Almost commuting unitary matrices related to time reversal

The behavior of fermionic systems depends on the geometry of the system and the symmetry class of the Hamiltonian and observables. Almost commuting matrices arise from band-projected position observables in such systems. One expects the mathematical behavior of almost commuting Hermitian matrices to depend on two factors. One factor will be the approximate polynomial relations satisfied by the matrices. The other factor is what algebra the matrices are in, either the matrices over A for A the real numbers, A the complex numbers or A the algebra of quaternions. There are potential obstructions keeping k-tuples of almost commuting operators from being close to a commuting k-tuple. We consider two-dimensional geometries and so this obstruction lives in KO_{-2}(A). This obstruction corresponds to either the Chern number or spin Chern number in physics. We show that if this obstruction is the trivial element in K-theory then the approximation by commuting matrices is possible.Comment: 33 pages, 2 figures. In version 2 some formulas have been corrected and some proofs have been rewritten to improve the expositio

Using an Ellipsoid Model to Track and Predict the Evolution and Propagation of Coronal Mass Ejections

We present a method for tracking and predicting the propagation and evolution of coronal mass ejections (CMEs) using the imagers on the STEREO and SOHO satellites. By empirically modeling the material between the inner core and leading edge of a CME as an expanding, outward propagating ellipsoid, we track its evolution in three-dimensional space. Though more complex empirical CME models have been developed, we examine the accuracy of this relatively simple geometric model, which incorporates relatively few physical assumptions, including i) a constant propagation angle and ii) an azimuthally symmetric structure. Testing our ellipsoid model developed herein on three separate CMEs, we find that it is an effective tool for predicting the arrival of density enhancements and the duration of each event near 1 AU. For each CME studied, the trends in the trajectory, as well as the radial and transverse expansion are studied from 0 to ~.3 AU to create predictions at 1 AU with an average accuracy of 2.9 hours.Comment: 18 pages, 11 figure

Testing real-time systems using TINA

The paper presents a technique for model-based black-box conformance testing of real-time systems using the Time Petri Net Analyzer TINA. Such test suites are derived from a prioritized time Petri net composed of two concurrent sub-nets specifying respectively the expected behaviour of the system under test and its environment.We describe how the toolbox TINA has been extended to support automatic generation of time-optimal test suites. The result is optimal in the sense that the set of test cases in the test suite have the shortest possible accumulated time to be executed. Input/output conformance serves as the notion of implementation correctness, essentially timed trace inclusion taking environment assumptions into account. Test cases selection is based either on using manually formulated test purposes or automatically from various coverage criteria specifying structural criteria of the model to be fulfilled by the test suite. We discuss how test purposes and coverage criterion are specified in the linear temporal logic SE-LTL, derive test sequences, and assign verdicts

Towards surface quantum optics with Bose-Einstein condensates in evanescent waves

We present a surface trap which allows for studying the coherent interaction of ultracold atoms with evanescent waves. The trap combines a magnetic Joffe trap with a repulsive evanescent dipole potential. The position of the magnetic trap can be controlled with high precision which makes it possible to move ultracold atoms to the surface of a glass prism in a controlled way. The optical potential of the evanescent wave compensates for the strong attractive van der Waals forces and generates a potential barrier at only a few hundred nanometers from the surface. The trap is tested with Rb Bose-Einstein condensates (BEC), which are stably positioned at distances from the surfaces below one micrometer

Weathering the Storm: Managing Older Adults With Breast Cancer Amid COVID-19 and Beyond

Caring for older patients with breast cancer presents unique clinical considerations because of preexisting and competing comorbidity, the potential for treatment-related toxicity, and the consequent impact on functional status. In the context of the COVID-19 pandemic, treatment decision making for older patients is especially challenging and encourages us to refocus our treatment priorities. While we work to avoid treatment delays and maintain therapeutic benefit, we also need to minimize the risk for severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) exposures, myelosuppression, general chemotherapy toxicity, and functional decline. Herein, we propose multidisciplinary care considerations for the aging patient with breast cancer, with the goal to promote a team-based, multidisciplinary treatment approach during the COVID-19 pandemic and beyond. These considerations remain relevant as we navigate the "new normal" for the approximately 30% of breast cancer patients aged 70 years and older who are diagnosed in the United States annually and for the thousands of older patients living with recurrent and/or metastatic disease

On the structure and evolution of a polar crown prominence/filament system

Polar crown prominences are made of chromospheric plasma partially circling the Suns poles between 60 and 70 degree latitude. We aim to diagnose the 3D dynamics of a polar crown prominence using high cadence EUV images from the Solar Dynamics Observatory (SDO)/AIA at 304 and 171A and the Ahead spacecraft of the Solar Terrestrial Relations Observatory (STEREO-A)/EUVI at 195A. Using time series across specific structures we compare flows across the disk in 195A with the prominence dynamics seen on the limb. The densest prominence material forms vertical columns which are separated by many tens of Mm and connected by dynamic bridges of plasma that are clearly visible in 304/171A two-color images. We also observe intermittent but repetitious flows with velocity 15 km/s in the prominence that appear to be associated with EUV bright points on the solar disk. The boundary between the prominence and the overlying cavity appears as a sharp edge. We discuss the structure of the coronal cavity seen both above and around the prominence. SDO/HMI and GONG magnetograms are used to infer the underlying magnetic topology. The evolution and structure of the prominence with respect to the magnetic field seems to agree with the filament linkage model.Comment: 24 pages, 14 figures, Accepted for publication in Solar Physics Journal, Movies can be found at http://www2.mps.mpg.de/data/outgoing/panesar

A minimum single-band model for low-energy excitations in superconducting Kx_xFe2_2Se2_2

We propose a minimum single-band model for the newly discovered iron-based superconducting K$_x$Fe$_2$Se$_2$. Our model is found to be numerically consistent with the five-orbital model at low energies. Based on our model and the random phase approximation, we study the spin fluctuation and the pairing symmetry of superconducting gap function. The $(\pi/2,\pi/2)$ spin excitation and the $d_{x^2-y^2}$ pairing symmetry are revealed. All of the results can well be understood in terms of the interplay between the Fermi surface topology and the local spin interaction, providing a sound picture to explain why the superconducting transition temperature is as high as to be comparable to those in pnictides and some cuprates. A common origin of superconductivity is elucidated for this compound and other high-T$_c$ materials.Comment: 5 pages, 4 figure

Structure Formation, Melting, and the Optical Properties of Gold/DNA Nanocomposites: Effects of Relaxation Time

We present a model for structure formation, melting, and optical properties of gold/DNA nanocomposites. These composites consist of a collection of gold nanoparticles (of radius 50 nm or less) which are bound together by links made up of DNA strands. In our structural model, the nanocomposite forms from a series of Monte Carlo steps, each involving reaction-limited cluster-cluster aggregation (RLCA) followed by dehybridization of the DNA links. These links form with a probability $p_{eff}$ which depends on temperature and particle radius $a$. The final structure depends on the number of monomers (i. e. gold nanoparticles) $N_m$, $T$, and the relaxation time. At low temperature, the model results in an RLCA cluster. But after a long enough relaxation time, the nanocomposite reduces to a compact, non-fractal cluster. We calculate the optical properties of the resulting aggregates using the Discrete Dipole Approximation. Despite the restructuring, the melting transition (as seen in the extinction coefficient at wavelength 520 nm) remains sharp, and the melting temperature $T_M$ increases with increasing $a$ as found in our previous percolation model. However, restructuring increases the corresponding link fraction at melting to a value well above the percolation threshold. Our calculated extinction cross section agrees qualitatively with experiments on gold/DNA composites. It also shows a characteristic ``rebound effect,'' resulting from incomplete relaxation, which has also been seen in some experiments. We discuss briefly how our results relate to a possible sol-gel transition in these aggregates.Comment: 12 pages, 10 figure

Specific Heat Study of the Magnetic Superconductor HoNi2B2C

The complex magnetic transitions and superconductivity of HoNi2B2C were studied via the dependence of the heat capacity on temperature and in-plane field angle. We provide an extended, comprehensive magnetic phase diagram for B // [100] and B // [110] based on the thermodynamic measurements. Three magnetic transitions and the superconducting transition were clearly observed. The 5.2 K transition (T_{N}) shows a hysteresis with temperature, indicating the first order nature of the transition at B=0 T. The 6 K transition (T_{M}), namely the onset of the long-range ordering, displays a dramatic in-plane anisotropy: T_{M} increases with increasing magnetic field for B // [100] while it decreases with increasing field for B // [110]. The anomalous anisotropy in T_{M} indicates that the transition is related to the a-axis spiral structure. The 5.5 K transition (T^{*}) shows similar behavior to the 5.2 K transition, i.e., a small in-plane anisotropy and scaling with Ising model. This last transition is ascribed to the change from a^{*} dominant phase to c^{*} dominant phase.Comment: 9 pages, 11 figure