Optinalysis: A New Method of Data Analysis and Comparison

The key concepts in symmetry detection and similarity, identity measures are automorphism and isomorphism respectively. Therefore, methods for symmetry detection and similarity, identity measures should be functionally bijective, inverse, and invariance under a set of mathematical operations. Nevertheless, few or no existing method is functional for these properties. In this paper, a new methodological paradigm, called optinalysis, is presented for symmetry detections, similarity, and identity measures between isoreflective or autoreflective pair of mathematical structures. The paradigm of optinalysis is the re-mapping of isoreflective or autoreflective pairs with an optical scale. Optinalysis is characterized as invariant under a set of transformations and its isoreflective polymorphism behaves on polynomial and non-polynomial models.

Research on Positioning Error Analysis and Compensation Experiment of the Dual-Driving Feed Worktable

The dual-driving feed worktable (DDFW) is widely used in feed system because of its high stability and load capacity, while its feed system is one of the important parts that affects the feed accuracy of machine tools. Due to the influence of assembly, manufacturing and other factors, the positioning error of DDFW is produced, which reduces the machining accuracy of the machine tools. Therefore, the research on the positioning error compensation of DDFW is of great significance. In this paper, the positioning error of DDFW is measured with absolute optical scale and the positioning error model of DDFW is established by modeling method of orthogonal polynomials at first. Then an electronic cam combined with virtual axis compensation strategy is designed for DDFW to reduce positioning error. Finally, the compensation experiment is carried out and the error compensation results are analyzed to verify the effectiveness of the error compensation strategy designed in this paper.

Single Gyroid and Inverse b.c.c. Photonic Crystals in Bird Feathers

Vivid, saturated structural colors are a conspicuous and important aspect of the appearance of many organisms. A huge diversity of underlying 3D ordered biophotonic nanostructures has been documented, for instance, within the chitinaceous exoskeletons of insects. Here, we report diverse, highly ordered, intracellular, 3D biophotonic crystals in vivid plumages from three families of birds, which have each evolved independently from quasi-ordered (glassy) ancestral states. These morphologies include exotic bi-continuous single gyroid β-keratin and air networks, inverse b.c.c. and inverse opal (r.h.c.p.) close-packings of air spheres in the medullary β-keratin of feather barbs. These self-assembled avian biophotonic crystals may serve as biomimetic inspiration for advanced multi-functional applications, as they suggest alternative routes to the synthesis of optical-scale photonic crystals, including the experimentally elusive single gyroid.Field CodesMaterials Science and Evolutionary BiologyOne Sentence SummaryEvolutionary disorder-order transitions in bird feathers suggest direct optical scale self-assembly of photonic crystals

Robust H i kinematics of gas-rich ultra-diffuse galaxies: hints of a weak-feedback formation scenario

ABSTRACT We study the gas kinematics of a sample of six isolated gas-rich low surface brightness galaxies, of the class called ultra-diffuse galaxies (UDGs). These galaxies have recently been shown to be outliers from the baryonic Tully–Fisher relation (BTFR), as they rotate much slower than expected given their baryonic mass, and to have a baryon fraction similar to the cosmological mean. By means of a 3D kinematic modelling fitting technique, we show that the H i in our UDGs is distributed in ‘thin’ regularly rotating discs and we determine their rotation velocity and gas velocity dispersion. We revisit the BTFR adding galaxies from other studies. We find a previously unknown trend between the deviation from the BTFR and the exponential disc scale length valid for dwarf galaxies with circular speeds ≲ 45 km s−1, with our UDGs being at the extreme end. Based on our findings, we suggest that the high baryon fractions of our UDGs may originate due to the fact that they have experienced weak stellar feedback, likely due to their low star formation rate surface densities, and as a result they did not eject significant amounts of gas out of their discs. At the same time, we find indications that our UDGs may have higher-than-average stellar specific angular momentum, which can explain their large optical scale lengths.

Mass distributions in disk galaxies

We present results on luminous and dark matter mass distributions in disk galaxies from the DiskMass Survey. As expected for normal disk galaxies, stars dominate the baryonic mass budget in the inner region of the disk; however, at about four optical scale lengths (hR) the atomic gas starts to become the dominant contributor. Unexpectedly, we find the total baryon to dark-matter fraction within a galaxy stays nearly constant with radius from 1hR out to at least 6hR, with a baryon fraction of 15–50% among galaxies. On average, only one third of the mass within 2.2hR in a disk galaxy is baryonic and these baryons appear to have had only a minor effect on the distribution of the dark matter.