The Camassa-Holm equation as a geodesic flow on the diffeomorphism group

Misiolek has shown that the Camassa-Holm (CH) equation is a geodesic flow on the Bott-Virasoro group. In this paper it is shown that the Camassa-Holm equation for the case $\kappa =0$ is the geodesic spray of the weak Riemannian metric on the diffeomorphism group of the line or the circle obtained by right translating the $H^1$ inner product over the entire group. This paper uses the right-trivialisation technique to rigorously verify that the Euler-Poincar\'{e} theory for Lie groups can be applied to diffeomorphism groups. The observation made in this paper has led to physically meaningful generalizations of the CH-equation to higher dimensional manifolds (see Refs. \cite{HMR} and \cite{SH}).Comment: 10 single-spaced pages, Geometric Methods in Fluid Equations: Submitted to the Journal of Mathematical Physic

Benzobisoxazole cruciforms: a tunable, cross-conjugated platform for the generation of deep blue OLED materials

Four new cross-conjugated small molecules based on a central benzo[1,2-d:4,5-d′]bisoxazole moiety possessing semi-independently tunable HOMO and LUMO levels were synthesized and the properties of these materials were evaluated experimentally and theoretically. The molecules were thermally stable with 5% weight loss occurring well above 350 °C. The cruciforms all exhibited blue emission in solution ranging from 433–450 nm. Host–guest OLEDs fabricated from various concentrations of these materials using the small molecule host 4,4′-bis(9-carbazolyl)-biphenyl (CBP) exhibited deep blue-emission with Commission Internationale de L'Eclairage (CIE) coordinates of (0.15 ≤ x ≤ 0.17, 0.05 ≤ y ≤ 0.11), and maximum luminance efficiencies as high as ∼2 cd A−1. These results demonstrate the potential of benzobisoxazole cruciforms as emitters for developing high-performance deep blue OLEDs.We would like to thank Dr Sarah Cady, Dr Kamel Harrata and Mr Steven Veysey of Iowa State University (ISU) Chemical Instrumentation Facility for compound analysis. We thank Eeshita Manna for technical assistance. We also thank the National Science Foundation (CHE-1413173) for financial support of this work. RK and JS were partially supported by Basic Energy Sciences, Division of Materials Science and Engineering, USDOE. Ames Laboratory is operated by Iowa State University for the US Department of Energy (USDOE) under Contract No. DE-AC 02-07CH11358. Computational resources were provided in part by the MERCURY consortium (http://mercuryconsortium.org/) under NSF grants CHE-0116435, CHE-0521063, CHE-0849677, and CHE-1229354. (CHE-1413173 - National Science Foundation; Basic Energy Sciences, Division of Materials Science and Engineering, USDOE; DE-AC 02-07CH11358 - Iowa State University for the US Department of Energy (USDOE); CHE-0116435 - MERCURY consortium under NSF; CHE-0521063 - MERCURY consortium under NSF; CHE-0849677 - MERCURY consortium under NSF; CHE-1229354 - MERCURY consortium under NSF)http://pubs.rsc.org/en/Content/ArticleLanding/2016/TC/C5TC03622D#!divAbstractPublished versio

The End of Constitutional Law?

Book review: On constitutional disobedience. By Louis Michael Seidman. New York, N.Y.: Oxford University Press. 2013. Pp. xii + 162. Reviewed by Adam Shinar

The End of Constitutional Law?

Book review: On constitutional disobedience. By Louis Michael Seidman. New York, N.Y.: Oxford University Press. 2013. Pp. xii + 162. Reviewed by Adam Shinar