Structural characterization of the ionic title complex, [MgBr(THF)5][Co(dpbz)2]·2THF [THF is tetrahydrofuran, C4H8O; dpbz is 1,2-bis(diphenylphosphanyl)benzene, C30H24P2], revealed a well-separated cation and anion co-crystallized with two THF solvent molecules that interact with the cation via weak C—H...O contacts. The geometry about the cobalt center is pseudotetrahedral, as is expected for a d10 metal center, only deviating from an ideal tetrahedral geometry because of the restrictive bite angles of the bidentate phosphane ligands. Three THF ligands of the cation and one co-crystallized THF solvent molecule are each disordered over two orientations. In the extended structure, the cations and THF solvent molecules are arranged in (100) sheets that alternate with layers of anions, the latter of which show various π-interactions, which may explain the particular packing arrangement.
more »
« less
Extended geometry of magical supergravities
A bstract We provide, through the framework of extended geometry, a geometrisation of the duality symmetries appearing in magical supergravities. A new ingredient is the general formulation of extended geometry with structure group of non-split real form. A simple diagrammatic rule for solving the section constraint by inspection of the Satake diagram is derived.
more »
« less
- Award ID(s):
- 2112859
- PAR ID:
- 10437585
- Date Published:
- Journal Name:
- Journal of High Energy Physics
- Volume:
- 2023
- Issue:
- 5
- ISSN:
- 1029-8479
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
We contribute to the foundations of tropical geometry with a view toward formulating tropical moduli problems, and with the moduli space of curves as our main example. We propose a moduli functor for the moduli space of curves and show that it is representable by a geometric stack over the category of rational polyhedral cones. In this framework, the natural forgetful morphisms between moduli spaces of curves with marked points function as universal curves. Our approach to tropical geometry permits tropical moduli problems—moduli of curves or otherwise—to be extended to logarithmic schemes. We use this to construct a smooth tropicalization morphism from the moduli space of algebraic curves to the moduli space of tropical curves, and we show that this morphism commutes with all of the tautological morphisms.more » « less
-
We present an efficient voxelization method to encode the geometry and attributes of 3D point clouds obtained from autonomous vehicles. Due to the circular scanning trajectory of sensors, the geometry of LiDAR point clouds is inherently different from that of point clouds captured from RGBD cameras. Our method exploits these specific properties to representing points in cylindrical coordinates instead of conventional Cartesian coordinates. We demonstrate that Region Adaptive Hierarchical Transform (RAHT) can be extended to this setting, leading to attribute encoding based on a volumetric partition in cylindrical coordinates. Experimental results show that our proposed voxelization outperforms conventional approaches based on Cartesian coordinates for this type of data. We observe a significant improvement in attribute coding performance with 5-10% reduction in bitrate and octree representation with 35-45% reduction in bits.more » « less
-
Acoustic metasurfaces are two-dimensional materials that impart non-trivial amplitude and phase shifts on incident acoustic waves at a predetermined frequency. While acoustic metasurfaces enable extraordinary wavefront engineering capabilities, they are not developed well enough to independently control the amplitude and phase of reflected and transmitted acoustic waves simultaneously, which are governed by their geometry. We aim to solve the inverse design problem of finding a geometry to achieve a specified set of acoustic properties. The geometry is modeled by discretizing the continuous space into a finite number of elements, where each element can either be filled with air or solid material. Full wave simulations are performed to obtain the acoustic properties for a given geometry. It is computationally infeasible to simulate all geometries. To address this challenge, we develop an experimental design-based algorithm to efficiently perform the simulations. The algorithm starts with a few geometries and adaptively adds geometries to the set, such that they fill the entire space of the desired acoustic properties using a small fraction of the possible geometries. We find that the geometry needs to have at least 7 × 7 elements to obtain any given acoustic property with a tolerance of 5.4% of its maximum range. This is achieved by simulating 24 000 geometries using the proposed algorithm, which is only [Formula: see text] of the 563 × 10 12 possible geometries. The method provides a general solution to the inverse design problem that can be extended to control more acoustic properties.more » « less
-
Structural characterization of the ionic title complex, [MgBr(THF) 5 ][Co(dpbz) 2 ]·2THF [THF is tetrahydrofuran, C 4 H 8 O; dpbz is 1,2-bis(diphenylphosphanyl)benzene, C 30 H 24 P 2 ], revealed a well-separated cation and anion co-crystallized with two THF solvent molecules that interact with the cation via weak C—H...O contacts. The geometry about the cobalt center is pseudotetrahedral, as is expected for a d 10 metal center, only deviating from an ideal tetrahedral geometry because of the restrictive bite angles of the bidentate phosphane ligands. Three THF ligands of the cation and one co-crystallized THF solvent molecule are each disordered over two orientations. In the extended structure, the cations and THF solvent molecules are arranged in (100) sheets that alternate with layers of anions, the latter of which show various π-interactions, which may explain the particular packing arrangement.more » « less
An official website of the United States government

