Finite motions from periodic frameworks with added symmetry

Recent work from authors across disciplines has made substantial contributions to counting rules (Maxwell type theorems) which predict when an infinite periodic structure would be rigid or flexible while preserving the periodic pattern, as an engineering type framework, or equivalently, as an idealized molecular framework. Other work has shown that for finite frameworks, introducing symmetry modifies the previous general counts, and under some circumstances this symmetrized Maxwell type count can predict added finite flexibility in the structure. In this paper we combine these approaches to present new Maxwell type counts for the columns and rows of a modified orbit matrix for structures that have both a periodic structure and additional symmetry within the periodic cells. In a number of cases, this count for the combined group of symmetry operations demonstrates there is added finite flexibility in what would have been rigid when realized without the symmetry. Given that many crystal structures have these added symmetries, and that their flexibility may be key to their physical and chemical properties, we present a summary of the results as a way to generate further developments of both a practical and theoretic interest.Comment: 45 pages, 13 figure

Grain orientation in high Tc superconductors by molten salt powder synthesis

The molten salt or the flux method is used to fabricate a grain oriented YBa2Cu3O(7-x) (123) superconductor. Here we suggest a two-stage approach in using the 'green phase', Y2BaCuO5 (211), as seed crystals in the formation of YBa2Cu3O(7-x). The process uses Y2BaCuO5 formed by molten salt synthesis. The Y2BaCuO5 phase was observed to be stable in water and in most of the salt systems. Salt processing can form a small quantity of anisotropic particles of Y2BaCuO5. This material can form the 123 phase when tape cast and sintered in the presence of the required levels of Ba and Cu

Symmetry adapted Assur decompositions

Assur graphs are a tool originally developed by mechanical engineers to decompose mechanisms for simpler analysis and synthesis. Recent work has connected these graphs to strongly directed graphs, and decompositions of the pinned rigidity matrix. Many mechanisms have initial configurations which are symmetric, and other recent work has exploited the orbit matrix as a symmetry adapted form of the rigidity matrix. This paper explores how the decomposition and analysis of symmetric frameworks and their symmetric motions can be supported by the new symmetry adapted tools.Comment: 40 pages, 22 figure

Rigidity of frameworks on expanding spheres

A rigidity theory is developed for bar-joint frameworks in $\mathbb{R}^{d+1}$ whose vertices are constrained to lie on concentric $d$-spheres with independently variable radii. In particular, combinatorial characterisations are established for the rigidity of generic frameworks for $d=1$ with an arbitrary number of independently variable radii, and for $d=2$ with at most two variable radii. This includes a characterisation of the rigidity or flexibility of uniformly expanding spherical frameworks in $\mathbb{R}^{3}$. Due to the equivalence of the generic rigidity between Euclidean space and spherical space, these results interpolate between rigidity in 1D and 2D and to some extent between rigidity in 2D and 3D. Symmetry-adapted counts for the detection of symmetry-induced continuous flexibility in frameworks on spheres with variable radii are also provided.Comment: 22 pages, 2 figures, updated reference

Coning, symmetry and spherical frameworks

In this paper, we combine separate works on (a) the transfer of infinitesimal rigidity results from an Euclidean space to the next higher dimension by coning, (b) the further transfer of these results to spherical space via associated rigidity matrices, and (c) the prediction of finite motions from symmetric infinitesimal motions at regular points of the symmetry-derived orbit rigidity matrix. Each of these techniques is reworked and simplified to apply across several metrics, including the Minkowskian metric \M^{d} and the hyperbolic metric \H^{d}. This leads to a set of new results transferring infinitesimal and finite motions associated with corresponding symmetric frameworks among \E^{d}, cones in $E^{d+1}$, \SS^{d}, \M^{d}, and \H^{d}. We also consider the further extensions associated with the other Cayley-Klein geometries overlaid on the shared underlying projective geometry.Comment: 38 pages, 7 figure

Contribution to the occurrence and distribution of culicid mosquitoes in Northrhine-Westphalia with special reference to the greater Bonn area

Mit dem Verschwinden der Malaria aus Deutschland in der Mitte des letzten Jahrhunderts sank auch das wissenschaftliche Interesse an Stechmücken. Seit Jahrzehnten sind keine großflächigen systematischen Studien zum Vorkommen und zur Verbreitung der einheimischen Culicidenarten mehr durchgeführt worden, da diese scheinbar keine Vektorfunktion mehr hatten. Lediglich saisonal bedingte Massenvermehrungen waren und sind Anlass zu gezielten Bekämpfungsaktionen, die auch aktuell regionale Daten zur Stechmückenfauna liefern (BECKER & KAISER 1995). Diese und weitere sporadische Studien aus den letzten Jahren (BASTIAN 2000; HERRMANN 2000; KAMPEN unveröffentl.) zeigen, dass potenzielle Malariaüberträger nach wie vor bei uns heimisch sind. Gerade die anhaltende Diskussion über ‚emerging and resurging infectious diseases’ in Verbindung mit möglichen Klima- und Umweltveränderungen (GRATZ 1999, 2004) sollte aber das allgemeine Interesse an den einheimischen (potenziellen) Vektoren wecken, um für Eventualitäten gewappnet zu sein. Der weltweite Massentourismus und Tierhandel sorgt nicht nur für ein permanentes Angebot an Infektionsquellen für einheimische hämatophage Arthropoden, sondern erleichtert auch die Einschleppung und Ausbreitung von allochthonen Vektoren. So gelangte etwa die Tigermücke Aedes albopictus, ein effizienter Gelbfieber- und Dengue-Vektor, zu Beginn der 1990er Jahre mit dem Gebrauchtreifenhandel nach Südeuropa (KNUDSEN et al. 1996) und wandert seitdem ständig weiter nach Norden (SCHAFFNER 2001; FLACIO et al. 2004; SCHOLTE et al. 2006). Doch auch Zugvögel bringen seit jeher Viren aus afrikanischen Ländern nach Europa undkönnen einheimische Vektoren infizieren (MALKINSON & BANET 2002). Bis auf wenige Ausnahmen blieben große Epidemien bisher aus. Nicht so in Nordamerika, wo 1999 auf bislang unbekanntem Wege das West Nil-Virus eingeschleppt wurde und sich bis 2003 über die gesamten Vereinigten Staaten ausbreitete (GOULD & FIKRIG 2004). Zahlreiche Todesfälle bei Menschen, Pferden und Vögeln, insbesondere auf eine Virusübertragung durch Culex pipiens zurückzuführen, waren die Folge. Mit dem Tahyna-, Sindbis- und West Nil-Virus kursieren mindestens drei pathogene Stechmückenassoziierte Viren auch in Europa (ASPÖCK 1996; LUNDSTRÖM 1999). Erst kürzlich wurde in toten Vögeln in Österreich erstmals das Usutu-Virus außerhalb Afrikas nachgewiesen (WEISSENBÖCK et al. 2002). Ob es humanpathogenes Potenzial hat, ist unbekannt. Schließlich sind Stechmücken als Überträger der caninen Filariose von Bedeutung, die gelegentlich auch den Menschen befallen kann und sich offenbar ebenfalls vom Mittelmeerraum nach Norden ausbreitet (MURO 1999; PAMPIGLIONE & RIVASI 2000). Die vorgestellte Studie soll einen Beitrag zur Aktualisierung unserer Kenntnisse zum Vorkommen, zur Verbreitung und zur Biologie einheimischer Culiciden liefern, die erforderlich sind, um auf autochthone Erregerübertragung in geeigneter Weise reagieren zu können.To update information on the indigenous culicid fauna (Diptera: Culicidae) of western Germany, aquatic mosquito stages were collected by water dipping and adults caught by specialized traps at various Northrhine-Westphalian localities in 2004. Out of 154 water basins checked, 75 turned out to be culicid breeding sites. 1404 larvae and pupae belonging to 17 species were collected. These comprised 7 Aedes-, 4 Culex-, 4 Anopheles- and 2 Culiseta-species. Cx. territans specimens added up to 44.7 % of the larval and pupal catches and together with the three other most abundant species, Cs. annulata (14.7 %), An. maculipennis s.s. (12.3 %) and Cx. torrentium (10 %), amounted to 81.8 % of all larvae and pupae collected. With regard to the adult stages, only 111 specimens belonging to 8 species were trapped probably owing to methodological reasons and/or to the particular mosquito-hostile climatic conditions in the summer of 2004. In contrast to the larval collections, the major part of the adults were Cx. torrentium with 34.2 %, followed by Cx. pipiens s.s. (21.6 %) and An. plumbeus (19.8 %), thus giving a completely different impression on the indigenous population abundances. 105 of the adults were caught by the BG sentinel, a newly developed odour trap emitting a quantified composition of selected mosquito attractants. The other 6 individuals were caught by a CO2-trap, whereas a mere light trap and an ovipositor trap were never successfu

A Giant Planet Around a Metal-poor Star of Extragalactic Origin

Stars in their late stage of evolution, such as Horizontal Branch stars, are still largely unexplored for planets. We report the detection of a planetary companion around HIP 13044, a very metal-poor star on the red Horizontal Branch, based on radial velocity observations with a high-resolution spectrograph at the 2.2-m MPG/ESO telescope. The star's periodic radial velocity variation of P=16.2 days caused by the planet can be distinguished from the periods of the stellar activity indicators. The minimum mass of the planet is 1.25 Jupiter masses and its orbital semi-major axis 0.116 AU. Because HIP 13044 belongs to a group of stars that have been accreted from a disrupted satellite galaxy of the Milky Way, the planet most likely has an extragalactic origin.Comment: 32 pages, 9 Figure

The visitor from an ancient galaxy: A planetary companion around an old, metal-poor red horizontal branch star

We report the detection of a planetary companion around HIP 13044, a metal-poor red horizontal branch star belonging to a stellar halo stream that results from the disruption of an ancient Milky Way satellite galaxy. The detection is based on radial velocity observations with FEROS at the 2.2-m MPG/ESO telescope. The periodic radial velocity variation of P=16.2 days can be distinguished from the periods of the stellar activity indicators. We computed a minimum planetary mass of 1.25 Jupiter masses and an orbital semimajor axis of 0.116 AU for the planet. This discovery is unique in three aspects: First, it is the first planet detection around a star with a metallicity much lower than few percent of the solar value; second, the planet host star resides in a stellar evolutionary stage that is still unexplored in the exoplanet surveys; third, the planetary system HIP 13044 most likely has an extragalactic origin in a disrupted former satellite of the Milky Way.Comment: 5 pages, 2 figures, 2 tables, submitted to the Proceedings of the 276th IAU Symposium "The Astrophysics of Planetary Systems

The orbit rigidity matrix of a symmetric framework

A number of recent papers have studied when symmetry causes frameworks on a graph to become infinitesimally flexible, or stressed, and when it has no impact. A number of other recent papers have studied special classes of frameworks on generically rigid graphs which are finite mechanisms. Here we introduce a new tool, the orbit matrix, which connects these two areas and provides a matrix representation for fully symmetric infinitesimal flexes, and fully symmetric stresses of symmetric frameworks. The orbit matrix is a true analog of the standard rigidity matrix for general frameworks, and its analysis gives important insights into questions about the flexibility and rigidity of classes of symmetric frameworks, in all dimensions. With this narrower focus on fully symmetric infinitesimal motions, comes the power to predict symmetry-preserving finite mechanisms - giving a simplified analysis which covers a wide range of the known mechanisms, and generalizes the classes of known mechanisms. This initial exploration of the properties of the orbit matrix also opens up a number of new questions and possible extensions of the previous results, including transfer of symmetry based results from Euclidean space to spherical, hyperbolic, and some other metrics with shared symmetry groups and underlying projective geometry.Comment: 41 pages, 12 figure