neighborhood of any orbit in a symplectic manifold endowed with a canonical proper symmetry. Our results generalize the constructions of Marle and Guillemin and Sternberg for canonical symmetries that have an associated momentum map. In these papers the momentum map played a crucial role in the construction of the tubular model. The present work shows that in the construction of the tubular model, the so-called Chu map, can be used instead, which exists for any canonical action, unlike the momentum map. Hamilton's equations for any invariant Hamiltonian function take on a particularly simple form in these tubular variables. As an application we will find situations, that we will call tubewise Hamiltonian, in which the existence of a standard momentum map in invariant neighborhoods is guaranteed.     

Schottky barrier formation in the low metal coverage limit

A theoretical discussion of the state of the art in the field of Schottky barrier formation is presented. The thin metal layer limit is analyzed for Al and In on GaAs(110), and the adsorption sites are determined as a function of the metal coverage. Intrinsic and extrinsic charge neutrality levels are also discussed for the In-case.     

Effect of substrate’s nature on the growth of HgBCCO thin films

The synthesis of HgBCCO films by spray pyrolysis on single crystals is investigated. It is shown that in conditions where the precursor is expected to give Hg-1223, Hg-1212 grows on LaAlO₃ (0 0 1) while Hg-1223 grows on MgO (0 0 1). The samples are analysed by X-ray pole figures, SEM and critical current measurements. Both samples were superconducting but the sample on MgO had a negligible I_c while 17 A was measured on LAO at 77 K (sf). These differences are analysed in terms of texture and microstructure and some conclusions concerning the growth are drawn. On LAO, the nucleation is probably epitaxial and the anisotropy of the growth inhibits the transformation into Hg-1223 while some interfacial contribution expected to occur on MgO makes this transformation easier.     

Determination of the second order susceptibility tensor in banana-shaped liquid crystals

Optical second harmonic generation (SHG) measurements have been carried out on the B2 phases of three liquid crystal materials composed of conventional banana-shaped molecules (P-10-O-PIMB, P-8-O-PIMB and P-8-PIMB). Quantitative values of the second order susceptibilities d_ij have been deduced from SHG measurements at oblique incidences on polydomain racemic samples under an electric field. The d_ij coefficients are in the range 1-10 pm V^-1.     

Singular Reduction of Poisson Manifolds

The conditions under which it is possible to reduce a Poisson manifold via a regular foliation have been completely characterized by Marsden and Ratiu. In this Letter we show that this characterization can be generalized in a natural way to the singular case and, as a corollary, we obtain that when the singular distribution is given by the tangent spaces to the orbits created by a Hamiltonian Lie group action, one reproduces the Universal Reduction Procedure of Arms, Cushman, and Gotay.