GG-Strands

A $G$-strand is a map $g(t,{s}):\,\mathbb{R}\times\mathbb{R}\to G$ for a Lie group $G$ that follows from Hamilton's principle for a certain class of $G$-invariant Lagrangians. The SO(3)-strand is the $G$-strand version of the rigid body equation and it may be regarded physically as a continuous spin chain. Here, $SO(3)_K$-strand dynamics for ellipsoidal rotations is derived as an Euler-Poincar\'e system for a certain class of variations and recast as a Lie-Poisson system for coadjoint flow with the same Hamiltonian structure as for a perfect complex fluid. For a special Hamiltonian, the $SO(3)_K$-strand is mapped into a completely integrable generalization of the classical chiral model for the SO(3)-strand. Analogous results are obtained for the $Sp(2)$-strand. The $Sp(2)$-strand is the $G$-strand version of the $Sp(2)$ Bloch-Iserles ordinary differential equation, whose solutions exhibit dynamical sorting. Numerical solutions show nonlinear interactions of coherent wave-like solutions in both cases. ${\rm Diff}(\mathbb{R})$-strand equations on the diffeomorphism group $G={\rm Diff}(\mathbb{R})$ are also introduced and shown to admit solutions with singular support (e.g., peakons).Comment: 35 pages, 5 figures, 3rd version. To appear in J Nonlin Sc

Coupling of nitrogen-vacancy centers in diamond to a GaP waveguide

The optical coupling of guided modes in a GaP waveguide to nitrogen-vacancy (NV) centers in diamond is demonstrated. The electric field penetration into diamond and the loss of the guided mode are measured. The results indicate that the GaP-diamond system could be useful for realizing coupled microcavity-NV devices for quantum information processing in diamond.Comment: 4 pages 4 figure

COMMENTARY: Confronting Maternal Mortality Due to Postpartum Hemorrhage and Unsafe Abortion: A Call for Commitment

No Abstrac

Effects of electromagnetic waves on the electrical properties of contacts between grains

A DC electrical current is injected through a chain of metallic beads. The electrical resistances of each bead-bead contacts are measured. At low current, the distribution of these resistances is large and log-normal. At high enough current, the resistance distribution becomes sharp and Gaussian due to the creation of microweldings between some beads. The action of nearby electromagnetic waves (sparks) on the electrical conductivity of the chain is also studied. The spark effect is to lower the resistance values of the more resistive contacts, the best conductive ones remaining unaffected by the spark production. The spark is able to induce through the chain a current enough to create microweldings between some beads. This explains why the electrical resistance of a granular medium is so sensitive to the electromagnetic waves produced in its vicinity.Comment: 4 pages, 5 figure

Minimum Surface Formation Energy for Three-Dimensional Intergranular Fracture

The minimum expended energy for fracture is the free energy required to form two new surfaces. For intergranular fracture, the minimum surface formation energy is complicated by the rough fracture surface, with area greater than the specimen cross-section. We utilize network optimization algorithms (max-flow/min-cut) to determine the minimum surface formation energies and surfaces for intergranular fracture in 3D polycrystals. For equiaxed grains and uniform boundary strength, the minimum energy fracture area is independent of grain size and is 45% larger than the specimen cross-section, and intergranular fracture will occur when surface energy is less than 1.6 times the grain boundary energy. The 3D fracture area is larger than projected from 2D systems. In systems with microcracked boundaries, the fracture surface deviates to preferentially include microcracked boundaries, creating interlocking grain configurations. Two-dimensional percolation of microcracks occurs at about 80% microcracked boundaries

SPRITE and ASSAM: web servers for side chain 3D-motif searching in protein structures

Similarities in the 3D patterns of amino acid side chains can provide insights into their function despite the absence of any detectable sequence or fold similarities. Search for protein sites (SPRITE) and amino acid pattern search for substructures and motifs (ASSAM) are graph theoretical programs that can search for 3D amino side chain matches in protein structures, by representing the amino acid side chains as pseudo-atoms. The geometric relationship of the pseudo-atoms to each other as a pattern can be represented as a labeled graph where the pseudo-atoms are the graph's nodes while the edges are the inter-pseudo-atomic distances. Both programs require the input file to be in the PDB format. The objective of using SPRITE is to identify matches of side chains in a query structure to patterns with characterized function. In contrast, a 3D pattern of interest can be searched for existing occurrences in available PDB structures using ASSAM. Both programs are freely accessible without any login requirement. SPRITE is available at http://mfrlab.org/grafss/sprite/while ASSAM can be accessed at http://mfrlab.org/grafss/assam/

Continuous data assimilation for global numerical weather prediction

A new configuration of the European Centre for Medium-Range Weather Forecasts (ECMWF) incremental 4D-Var data assimilation (DA) system is introduced which builds upon the quasi-continuous DA concept proposed in the mid-1990s. Rather than working with a fixed set of observations, the new 4D-Var configuration exploits the near-continuous stream of incoming observations by introducing recently arrived observations at each outer loop iteration of the assimilation. This allows the analysis to benefit from more recent observations. Additionally, by decoupling the start time of the DA calculations from the observational data cut-off time, real-time forecasting applications can benefit from more expensive analysis configurations that previously could not have been considered. In this work we present results of a systematic comparison of the performance of a Continuous DA system against that of two more traditional baseline 4D-Var configurations. We show that the quality of the analysis produced by the new, more continuous configuration is comparable to that of a conventional baseline that has access to all of the observations in each of the outer loops, which is a configuration not feasible in real-time operational numerical weather prediction. For real-time forecasting applications, the Continuous DA framework allows configurations which clearly outperform the best available affordable non-continuous configuration. Continuous DA became operational at ECMWF in June 2019 and led to significant 2 to 3% reductions in medium-range forecast root mean square errors, which is roughly equivalent to 2-3 hr of additional predictive skill.Peer reviewe

In-flight absolute radiometric calibration of the thematic mapper

In order to determine temporal changes of the absolute radiometric calibration of the entire TM system in flight spectroradiometric measurements of the ground and the atmosphere were made simultaneously with TM image collections over the White Sands, New Mexico area. By entering the measured values in an atmospheric radiative transfer program, the radiance levels in four of the spectral bands of the TM were determined, band 1:0.45 to 0.52 micrometers, band 2:0.53 to 0.61 micrometers band 3:0.62 to 0.70 micrometers and 4:0.78 to 0.91 micrometers. These levels were compared to the output digital counts from the detectors that sampled the radiometrically measured ground area, thus providing an absolute radiometric calibration of the entire TM system utilizing those detectors

In-flight absolute radiometric calibration of the thematic mapper

The TM multispectral scanner system was calibrated in an absolute manner before launch. To determine the temporal changes of the absolute radiometric calibration of the entire system, spectroradiometric measurements of the ground and the atmosphere were made simultaneously with TM collections over White Sands, New Mexico. By entering the measured values in an atmospheric radiative transfer program, the radiance levels of the in four of the spectral bands of the TM were determined. Tables show values for the reflectance of snow at White Sands measured by a modular 8 channel radiometer, and values for exoatmospheric irradiance within the TM passbands, calculated for the Earth-Sun distance using a solar radiometer