Classification of All Poisson-Lie Structures on an Infinite-Dimensional Jet Group

A local classification of all Poisson-Lie structures on an infinite-dimensional group $G_{\infty}$ of formal power series is given. All Lie bialgebra structures on the Lie algebra {\Cal G}_{\infty} of $G_{\infty}$ are also classified.Comment: 11 pages, AmSTeX fil

Hamiltonian type Lie bialgebras

We first prove that, for any generalized Hamiltonian type Lie algebra $L$, the first cohomology group $H^1(L,L \otimes L)$ is trivial. We then show that all Lie bialgebra structures on $L$ are triangular.Comment: LaTeX, 16 page

Lie bialgebras of generalized Witt type

In a paper by Michaelis a class of infinite-dimensional Lie bialgebras containing the Virasoro algebra was presented. This type of Lie bialgebras was classified by Ng and Taft. In this paper, all Lie bialgebra structures on the Lie algebras of generalized Witt type are classified. It is proved that, for any Lie algebra $W$ of generalized Witt type, all Lie bialgebras on $W$ are coboundary triangular Lie bialgebras. As a by-product, it is also proved that the first cohomology group $H^1(W,W \otimes W)$ is trivial.Comment: 14 page

The Chemical and Electronic Structure of the Neutral Flavin Radical as Revealed by Electron Spin Resonance Spectroscopy of Chemically and Isotopically Substituted Derivatives

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/65670/1/j.1432-1033.1970.tb00277.x.pd

Phase-Locked Spatial Domains and Bloch Domain Walls in Type-II Optical Parametric Oscillators

We study the role of transverse spatial degrees of freedom in the dynamics of signal-idler phase locked states in type-II Optical Parametric Oscillators. Phase locking stems from signal-idler polarization coupling which arises if the cavity birefringence and/or dichroism is not matched to the nonlinear crystal birefringence. Spontaneous Bloch domain wall formation is theoretically predicted and numerically studied. Bloch walls connect, by means of a polarization transformation, homogeneous regions of self-phase locked solutions. The parameter range for their existence is analytically found. The polarization properties and the dynamics of walls in one- and two transverse spatial dimensions is explained. Transition from Bloch to Ising walls is characterized, the control parameter being the linear coupling strength. Wall dynamics governs spatiotemporal dynamical states of the system, which include transient curvature driven domain growth, persistent dynamics dominated by spiraling defects for Bloch walls, and labyrinthine pattern formation for Ising walls.Comment: 27 pages, 16 figure

A robust, scanning quantum system for nanoscale sensing and imaging

Controllable atomic-scale quantum systems hold great potential as sensitive tools for nanoscale imaging and metrology. Possible applications range from nanoscale electric and magnetic field sensing to single photon microscopy, quantum information processing, and bioimaging. At the heart of such schemes is the ability to scan and accurately position a robust sensor within a few nanometers of a sample of interest, while preserving the sensor's quantum coherence and readout fidelity. These combined requirements remain a challenge for all existing approaches that rely on direct grafting of individual solid state quantum systems or single molecules onto scanning-probe tips. Here, we demonstrate the fabrication and room temperature operation of a robust and isolated atomic-scale quantum sensor for scanning probe microscopy. Specifically, we employ a high-purity, single-crystalline diamond nanopillar probe containing a single Nitrogen-Vacancy (NV) color center. We illustrate the versatility and performance of our scanning NV sensor by conducting quantitative nanoscale magnetic field imaging and near-field single-photon fluorescence quenching microscopy. In both cases, we obtain imaging resolution in the range of 20 nm and sensitivity unprecedented in scanning quantum probe microscopy

Polarisation Patterns and Vectorial Defects in Type II Optical Parametric Oscillators

Previous studies of lasers and nonlinear resonators have revealed that the polarisation degree of freedom allows for the formation of polarisation patterns and novel localized structures, such as vectorial defects. Type II optical parametric oscillators are characterised by the fact that the down-converted beams are emitted in orthogonal polarisations. In this paper we show the results of the study of pattern and defect formation and dynamics in a Type II degenerate optical parametric oscillator for which the pump field is not resonated in the cavity. We find that traveling waves are the predominant solutions and that the defects are vectorial dislocations which appear at the boundaries of the regions where traveling waves of different phase or wave-vector orientation are formed. A dislocation is defined by two topological charges, one associated with the phase and another with the wave-vector orientation. We also show how to stabilize a single defect in a realistic experimental situation. The effects of phase mismatch of nonlinear interaction are finally considered.Comment: 38 pages, including 15 figures, LATeX. Related material, including movies, can be obtained from http://www.imedea.uib.es/Nonlinear/research_topics/OPO

A thin layer angiogenesis assay: a modified basement matrix assay for assessment of endothelial cell differentiation

BACKGROUND: Basement matrices such as Matrigel™ and Geltrex™ are used in a variety of cell culture assays of anchorage-dependent differentiation including endothelial cell tube formation assays. The volumes of matrix recommended for these assays (approximately 150 μl/cm(2)) are costly, limit working distances for microscopy, and require cell detachment for subsequent molecular analysis. Here we describe the development and validation of a thin-layer angiogenesis (TLA) assay for assessing the angiogenic potential of endothelial cells that overcomes these limitations. RESULTS: Geltrex™ basement matrix at 5 μl/cm(2) in 24-well (10 μl) or 96-well (2 μl) plates supports endothelial cell differentiation into tube-like structures in a comparable manner to the standard larger volumes of matrix. Since working distances are reduced, high-resolution single cell microscopy, including DIC and confocal imaging, can be used readily. Using MitoTracker dye we now demonstrate, for the first time, live mitochondrial dynamics and visualise the 3-dimensional network of mitochondria present in differentiated endothelial cells. Using a standard commercial total RNA extraction kit (Qiagen) we also show direct RNA extraction and RT-qPCR from differentiated endothelial cells without the need to initially detach cells from their supporting matrix. CONCLUSIONS: We present here a new thin-layer assay (TLA) for measuring the anchorage-dependent differentiation of endothelial cells into tube-like structures which retains all the characteristics of the traditional approach but with the added benefit of a greatly lowered cost and better compatibility with other techniques, including RT-qPCR and high-resolution microscopy. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/s12860-014-0041-5) contains supplementary material, which is available to authorized users