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Mirror Symmetry (mirror + symmetry)
Selected AbstractsBrane tilings and their applicationsFORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 6 2008M. Yamazaki Abstract We review recent developments in the theory of brane tilings and four-dimensional ,, = 1 supersymmetric quiver gauge theories. This review consists of two parts. In part I, we describe foundations of brane tilings, emphasizing the physical interpretation of brane tilings as fivebrane systems. In part II, we discuss application of brane tilings to AdS/CFT correspondence and homological mirror symmetry. More topics, such as orientifold of brane tilings, phenomenological model building, similarities with BPS solitons in supersymmetric gauge theories, are also briefly discussed. This paper is a revised version of the author's master's thesis submitted to Department of Physics, Faculty of Science, the University of Tokyo on January 2008, and is based on his several papers and some works in progress [1,7]. [source] Compactifications on half-flat manifolds,FORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 3 2005S. Gurrieri Abstract We review various aspects of compactifications of heterotic and type II supergravities on six dimensional manifolds. In the general framework of non-Kähler compactifications, emphasis is made on a particular class of manifolds with SU(3)-structure named half-flat. We recall how these manifolds appeared in the context of mirror symmetry of type II theories, providing mirror configurations to Calabi-Yau compactifications with NS-NS electric fluxes. In the heterotic sector, they generate a potential for all moduli, and are expected to break the E8 × E8 gauge group down to SO(10) × E8 in 4 dimensions. [source] Technical Note: Accounting for anatomical symmetry in the first-order optical character of left and right eyesOPHTHALMIC AND PHYSIOLOGICAL OPTICS, Issue 4 2007W. F. Harris Abstract In quantitative analyses of the optical character of eyes (and related systems) it is sometimes necessary to deal with left and right eyes in the same context. In accounting for anatomical symmetry (mirror symmetry in the mid-sagittal plane) one treats a cylinder axis at 20°, say, in a left eye as equivalent to an axis at 160° in a right eye. But this is only one aspect of the linear optical character of an eye. The purpose of this note is to show how to account for anatomical symmetry in the linear optical character of eyes in general. In particular the note shows how to modify the optical properties of left (or right) eyes so that anatomical symmetry is accounted for in quantitative analyses in contexts in which both left and right eyes are involved. [source] Polymorphism and piezochromicity in the three-dimensional network-based phosphate RbCuPO4ACTA CRYSTALLOGRAPHICA SECTION B, Issue 4 2010Paul F. Henry Rubidium copper phosphate, RbCuPO4, forms two room-temperature polymorphs that have been investigated with neutron powder diffraction. Polymorph (II) can be converted quantitatively into (I) by grinding the material or by pelletization, and the phase transition is accompanied by a significant colour change from very pale green to sky blue. Polymorph (II) can be obtained essentially free of (I) by quenching from 723,K. Each polymorph shows two unique Cu atoms: in (I) both sites are four-coordinate in a 2:1 ratio, whereas in (II) the atoms are four- and five-coordinate in a 1:1 ratio. In each case these sites are linked by phosphate tetrahedra to form three-dimensional frameworks based on the 42638- a four-connected net. The Rb atoms are hosted in the six- and eight-ring channels that are similar to those observed in zeolite ABW. The (II) , (I) phase transition is also accompanied by a volume reduction of 2.1% even though the average coordination of the Cu atoms also falls. The structures of the polymorphs are critically examined and compared with those of KNiPO4 and KCuPO4 in terms of hexagonal close packing containing ordered phosphate arrays. As a result of buckling of the six-ring layers, one-dimensional chains of dimerized copper polyhedra are identified in (II), chains that become trimers with mirror symmetry in (I). [source] Flux growth and structure of two compounds with the EuIn2P2 structure type, AIn2P2 (A = Ca and Sr), and a new structure type, BaIn2P2ACTA CRYSTALLOGRAPHICA SECTION C, Issue 10 2009Japheth F. Rauscher Single crystals of the new Zintl phases AIn2P2 [A = Ca (calcium indium phosphide), Sr (strontium indium phosphide) and Ba (barium indium phosphide)] have been synthesized from a reactive indium flux. CaIn2P2 and SrIn2P2 are isostructural with EuIn2P2 and crystallize in the space group P63/mmc. The alkaline earth cations A are located at a site with m symmetry; In and P are located at sites with 3m symmetry. The structure type consists of layers of A2+ cations separated by [In2P2]2, anions that contain [In2P6] eclipsed ethane-like units that are further connected by shared P atoms. This yields a double layer of six-membered rings in which the In,In bonds are parallel to the c axis and to one another. BaIn2P2 crystallizes in a new structure type in the space group P21/m with Z = 4, with all atoms residing on sites of mirror symmetry. The structure contains layers of Ba2+ cations separated by [In2P2]2, layers of staggered [In2P6] units that form a mixture of four-, five- and six-membered rings. As a consequence of this more complicated layered structure, both the steric and electronic requirements of the large Ba2+ cation are met. [source] A polymorph of tetrakis(acetonitrile-,N)copper(I) tetrafluoridoborateACTA CRYSTALLOGRAPHICA SECTION C, Issue 2 2009Jan W. Bats A P212121 polymorph of the title compound, [Cu(CH3CN)4]BF4, is reported. The crystal structure is very similar to the structure of the Pna21 polymorph reported by Jones & Crespo [Acta Cryst. (1998), C54, 18,20]. The anions and one of the three independent cations occupy similar positions in both polymorphs. Two of the four symmetry-related positions of the other two cations are also identical in the two polymorphs, and the other two positions are related by mirror symmetry. The crystal used for the structure determination contained a volume fraction of 0.088,(7) of the Pna21 polymorph. [source] 3,6-Bis(dimethylamino)-10-propylacridinium iodideACTA CRYSTALLOGRAPHICA SECTION C, Issue 11 2001Raffaella Puliti In the title compound, C20H26N3+·I,, the acridinium moiety shows mirror symmetry about the central C,N vector. The fused tricyclic system is only approximately planar and the geometry is affected by the presence of both dimethylamino groups and the propyl substitution at the central N atom. The propyl chain adopts an extended trans conformation and the plane through the chain C atoms is perpendicular to the mean plane through the rings. The I, ion is involved in short-range hydrogen-bonding interactions with two centrosymmetrically related cations via three activated acridinium C atoms. Stacks of acridinium cations propagate through the crystal along the c direction. The ring overlap is partial, but the dimethylamino groups also participate in the stacking. [source] | ||||||||||