Two matrix-based lattice construction techniques

Let m and n be integers greater than 1. Given lattices A and B of dimensions m and n, respectively, a technique for constructing a lattice from them of dimension m+n-1 is introduced. Furthermore, if A and B possess bases satisfying certain conditions, then a second technique yields a lattice of dimension m+n-2. The relevant parameters of the new lattices are given in terms of the respective parameters of A,B, and a lattice C isometric to a sublattice of A and B. Denser sphere packings than previously known ones in dimensions 52, 68, 84, 248, 520, and 4098 are obtained. © 2012 Elsevier Inc. All rights reserved.

A new number field construction of the lattice E8

Known number theoretical constructions of the lattice E8 use the cyclotomic fields Q(ζ15), Q(ζ20), and Q(ζ24). In this work, an infinite family of Abelian number fields yielding rotated versions of the lattice E 8 is exhibited. © 2012 The Managing Editors.

A family of asymptotically good lattices having a lattice in each dimension

A new constructive family of asymptotically good lattices with respect to sphere packing density is presented. The family has a lattice in every dimension n >= 1. Each lattice is obtained from a conveniently chosen integral ideal in a subfield of the cyclotomic field Q(zeta(q)) where q is the smallest prime congruent to 1 modulo n.

Computations of the flow past a still sphere at moderate reynolds numbers using an immersed boundary method

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

An Extension of Craig's Family of Lattices

Let p be a prime, and let zeta(p) be a primitive p-th root of unity. The lattices in Craig's family are (p - 1)-dimensional and are geometrical representations of the integral Z[zeta(p)]-ideals < 1 - zeta(p)>(i), where i is a positive integer. This lattice construction technique is a powerful one. Indeed, in dimensions p - 1 where 149 <= p <= 3001, Craig's lattices are the densest packings known. Motivated by this, we construct (p - 1)(q - 1)-dimensional lattices from the integral Z[zeta(pq)]-ideals < 1 - zeta(p)>(i) < 1 - zeta(q)>(j), where p and q are distinct primes and i and fare positive integers. In terms of sphere-packing density, the new lattices and those in Craig's family have the same asymptotic behavior. In conclusion, Craig's family is greatly extended while preserving its sphere-packing properties.

Hopf solitons and area-preserving diffeomorphisms of the sphere

We consider a (3+1)-dimensional local field theory defined on the sphere S-2. The model possesses exact soliton solutions with nontrivial Hopf topological charges and an infinite number of local conserved currents. We show that the Poisson bracket algebra of the corresponding charges is isomorphic to that of the area-preserving diffeomorphisms of the sphere S-2. We also show that the conserved currents under consideration are the Noether currents associated to the invariance of the Lagrangian under that infinite group of diffeomorphisms. We indicate possible generalizations of the model.

Salt-induced sphere-to-disk transition of octadecyltrimethylammonium bromide micelles

We have used surface tension measurements, differential scanning calorimetry (DSC), dynamic light scattering (DLS), and cryo-transmission electron microscopy (cryo-TEM) to investigate the dynamic and structural behavior of octadecyltrimethylammonium bromide (C(18)TAB) micelles in water and NaBr solution. The surface tension data for fixed C(18)TAB concentrations of 25 mM and varied NaBr additions (0-50 mM) shows that the critical micelle concentration (cmc) increases after an initial decrease at 0.5 mM NaBr. This unusual effect has been explained using results from DSC and DLS. At low salt concentrations (below ca. 25 mM) the relaxation time distribution is bimodal with a dominant fast mode due to spherical micelles. Above ca. 35 mM NaBr disklike structures are favored and the relaxation time distribution is more closely unimodal. The postulated sphere-to-disk transition is supported by cryo-TEM micrographs. A pronounced increase in the micellar effective hydrodynamic radius (R-H) is observed as the NaBr concentration is increased above about 35 mM; below 35 mM the R-H of the spherical micelles changes Little with ionic strength.

Morphology and topography analysis of mesoporous titania templated by micrometric latex sphere arrays

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Sphere of influence and gravitational capture radius: a dynamical approach

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Composition of the first coordination sphere of Ni2+ in concentrated aqueous NiBr2 solutions by x-ray diffraction

Two concentrated solutions of NiBr2 have been examined by x-ray diffraction. The Fourier transformed scattering data indicate inner complex formation between Ni2 + and Br- ions. Average numbers of bonded bromide ions per nickel atom have been determined for each solution and the reliability of the complexation numbers as well as of the other structural parameters has been critically examined. © 1985 American Institute of Physics.

Bifundamental fuzzy 2-Sphere and fuzzy killing spinors

We review our construction of a bifundamental version of the fuzzy 2-sphere and its relation to fuzzy Killing spinors, first obtained in the context of the ABJM membrane model. This is shown to be completely equivalent to the usual (adjoint) fuzzy sphere. We discuss the mathematical details of the bifundamental fuzzy sphere and its field theory expansion in a model-independent way. We also examine how this new formulation affects the twisting of the fields, when comparing the field theory on the fuzzy sphere background with the compactification of the 'deconstructed' (higher dimensional) field theory.

Shvo's catalyst in chemoenzymatic dynamic kinetic resolution of amines-inner or outer sphere mechanism?

Evidence is provided for the inner-sphere mechanism with actual metal coordination of the racemic amine in the crucial hydrogen transfer step promoted by Shvo's catalyst of the chemoenzymatic dynamic kinetic resolution (DKR) of amines. Key intermediates involved in this H-transfer step were intercepted and continuously monitored by electrospray ionization mass spectrometry (ESI-MS) and characterized by their dissociation chemistries via ESI-MS/MS. © 2013 The Royal Society of Chemistry.

COINCIDENCES OF FIBREWISE MAPS BETWEEN SPHERE BUNDLES OVER THE CIRCLE

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)