Differential geometry of intersection curves in R(4) of three implicit surfaces

We present algorithms for computing the differential geometry properties of intersection Curves of three implicit surfaces in R(4), using the implicit function theorem and generalizing the method of X. Ye and T. Maekawa for 4-dimension. We derive t, n, b(1), b(2) vectors and curvatures (k(1), k(2), k(3)) for transversal intersections of the intersection problem. (C) 2008 Elsevier B.V. All rights reserved.

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.

Quantum geometry of chiral bosons on a circle

We extend the geometric treatment done for the Majorana-Weyl fermions in two dimensions by Sanielevici and Semenoff to chiral bosons on a circle. For this case we obtain a generalized Floreanini-Jackiw Lagrangian density, and the corresponding gravitational (or Virasoro) anomalies are found as expected. © 1989 The American Physical Society.

On the geometry of non-classical curves

In this paper we relate the numerical invariants attached to a projective curve, called the order sequence of the curve, to the geometry of the varieties of tangent linear spaces to the curve and to the Gauss maps of the curve. © 1992 Sociedade Brasileira de Matemática.

The surface geometry of exotic nuclei

We analyze the surface geometry of the spherical even-even Ca, Ni, Sn and Pb nuclei using two approaches: The relativistic Dirac-Hartree-Bogoliubov one with several parameter sets and the non-relativistic Hartree-Fock-Bogoliubov one with the Gogny force. The proton and neutron density distributions are fitted to two-parameter Fermi density distributions to obtain the half-density radii and diffuseness parameters. Those parameters allow us to determine the nature of the neutron skins predicted by the models. The calculations are compared with existing experimental data. © 2007 American Institute of Physics.

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.

Geosynthetic-Reinforced Soil Structure Built to Restore Original Geometry of a 12 m High Slope After Failure Using Local Soil

This paper presents a study case in which a geosynthetic-reinforced soil (GRS) structure was used to rebuild a 12 m high slope after its failure. The failed slope is located between the parking lot of a private company and a public school. Due to surrounding structures restrictions, this project required a solution with rapidity in execution. In addition, as a requirement established by its owner, this structure should recover the original geometry of the slope. Besides the importance regarding surrounding constructions, an interesting aspect of this study case relies on the versatility of geosynthetic materials. A woven geotextile was used as reinforcement. Five other geosynthetic materials were used in this study case. Facing comprised a geocell filled with local soil cover and grass mats, resulting in a green facing. A geonet was used to hold the grass mats in place before grass roots development. Regarding the drainage system, geocomposite drains and geopipes were installed to drain subsurface water. A nonwoven geotextile was used as filter in drainage trenches, which were placed near the structure toe. Additionally to the GRS structure, the lower portion of the slope was reinforced with soil nailing technique. The face of the nailed soil portion was covered with sandbags and shotcrete. It emphasizes the flexibility of GRS structures regarding their application with other technical options in Geotechnical Engineering. The economic aspect of this study case also deserves attention. It did not require soil transportation and other design and construction steps, e.g. concrete structures design and construction.

Cartan geometry of spacetimes with a nonconstant cosmological function Lambda

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

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.

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.

Boundary identification criteria and geometry analysis of Al 7050 stretch zone from elevation profiles

This article describes the development of a method for analysis of the shape of the stretch zone surface based on parallax measurement theory and using digital image processing techniques. Accurate criteria for the definition of the boundaries of the stretch zone are established from profiles of fracture surfaces obtained from crack tip opening displacement tests on Al-7050 alloy samples. The elevation profiles behavior analysis is based on stretch zone width and height parameters. It is concluded that the geometry of the stretch zone profiles under plane strain conditions can be described by a semi-parabolic relationship. (C) Elsevier B.V., 1999. All rights reserved.

Bundle Block Adjustment of CBERS-2B HRC Imagery Combining Control Points and Lines

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

Static simulation of bulk and selected surfaces of anatase TiO2

A theoretical investigation has been carried out to characterize bulk and selected surfaces of anatase TiO2. The calculations are performed using a B3LYP hybrid functional and 6-31G basis set within the periodic density functional approximation. Optimization procedures have been employed to determine the equilibrium geometry of the crystal and slab surface models. The compressibility, band structure, and the bulk and surface charge distributions are reported. The surface relative energies are identified to follow the sequence: (001) < (101) < (100) much less than (110) < < < (111), from the most stable surface to the least stable one. Relaxation of (001) and (101) surfaces are moderate, with no displacements exceeding; approximate to0.19 Angstrom. The theoretical results are compared with previous theoretical studies and available experimental data. (C) 2001 Elsevier B.V. B.V. All rights reserved.

DFT study of alpha-alanine as a function of the medium polarity

The zwitterionic (Z) form, neutral (N) form and transition structure (TS) connecting N to Z, have been studied at the B3LYP/6-31++G** level of calculation by using the SCRF methodology. The intramolecular proton transfer from oxygen to nitrogen atoms of alpha -alanine and vibrational spectrum were analyzed in the different environments employed: acetonitrile, ethanol, carbon tetrachloride and gas phase. The Z species is a stationary point in acetonitrile and ethanol, but not in carbon tetrachloride and gas phase media. The geometry of N, Z and TS was similar in acetonitrile and ethanol. The vibrational spectrum of Z was similar in the two solvents studied. (C) 2001 Elsevier B.V. B.V. All lights reserved.

On the stabilising effect of gyroscopic moments in an automotive turbocharger

Automotive turbochargers, which operate at very high speeds, exceeding 180,000 r/min, exhibit two strong sub-harmonic modes of vibrations due to oil-whirl instability. These are a conical mode and an in-phase whirl mode. The gyroscopic effects can be very important in such a rotor system. This article presents a theoretical investigation into these effects on the conical whirl instability of a turbocharger induced by the angular (tilting) motion of a rigid rotor. A simplified linear model is used to analyse the rotor-bearing system by investigating the effects of the gyroscopic moment on the internal moments. A gyroscopic coefficient, defined by the geometry of the rotor, is shown to govern the stability of the conical whirl motion. A threshold value of 1/2 is determined for this coefficient to suppress the conical whirl. This value remains unaffected if the rotor is asymmetric and is supported by floating ring bearings, which is the case in a practical turbocharger.