Ordered phase and phase transitions in the three-dimensional generalized six-state clock model

We study the three-dimensional generalized six-state clock model at values of the energy parameters, at which the system is considered to have the same behavior as the stacked triangular antiferromagnetic Ising model and the three-state antiferromagnetic Potts model. First, we investigate ordered phases by using the Monte Carlo twist method (MCTM). We confirmed the existence of an incompletely ordered phase (IOP1) at intermediate temperature, besides the completely ordered phase (COP) at low-temperature. In this intermediate phase, two neighboring states of the six-state model mix, while one of them is selected in the low temperature phase. We examine the fluctuation the mixing rate of the two states in IOP1 and clarify that the mixing rate is very stable around 1:1. The high temperature phase transition is investigated by using non-equilibrium relaxation method (NERM). We estimate the critical exponents beta=0.34(1) and nu=0.66(4). These values are consistent with the 3D-XY universality class. The low temperature phase transition is found to be of first-order by using MCTM and the finite-size-scaling analysis

Ordered phase and scaling in ZnZ_n models and the three-state antiferromagnetic Potts model in three dimensions

Based on a Renormalization-Group picture of $Z_n$ symmetric models in three dimensions, we derive a scaling law for the $Z_n$ order parameter in the ordered phase. An existing Monte Carlo calculation on the three-state antiferromagnetic Potts model, which has the effective $Z_6$ symmetry, is shown to be consistent with the proposed scaling law. It strongly supports the Renormalization-Group picture that there is a single massive ordered phase, although an apparently rotationally symmetric region in the intermediate temperature was observed numerically.Comment: 5 pages in REVTEX, 2 PostScript figure

A small satellite version of a soft x-ray polarimeter

We describe a new implementation of a broad-band soft X-ray polarimeter, substantially based on a previous design. This implementation, the Pioneer Soft X-ray Polarimeter (PiSoX) is a SmallSat, designed for NASA’s call for Astrophysics Pioneers, small missions that could be CubeSats, balloon experiments, or SmallSats. As in REDSoX, the grating arrangement is designed optimally for the purpose of polarimetry with broad-band focussing optics by matching the dispersion of the spectrometer channels to laterally graded multilayers (LGMLs). The system can achieve polarization modulation factors over 90%. For PiSoX, the optics are lightweight Si mirrors in a one-bounce parabolic configuration. High efficiency, blazed gratings from opposite sectors are oriented to disperse to a LGML forming a channel covering the wavelength range from 35 Å to 75 Å (165 - 350 eV). Upon satellite rotation, the intensities of the dispersed spectra, after reflection and polarizing by the LGMLs, give the three Stokes parameters needed to determine a source’s linear polarization fraction and orientation. The design can be extended to higher energies as LGMLs are developed further. We describe examples of the potential scientific return from instruments based on this design.Accepted manuscrip

Rotationally symmetric ordered phase in the three-state antiferromagnetic Potts model

Physical Review B - Condensed Matter and Materials Physics5352210-2212PRBM

Absolute surface metrology of X-ray telescope mirrors through axial shift mapping

The next generation of X-ray telescopes will require mirror segments to be characterized to a surface uncertainty of 5 nm RMS or better. We present axial shift mapping, a Fizeau interferometry method to characterized near-cylindrical null correctors and surfaces. We extend our previously tested technique to cylindrical optics of similar dimensions to X-ray telescope mirrors. We report on progress towards full surface extraction of a cylindrical optic using axial shift mapping. © 2023 SPIE.Immediate accessThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]

Axial shift mapping metrology for X-ray telescope mirrors

The next generation of high-resolution X-ray telescopes will require mirror segments characterized to 5 nm uncertainty or better. This is difficult to achieve due to the mirror segment’s off-axis hyperbolic and parabolic shape and the challenge of manufacturing and testing a cylindrical null lens. In a typical Fizeau interferometer setup, errors in the assumed perfect null lens will be coupled into the final surface figure, increasing uncertainty. To combat the higher uncertainty of the cylindrical null corrector, we have been developing lateral shift mapping, an absolute metrology technique using a Fizeau interferometer. In this technique, the surface under test is laterally shifted between measurements while the reference surface does not move. Contributions to the interferogram due to the surface under test will move, while contributions due to the reference will stay static. Using this information, we can extract the true surface under test with low uncertainty. There is a quadratic ambiguity that arises due to the extraction method being akin to an integration. We have shown in the past our ability to utilize lateral shift mapping to extract flat surfaces to sub-nanometer uncertainties by comparing our results to a three-flat test. We also demonstrated that we can eliminate the quadratic ambiguity in flats using an external measurement with an autocollimator. We are expanding this method from optical flats to cylindrical surfaces, creating axial shift mapping. We will report on progress toward sub-nanometer measurements of cylindrical mirrors using axial shift mapping. © 2022 SPIE. All rights reserved.Immediate accessThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]

Lateral shift mapping metrology for X-ray telescope mirrors

Currently, high-resolution X-ray telescope mirrors, such as for the Lynx X-Ray Observatory concept, are measured using a Fizeau interferometer with a cylindrical null corrector. Uncertainties in the null wavefront directly couple into the surface measurement uncertainty, including the axial figure and cone angle variation. We extend the absolute surface metrology method of lateral shift mapping for measuring X-ray telescope mirror segments. Lateral shift mapping involves laterally shifting the surface under test relative to the null to multiple positions. The null wavefront can be extracted from the difference between these shifted measurements, leaving only the surface under test. Accurately extracting quadratic terms of the surface under test requires measuring its tilt during shifting. We will show surface metrology results of optical flats measured by Fizeau-based lateral shift mapping with the required angle measured using an autocollimator and compare these results against a three-flat test. We will show how we plan to extend this method to conical X-ray telescope mirror metrology. The lateral shift mapping method reduces the uncertainty introduced by the cylindrical null, a critical step toward making high-resolution X-ray telescope mirrors. © 2021 SPIE.Immediate accessThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]

Characterization of a chip-based bioreactor for three-dimensional cell cultivation via magnetic resonance imaging

We describe the characterization of a chip-based platform (3D-KITChip) for the three-dimensional cultivation of cells under perfusion conditions via magnetic resonance imaging (MRI). Besides the chip, the microfluidic system is comprised of a bioreactor housing, a medium supply, a pump for generating active flow conditions as well as a gas mixing station. The closed circulation loop is ideally suited for a characterization via MRI since the small bioreactor setup with active perfusion, driven by the pump from outside the coils, not only is completely MRI-compatible but also can be transferred into the magnetic coil of an experimental animal scanner. We have found that the two halves of the chip inside the bioreactor are homogeneously perfused with cell culture medium both with and without cells inside the 3D-KITChip. In addition, the homogeneity of perfusion is nearly independent from the flow rates investigated in this study, and furthermore, the setup shows excellent washout characteristics after spiking with Gadolinium-DOTA which makes it an ideal candidate for drug screening purposes. We, therefore, conclude that the 3D-KITChip is well suited as a platform for high-density three-dimensional cell cultures, especially those requiring a defined medium flow and/or gas supply in a precisely controllable three dimensional environment, like stem cells

Adjacency-preserving spatial treemaps

Rectangular layouts, subdivisions of an outer rectangle into smaller rectangles, have many applications in visualizing spatial information, for instance in rectangular cartograms in which the rectangles represent geographic or political regions. A spatial treemap is a rectangular layout with a hierarchical structure: the outer rectangle is subdivided into rectangles that are in turn subdivided into smaller rectangles. We describe algorithms for transforming a rectangular layout that does not have this hierarchical structure, together with a clustering of the rectangles of the layout, into a spatial treemap that respects the clustering and also respects to the extent possible the adjacencies of the input layout