Fluctuating commutative geometry

We use the framework of noncommutative geometry to define a discrete model for fluctuating geometry. Instead of considering ordinary geometry and its metric fluctuations, we consider generalized geometries where topology and dimension can also fluctuate. The model describes the geometry of spaces with a countable number n of points. The spectral principle of Connes and Chamseddine is used to define dynamics. We show that this simple model has two phases. The expectation value , the average number of points in the universe, is finite in one phase and diverges in the other. Moreover, the dimension delta is a dynamical observable in our model, and plays the role of an order parameter. The computation of is discussed and an upper bound is found, < 2. We also address another discrete model defined on a fixed d = 1 dimension, where topology fluctuates. We comment on a possible spontaneous localization of topology.

3D hydrogen-bonded network built from copper(II) complexes of 1,3-propanediamine

The reaction of Cu(NO3)(2).3H(2)O with 1,3-propanediamine (pn), in the presence of NaN3, afforded a 1:1 co-crystal formed by [Cu(NO3)(2)(pn)(2)] and [Cu(N-3)(NO3)(pn)(2)] (1 and 2), which were characterized by elemental analysis, IR spectroscopy and single crystal X-ray diffraction. In both compounds, the copper(II) centers are in a distorted octahedral environment, formed by four N atoms of two bidentate pn ligands in the basal plane, whereas the axial bonds are formed by two O atoms from the nitrate ligands in 1 and one O atom from the nitrate ligand and one N atom from the azide ion in 2. The asymmetric unit of the crystal consists of two crystallographically independent 1 and 2 complexes, which are held together in a 3D network by a series of N - H center dot center dot center dot O and N - H center dot center dot center dot N hydrogen bonds, as well C - H center dot center dot center dot O interactions. New supramolecular synthons are identified by the occurrence of two geometrically distinct molecular recognition patterns involving the NO3- ion and amino groups from pn ligands.

Association of 3D Reconstruction and Conventional Radiography for the Description of the Appendicular Skeleton of Chelonoidis carbonaria (Spix, 1824)

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

Tensor3D: A computer graphics program to simulate 3D real-time deformation and visualization of geometric bodies

Tensor3D is a geometric modeling program with the capacity to simulate and visualize in real-time the deformation, specified through a tensor matrix and applied to triangulated models representing geological bodies. 3D visualization allows the study of deformational processes that are traditionally conducted in 2D, such as simple and pure shears. Besides geometric objects that are immediately available in the program window, the program can read other models from disk, thus being able to import objects created with different open-source or proprietary programs. A strain ellipsoid and a bounding box are simultaneously shown and instantly deformed with the main object. The principal axes of strain are visualized as well to provide graphical information about the orientation of the tensor's normal components. The deformed models can also be saved, retrieved later and deformed again, in order to study different steps of progressive strain, or to make this data available to other programs. The shape of stress ellipsoids and the corresponding Mohr circles defined by any stress tensor can also be represented. The application was written using the Visualization ToolKit, a powerful scientific visualization library in the public domain. This development choice, allied to the use of the Tcl/Tk programming language, which is independent on the host computational platform, makes the program a useful tool for the study of geometric deformations directly in three dimensions in teaching as well as research activities. (C) 2007 Elsevier Ltd. All rights reserved.

Study of plasma immersion ion implantation into silicon substrate using magnetic mirror geometry

The effect of magnetic field enhanced plasma immersion ion implantation (PIII) in silicon substrate has been investigated at low and high pulsed bias voltages. The magnetic field in magnetic bottle configuration was generated by two magnetic coils installed outside the vacuum chamber. The presence of both, electric and magnetic field in PIII creates a system of crossed E x B fields, promoting plasma rotation around the target. The magnetized electrons drifting in crossed E x B fields provide electron-neutral collision. Consequently, the efficient background gas ionization augments the plasma density around the target where a magnetic confinement is achieved. As a result, the ion current density increases, promoting changes in the samples surface properties, especially in the surface roughness and wettability and also an increase of implantation dose and depth. (C) 2012 Elsevier B. V. All rights reserved.

Evaluation of Different Methods of Optical Impression Making on the Marginal Gap of Onlays Created with CEREC 3D

Objectives: This study evaluated the marginal gaps on several surfaces of onlays created with the Cerec 3D system using one intraoral and two extraoral optical impression methods. Methods: A human molar (#19) was mounted with its adjacent teeth on a typodont (Frasaco) and prepared for a MODL onlay. The typodont was assembled in the mannequin head in order to simulate clinical conditions. The same operator took 36 individual optical impressions using a CEREC 3D camera. For group 1 (IP), a thin layer of titanium dioxide powder (CEREC powder-VITA) was applied directly onto the surface of the preparation for imaging (n=12). For group 2 (EP), a sectional impression was taken with hydrocolloid Identic Syringable (Dux Dental), a die made with polyvinylsiloxane KwikkModel Scan (R-dental Dentalerzeugnisse GmbH) and powdered with titanium dioxide for imaging (n=12). For group 3 (ES), a sectional impression was taken with PVS and a sectional stock tray, a die fabricated in stone (Diamond die- HI-TEC Dental Products) and the die being imaged without powdering (n=12). One operator designed and machined the onlays in Vita Blocks Mark II for Cerec (VITA) using a CEREC 3D. The marginal gaps (pm) were measured with an optical microscope (50x) at 12 points, three on each surface of the MODL. The results were analyzed by two-way ANOVA/Tukey's (p=0.05). Results: The overall mean marginal gaps (mu m) for the three methods were: IP=111.6 (+/- 34.0); EP=161.4 (+/- 37.6) and ES=116.8 (+/- 42.3). IP and ES were equal, but both were significantly less than EP. The pooled mean marginal gaps (mu m) for the occlusal = 110.5 (+/- 39) and lingual = 111.5 (+/- 30.5) surfaces were equivalent and significantly less than the distal = 136.5 (+/- 42.5) and mesial = 161.1 (+/- 43.3). Conclusion: The marginal gap of CEREC 3D onlay restorations was not different when the optical impression was taken intraorally vs extraorally using a stone cast that does not require powdering. The lingual and occlusal surfaces showed the lowest gaps.

Terbium(III) and dysprosium(III) 8-connected 3D networks containing 2,5-thiophenedicarboxylate anion: Crystal structures and photoluminescence studies

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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.

Combining genetic algorithm and simulated annealing: A molecular geometry optimization study

We introduce a new hybrid approach to determine the ground state geometry of molecular systems. Firstly, we compared the ability of genetic algorithm (GA) and simulated annealing (SA) to find the lowest energy geometry of silicon clusters with six and 10 atoms. This comparison showed that GA exhibits fast initial convergence, but its performance deteriorates as it approaches the desired global extreme. Interestingly, SA showed a complementary convergence pattern, in addition to high accuracy. Our new procedure combines selected features from GA and SA to achieve weak dependence on initial parameters, parallel search strategy, fast convergence and high accuracy. This hybrid algorithm outperforms GA and SA by one order of magnitude for small silicon clusters (Si6 and Si10). Next, we applied the hybrid method to study the geometry of a 20-atom silicon cluster. It was able to find an original geometry, apparently lower in energy than those previously described in literature. In principle, our procedure can be applied successfully to any molecular system. © 1998 Elsevier Science B.V.

Energy and angular momentum of the gravitational field in the teleparallel geometry

The Hamiltonian formulation of the teleparallel equivalent of general relativity is considered. Definitions of energy, momentum and angular momentum of the gravitational field arise from the integral form of the constraint equations of the theory. In particular, the gravitational energy-momentum is given by the integral of scalar densities over a three-dimensional spacelike hypersurface. The definition for the gravitational energy is investigated in the context of the Kerr black hole. In the evaluation of the energy contained within the external event horizon of the Kerr black hole, we obtain a value strikingly close to the irreducible mass of the latter. The gravitational angular momentum is evaluated for the gravitational field of a thin, slowly rotating mass shell. © 2002 The American Physical Society.

Gravitational energy of Kerr and Kerr anti-de Sitter space-times in the teleparallel geometry

In the context of the hamiltonian formulation of the teleparallel equivalent of general relativity we compute the gravitational energy of Kerr and Kerr Anti-de Sitter (Kerr-AdS) space-times. The present calculation is carried out by means of an expression for the energy of the gravitational field that naturally arises from the integral form of the constraint equations of the formalism. In each case, the energy is exactly computed for finite and arbitrary spacelike two-spheres, without any restriction on the metric parameters. In particular, we evaluate the energy at the outer event horizon of the black holes. © SISSA/ISAS 2003.

Reversible holographic 3D data storage in oxide glasses using visible lasers

Antimony based glasses have been investigated for the first time regarding the possibility of holographic data storage using visible lasers sources. Changes in both refractive index and the absorption coefficient were measured using a holographic setup. The modulation of the optical constants is reversible by heat treatment. Bragg gratings were written under visible light of an Ar laser and erased thermally.