Will the real Kasner metric please stand up

The Kasner metric is one of the more widely studied metrics. Its usefulness for the construction of cosmological models and its utility for certain studies of elementary particles has made it particularly attractive for exploitation. Because of its simplicity it has been rediscovered many times and is itself very closely related to metrics given several years earlier by Weyl, Levi-Civita, and Wilson. The form in which Kasner presented it has been virtually forgotten in favor of the dynamic form of the synchronous Bianchi I metric. Kasner metrics may be either static or dynamic. To each static metric there is acognate dynamic metric andvice versa, and the two are related by a complex coordinate transformation. The characterization of a Kasner metric is by means of a set of parameters. It is possible for these to take on complex values with interesting consequences, In the discussion a curious error in the original paper is rectified and some new Kasner metrics are presented. The discussion throughout is confined to the vacuum metric.     

Terahertz imaging through self-mixing in a quantum cascade laser

We demonstrate terahertz (THz) frequency imaging using a single quantum cascade laser (QCL) device for both generation and sensing of THz radiation. Detection is achieved by utilizing the effect of self-mixing in the THz QCL, and, specifically, by monitoring perturbations to the voltage across the QCL, induced by light reflected from an external object back into the laser cavity. Self-mixing imaging offers high sensitivity, a potentially fast response, and a simple, compact optical design, and we show that it can be used to obtain high-resolution reflection images of exemplar structures.     

Phase clustering in complex networks of delay-coupled oscillators

We study the clusterization of phase oscillators coupled with delay in complex networks. For the case of diffusive oscillators, we formulate the equations relating the topology of the network and the phases and frequencies of the oscillators (functional response). We solve them exactly in directed networks for the case of perfect synchronization. We also compare the reliability of the solution of the linear system for non-linear couplings. Taking advantage of the form of the solution, we propose a frequency adaptation rule to achieve perfect synchronization. We also propose a mean-field theory for uncorrelated random networks that proves to be pretty accurate to predict phase synchronization in real topologies, as for example, the Caenorhabditis elegans or the autonomous systems connectivity.     

Autoionization mediated by electron transfer

Electron-electron coincidence spectra of Ar-Kr clusters after photoionization have been measured. An electron with the kinetic energy range from 0 to approximately 1 eV is found in coincidence with the Ar 3s cluster photoelectron. The low kinetic energy electron can be attributed to an Ar + Kr+ + Kr+ final state which forms after electron transfer mediated decay. This autoionization mechanism results from a concerted transition involving three different atoms in a van der Waals cluster; it was predicted theoretically, but hitherto not observed.     

Depth-Encoded Spectral Domain Phase Microscopy for Simultaneous Multi-Site Nanoscale Optical Measurements

Spectral domain phase microscopy (SDPM) is an extension of spectral domain optical coherence tomography (SDOCT) that exploits the extraordinary phase stability of spectrometer-based systems with common-path geometry to resolve sub-wavelength displacements within a sample volume. This technique has been implemented for high resolution axial displacement and velocity measurements in biological samples, but since axial displacement information is acquired serially along the lateral dimension, it has been unable to measure fast temporal dynamics in extended samples. Depth-Encoded SDPM (DESDPM) uses multiple sample arms with unevenly spaced common path reference reflectors to multiplex independent SDPM signals from separate lateral positions on a sample simultaneously using a single interferometer, thereby reducing the time required to detect unique optical events to the integration period of the detector. Here, we introduce DESDPM and demonstrate the ability to acquire useful phase data concurrently at two laterally separated locations in a phantom sample as well as a biological preparation of spontaneously beating chick cardiomyocytes. DESDPM may be a useful tool for imaging fast cellular phenomena such as nervous conduction velocity or contractile motion.     

Minimal Model Fusion Rules From 2-Groups

The fusion rules for the (p,q)-minimal model representations of the Virasoro algebra are shown to come from the group in the following manner. There is a partition into disjoint subsets and a bijection between and the sectors of the (p,q)-minimal model such that the fusion rules correspond to where .     

Reproducibility of myelin water fraction analysis: a comparison of region of interest and voxel-based analysis methods

This study compared region of interest (ROI) and voxel-based analysis (VBA) methods to determine the optimal method of myelin water fraction (MWF) analysis. Twenty healthy controls were scanned twice using a multi-echo T₂ relaxation sequence and ROIs were drawn in white and grey matter. MWF was defined as the fractional signal from 15 to 40 ms in the T₂ distribution. For ROI analysis, the mean intensity of voxels within an ROI was fit using non-negative least squares. For VBA, MWF was obtained for each voxel and the mean and median values within an ROI were calculated. There was a slightly higher correlation between Scan 1 and 2 for the VBA method (R²=0.98) relative to the ROI method (R²=0.95), and the VBA mean square difference between scans was 300% lower, indicating VBA was the most consistent between scans. For the VBA method, mean MWF was found to be more reproducible than median MWF. As the VBA method is more reproducible and gives more options for visualization and analysis of MWF, it is recommended over the ROI method of MWF analysis.     

Micromachined array tip for multifocus fiber-based optical coherence tomography

High-resolution optical coherence tomography demands a large detector bandwidth and a high numerical aperture for real-time imaging, which is difficult to achieve over a large imaging depth. To resolve these conflicting requirements we propose a novel multifocus fiber-based optical coherence tomography system with a micromachined array tip. We demonstrate the fabrication of a prototype four-channel tip that maintains a 9-14-microm spot diameter with more than 500 microm of imaging depth. Images of a resolution target and a human tooth were obtained with this tip by use of a four-channel cascaded Michelson fiber-optic interferometer, scanned simultaneously at 8 kHz with geometric power distribution across the four channels.     

Development of a laser photothermoacoustic frequency-swept system for subsurface imaging: theory and experiment

In conventional biomedical photoacoustic imaging systems, a pulsed laser is used to generate time-of-flight acoustic information of the subsurface features. This paper reports the theoretical and experimental development of a new frequency-domain (FD) photo-thermo-acoustic (PTA) principle featuring frequency sweep (chirp) and heterodyne modulation and lock-in detection of a continuous-wave laser source at 1064 nm wavelength. PTA imaging is a promising new technique which is being developed to detect tumor masses in turbid biological tissue. Owing to the linear relationship between the depth of acoustic signal generation and the delay time of signal arrival to the transducer, information specific to a particular depth can be associated with a particular frequency in the chirp signal. Scanning laser modulation with a linear frequency sweep method preserves the depth-to-delay time linearity and recovers FD-PTA signals from a range of depths. Preliminary results performed on rubber samples and solid tissue phantoms indicate that the FD-PTA technique has the potential to be a reliable tool for biomedical depth-profilometric imaging.