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Topological Characteristics (topological + characteristic)

Distribution by Scientific Domains

Chemistry	40%

Selected Abstracts

Nanocarbon materials: probing the curvature and topology effects using phonon spectra

JOURNAL OF RAMAN SPECTROSCOPY, Issue 9 2009
Sanju Gupta
Abstract Much has been learned from the use of resonance Raman spectroscopy and high-resolution transmission electron microscopy techniques about the micro-/nanoscopic structure of various nanostructured carbons. However, they still possess some features that are not entirely understood particularly in terms of topological characteristics, which go beyond making a distinction with just the geometrical structure at nanoscale. To effectively utilize the potential of these materials for technological needs, understanding both the geometrical and topological structure and perhaps relating these attributes to physical (optical/electronic, lattice vibrational) properties become indispensable. Here, we make an attempt to describe the differences between various nanostructures and provide geometrical and topological property assessment semiquantitatively by monitoring the phonon spectra using resonance Raman spectroscopy thereby also capturing the electronic spectra. We elucidate the notion of global topology and curvature for a range of technologically important nanoscale carbons including tubular (single-, double- and multiwalled nanotubes, peapod), spherical (hypo- and hyperfullerenes, onion-like carbon) and complex (nanocones, nanohorns, nanodisks and nanorings) geometries. To demonstrate the proof-of-concept, we determined the variation in the prominent Raman bands of the respective materials, represented as D, G and D* (the overtone of D) bands, as a possible topological or curvature trend due to their sensitivity toward structural modification. The latter arises from local topological defects such as pentagons giving rise to curved nanocarbons. In this study, we provide systematics of their variation with respect to their geometric forms and compare with highly oriented pyrolytic graphite and monolayer graphene since the nanocarbons discussed are their derivatives. Once established, this knowledge will provide a powerful machinery to understand newer nanocarbons and indeed point to an unprecedented emergent paradigm of global topology/curvature , property , functionality relationship. We emphasize that these concepts are applicable to other topologically distinct nanomaterials, which include boron-nitride (BN) nanotubes and nanotori, helical gold nanotubes and Möbius conjugated organics. Copyright © 2009 John Wiley & Sons, Ltd. [source]

X-ray diffraction by a crystal in a permanent external electric field: electric-field-induced structural response in ,-GaPO4

ACTA CRYSTALLOGRAPHICA SECTION A, Issue 1 2006
Semen Gorfman
For the first time, site-selective distortion has been investigated for two different structural units in the ternary compound ,-GaPO4 under the influence of a permanent external electric field. Based on 54 measured reflection intensities, the electric-field-induced distortion of PO4 and GaO4 tetrahedra in ,-GaPO4 crystals is evaluated using a model of pseudoatomic displacements introduced recently [Gorfman, Tsirelson & Pietsch (2005). Acta Cryst. A61, 387396]. A stronger variation of the P,O bond lengths in the PO4 tetrahedron was found compared to the bonds in the GaO4 tetrahedron. The different distortions of the tetrahedra owing to the electric field were analysed in terms of the valence charge density of ,-GaPO4 and its topological characteristics. The larger charge of the P pseudoatom compared to the Ga atom was recognized as the main reason for the higher sensitivity of the PO4 tetrahedron to a permanent external electric field. [source]

SOLUTIONS FOR EXTERIOR ORIENTATION IN PHOTOGRAMMETRY: A REVIEW

THE PHOTOGRAMMETRIC RECORD, Issue 100 2002
Pierre Grussenmeyer
Abstract The determination of the attitude, the position and the intrinsic geometric characteristics of the camera is recognised as the fundamental photogrammetric problem. It can be summarised as the determination of camera interior and exterior orientation parameters, as well as the determination of 3D coordinates of object points. The term "exterior orientation" of an image refers to its position and orientation related to an exterior (object space) coordinate system. Several methods can be applied to determine the parameters of the orientation of one, two or more photos. The orientation can be processed in steps (as relative and absolute orientation) but simultaneous methods (such as bundle adjustments) are now available in many software packages. Several methods have also been developed for the orientation of single images. They are based in general on geometric and topological characteristics of imaged objects. This paper presents a survey of classical and modern methods for the determination of the exterior parameters in photogrammetry, some of which are available as software packages (with practical examples) on the Internet. The methods presented are classified in three principal groups. In the first. a selection of approximate methods for applications that do not require great accuracy is presented. Such methods are also used to calculate values required for iterative processes. In the second group, standard point-bused methods derived from collinearity, coplanarity or coangularity conditions are briefly reviewed, followed by line-based approaches. The third group represents orientation methods based on constraints and on concepts of projective geometry, which are becoming of increasing interest for photogrammetrists. In the last section, the paper gives a summary of existing strategies for automatic exterior orientation in aerial photogrammetry. Résumé La détermination de l'attitude, de la position et des caractéristiques intrinsèques de la chambre photographique constitue un problème fondamental en photogrammétrie. Il se résume à la détermination des paramètres de l'orientation de la chambre de prise de vue (paramètres des orientations externe et interne), ainsi qu'à la détermination des coordonnées 30 des points de l'objet. L'orientation externe se rapporte à la détermination de la position et de l'orientation d'une chambre par rapport à un système externe de coordonnées. Différentes méthodes peuvent être utilisées pour calculer les éléments dorientation externe d'une photo, d'un couple ou de plusieurs photos. Le calcul de l'orientation peut être réalisé par étapes (par exemple les orientations relative et absolue) mais les méthodes simultanées (la compensation par faisceaux par exemple) sont actuellement proposées dans la plupart des logiciels. Plusieurs méthodes ont aussi été développées pour l'orientation d'images isolées. Ells sont basées en général sur les caactéristiques géométriques et topologiques des objets photographiés. Dans cet article on présente un ensemble de méthodes classiques et modernes pour la détermination des paramètres de l'orientation externe, certaines d'entre elles étant téléchargeables sous la forme d'applications sur Internet. Les méthodes présentées sont classées en trois groupes principaux. Le premier groupe contient une sélection de méthodes approximatives utilisées d'habitude quand une grande précision n'est pas exigée, ou encore pour calculer des vuleurs approchées des paramètres extrinsèques requises pour les méthodes itératives rigoureuses. Dans le deuxième groupe, on rappelle brièvement les jondements des méthodes basées sur les conditions photogrammétriques fondamentales (la colinéarité, la coplanéité et la coangularité). Dans ce groupe, les méthodes basées sur l'extraction des points ou des lignes sont également abordées. Le troisième groupe traite des méthodes d'orientation basées sur les contraintes et les concepts de la géométrie projective, de plus en plus utilisées par les photogrammètres. Le dernier paragraphe se rapporte aux méthodes destinées à automatiser le calcul de l'orientation externe en photogrammétrie aérienne. Zusummenfussung Die Bestimmung der Neigung, der Position und den geometrischen parametern der Kamera wird als das fundamentale Problem der Photogrammetrie angesehen. Es kann zusammenfassend sowohl als die Bestimmung der Parameter der inneren und äusseren Orientierung der Kamera angesehen werden, als auch als die Bestimmung von 3D Koordinaten von Objektpunkten. Der Ausdruck "äussere Orientierung" eines Bildes bezieht sich auf die Lage und Orientierung bezogen auf ein äusseres (Objektraum-) Koordinatensystem. Es können verschiedene Methoden angewandt werden, um die Parameter von einem, zwei oder mehreren Bildern zu bestimmen. Die orientierung kann in Schritten erfolgen, was als Relative und Absolute Orientierung bezeichnet wird, aber auch simultane Methoden, wie die Bündelausgleichung, sind in vielen Softwarepaketen implementiert. Es wurden auch Methoden für die Orientierung von Einzelbildern entwickelt, die geometrische und topologische Eigenschaften der abgebildeten Objekte nutzen. In diesem Beitrag wird Beitrag wird eine Studie klassischer und moderner Methoden der Photogrammetrie zur Bestimmung der Parameter der äßeren Orientierung vorgestellt, wovon einige in Softwarepaketen zur Verfügung stehen, die von praktischen Beispielen im Internet ergänzt werden. Die untersuchten Methoden werden in drei Hauptgruppen eingeteilt. In einer ersten Gruppe werden Näherungslösungen vorgestellt, die für Anwendungen mit geringen Genauigkeitsanforderungen geeignet sind. Diese Methoden werden ansonsten für die Näherngswertberechunggen für iterative Prozesse verwendet. IN der zweiten Gruppe werden zuerst die punktbasierten Standardmethoden vorgestellt, die von Bedingungen zur Kollinearität. Koplanarität und Kowinkligkeit abgeletet sind. Danach folgen linienbasierte Ansätze. Die dritte Gruppe umfasst Orientierungsmethoden, die auf Zwangsbedingungen und auf Konzepte der projektiven Geometrie aufbauen, die für Photogrammeter von zunehmendem Interesse sind, Im letzten Abschnitt wird eine Zusammenfassung existierender Strategien für eine automatische äussere orientierung in der Luftbildphotogrammetrie gegeben. [source]

Solutions for Exterior Orientation in Photogrammetry: A Review

THE PHOTOGRAMMETRIC RECORD, Issue 100 2002
Pierre Grussenmeyer
The determination of the attitude, the position and the intrinsic geometric characteristics of the camera is recognised as the fundamental photogrammetric problem. It can be summarised as the determination of camera interior and exterior orientation parameters, as well as the determination of 3D coordinates of object points. The term "exterior orientation"of an image refers to its position and orientation related to an exterior (object space) coordinate system. Several methods can be applied to determine the parameters of the orientation of one, two or more photos. The orientation can be processed in steps (as relative and absolute orientation) but simultaneous methods (such as bundle adjustments) are now available in many software packages. Several methods have also been developed for the orientation of single images. They are based in general on geometric and topological characteristics of imaged objects. This paper presents a survey of classical and modern methods for the determination of the exterior parameters in photogrammetry, some of which are available as software packages (with practical examples) on the Internet. The methods presented are classified in three principal groups. In the first, a selection of approximate methods for applications that do not require great accuracy is presented. Such methods are also used to calculate values required for iterative processes. In the second group, standard point,based methods derived from collinearity, coplanarity or coangularity conditions are briefly reviewed, followed by line,based approaches. The third group represents orientation methods based on constraints and on concepts of projective geometry, which are becoming of increasing interest for photogrammetrists. In the last section, the paper gives a summary of existing strategies for automatic exterior orientation in aerial photogrammetry. [source]

The mathematical pendulum from Gauß via Jacobi to Riemann

ANNALEN DER PHYSIK, Issue 6 2009
W. Dittrich
Abstract The goal of this article is to introduce double-periodic elliptic functions on the basis of a "simple" mechanical system, that of the mathematical pendulum. Thereby it is not geometry that is in the foreground, as in Gauß's analysis of the lemniscatian curve, but rather the calculation of the specific attributes of elliptic functions with the aid of a periodic integrable system. Not the spatial degree of freedom, but the time variable is continued into the complex plane. This will make it possible for us to not only identify the known real period of the pendulum oscillation, but also to detect a second imaginary period. Only then does the solution of the equation of motion become a Jacobi-type elliptic function. Using the Cauchy integral theorem, which Gauß was already familiar with, as well as the simplest Riemannian surface of the function , we want to calculate the analytic and topological characteristics of the oscillatory motion of a pendulum. Our intent is to show that elliptic functions could have appeared much earlier than 1796 in the literature. Admittedly, for this the field of complex numbers was necessary, as represented in the Gaußian plane of complex numbers. However, Gauß was unwilling to publish his findings because of his "fear of the cry of the Boeotians". [source]