On the blow-up structure for the generalized periodic Camassa-Holm and Degasperis-Procesi equations

Considered herein are the generalized Camassa-Holm and Degasperis-Procesi equations in the spatially periodic setting. The precise blow-up scenarios of strong solutions are derived for both of equations. Several conditions on the initial data guaranteeing the development of singularities in finite time for strong solutions of these two equations are established. The exact blow-up rates are also determined. Finally, geometric descriptions of these two integrable equations from non-stretching invariant curve flows in centro-equiaffine geometries, pseudo-spherical surfaces and affine surfaces are given.Comment: 26 page

3-Chloro-N′-(3,5-dibromo-2-hy­droxy­benzyl­idene)benzohydrazide methanol monosolvate

The title Schiff base compound, C14H9Br2ClN2O2·CH3OH, features an intra­molecular O—H⋯N hydrogen bond, which contributes to the planarity of the mol­ecule: the dihedral angle between the two benzene rings is 4.6 (2)°. In the crystal, pairs of adjacent mol­ecules are linked through inter­molecular N—H⋯O and O—H⋯O hydrogen bonds, forming dimers. The methanol solvent mol­ecule is linked by inter­molecular O—H⋯O hydrogen bonds

4-(2-Carb­oxy­vin­yl)pyridinium iodide

In the crystal structure of the title salt, C8H8NO2 +·I−, the cations and anions are linked by bifurcated N—H⋯(O,I) hydrogen bonds. A near-linear O—H⋯I hydrogen bond also exists between the cation and anion, resulting in a two-dimensional network. In the cation, the carboxyl group is twisted with respect to the pyridine ring at a dihedral angle of 15.34 (17)°

An Improved Unscented Kalman Filter for Discrete Nonlinear Systems with Random Parameters

This paper investigates the nonlinear unscented Kalman filtering (UKF) problem for discrete nonlinear dynamic systems with random parameters. We develop an improved unscented transformation by incorporating the random parameters into the state vector to enlarge the number of sigma points. The theoretical analysis reveals that the approximated mean and covariance via the improved unscented transformation match the true values correctly up to the third order of Taylor series expansion. Based on the improved unscented transformation, an improved UKF method is proposed to expand the application of the UKF for nonlinear systems with random parameters. An application to the mobile source localization with time difference of arrival (TDOA) measurements and sensor position uncertainties is provided where the simulation results illustrate that the improved UKF method leads to a superior performance in comparison with the normal UKF method

Cavity Optics in Organic Semiconductors: From Light-Extraction of OLEDs to Exciton-Polaritons

Organic optoelectronics has been an active topic of research and development over the past decades. While organic photovoltaic cells, transistors and other organic electronics are still in transition to commercialization, organic light-emitting devices have revolutionized displays of mobile phones and TVs. Due to the intrinsic properties of organic materials, electron-hole pairs, called excitons, are responsible for optical transitions and, thus, are crucial to organic optoelectronics. Understanding exciton-photon interactions and managing photons are critical to high performance light-emitting devices. This thesis aims at understanding this topic and providing potential solutions. The first part of this thesis focuses on the optical power distribution in organic light-emitting diodes and providing practical solutions to the limited light-extraction efficiencies. We begin by reviewing the operation and optics of light-emitting devices and modeling methods for device optics. Based on our calculations, we identify the problem of extracting light trapped in high refractive index regions of the devices, and propose principles of designs for light-extraction structures. Different light-extraction methods are demonstrated for both bottom and top-emitting devices. The second part of the thesis deals with the physics and application of the strong coupling of exciton and photons in organic semiconductors. A new particle, called the exciton-polariton, emerges as a result from the strong coupling between Frenkel excitons in organic materials and photons. We review the progress of organic exciton-polariton research in the topic of polariton lasing and long-range transport. We demonstrate the polariton laser threshold dependence on temperature and on amplified spontaneous emission. Additionally, we show Frenkel excitons in an amorphous organic film couple with Bloch surface wave. The coupling strength reaches the ultra-strong coupling regime by controlling the organic film thickness. The propagation of the exciton-polaritons with different coupling strengths shows that the more photonic fraction results in longer transport.PHDElectrical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/155157/1/quyue_1.pd