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Over three decades ago the advection-diffusion equation for a steady fluid velocity field was homogenized, leading to a Stieltjes integral representation for the effective diffusivity, which is given in terms of a spectral measure of a compact self-adjoint operator and the P\'eclet number of the fluid flow. This result was recently extended to space-time periodic flows, instead involving an unbounded self-adjoint operator. Pad\'e approximants provide rigorous upper and lower bounds for Stieltjes functions in terms of the moments of the spectral measure. However, with the lack of a method for calculating the moments of the spectral measure for general fluid velocity fields, the utility of this powerful mathematical framework for calculating bounds for the effective diffusivity has not been fully realized. Here we significantly expand the applicability of this framework by providing an iterative method that enables an arbitrary number of moments, hence bounds, to be calculated analytically in closed form for both spatially and space-time periodic flows. The method is demonstrated for periodic flows in two spatial dimensions. The known asymptotic behavior of the effective diffusivity for a steady flow is accurately captured by high order upper and lower bounds, demonstrating the ability of the method to provide accurate estimates for the effective diffusivity for a broad range of parameter values., Comment: 20 pages, 6 figures, and 2 tables

The Astropy Project supports and fosters the development of open-source and openly-developed Python packages that provide commonly needed functionality to the astronomical community. A key element of the Astropy Project is the core package $\texttt{astropy}$, which serves as the foundation for more specialized projects and packages. In this article, we summarize key features in the core package as of the recent major release, version 5.0, and provide major updates for the Project. We then discuss supporting a broader ecosystem of interoperable packages, including connections with several astronomical observatories and missions. We also revisit the future outlook of the Astropy Project and the current status of Learn Astropy. We conclude by raising and discussing the current and future challenges facing the Project., Comment: 43 pages, 5 figures. To appear in ApJ. The author list has two parts: the authors that made significant contributions to the writing and/or coordination of the paper, followed by maintainers of and contributors to the Astropy Project. The position in the author list does not correspond to contributions to the Astropy Project as a whole

Predictions for the Higgs masses are a distinctive feature of supersymmetric extensions of the Standard Model, where they play a crucial role in constraining the parameter space. The discovery of a Higgs boson and the remarkably precise measurement of its mass at the LHC have spurred new efforts aimed at improving the accuracy of the theoretical predictions for the Higgs masses in supersymmetric models. The "Precision SUSY Higgs Mass Calculation Initiative" (KUTS) was launched in 2014 to provide a forum for discussions between the different groups involved in these efforts. This report aims to present a comprehensive overview of the current status of Higgs-mass calculations in supersymmetric models, to document the many advances that were achieved in recent years and were discussed during the KUTS meetings, and to outline the prospects for future improvements in these calculations., Comment: iv, 79 pages; 5 figures. v2: iv, 99 pages; added appendix on public codes for the Higgs-mass calculation in SUSY models. v3: minor modifications, references updated; matches version published in EPJC. v4: hyperlinks enabled

Magnetic reconnection underlies many explosive phenomena in the heliosphere and in laboratory plasmas. The new research capabilities in theory/simulations, observations, and laboratory experiments provide the opportunity to solve the grand scientific challenges summarized in this whitepaper. Success will require enhanced and sustained investments from relevant funding agencies, increased interagency/international partnerships, and close collaborations of the solar, heliospheric, and laboratory plasma communities. These investments will deliver transformative progress in understanding magnetic reconnection and related explosive phenomena including space weather events., Comment: 4 pages (including a title page), white paper submitted to Helio2050 workshop at https://www.hou.usra.edu/meetings/helio2050/. arXiv admin note: substantial text overlap with arXiv:2004.00079

This white paper summarizes major scientific challenges and opportunities in understanding magnetic reconnection and related explosive phenomena as a fundamental plasma process., Comment: 6 pages, 1 figure, white paper submitted to both Plasma 2020 and Astro 2020 Decadal Surveys

In cuprate superconductors, high magnetic fields have been used extensively to suppress superconductivity and expose the underlying normal state. Early measurements revealed insulating-like behavior in underdoped material versus temperature $T$, in which resistivity increases on cooling with a puzzling $\log(1/T)$ form. We instead use microwave measurements of flux-flow resistivity in YBa$_2$Cu$_3$O$_{6+y}$ and Tl$_2$Ba$_2$CuO$_{6+\delta}$ to study charge transport deep inside the superconducting phase, in the low temperature and low field regime. Here, the transition from metallic low-temperature resistivity ($d\rho/dT>0$) to a $\log(1/T)$ upturn persists throughout the superconducting doping range, including a regime at high carrier dopings in which the field-revealed normal-state resistivity is Fermi-liquid-like. The $\log(1/T)$ form is thus likely a signature of $d$-wave superconducting order, and the field-revealed normal state's $\log(1/T)$ resistivity may indicate the free-flux-flow regime of a phase-disordered $d$-wave superconductor., Comment: 6 pages, 3 figures + Supplementary Material

The Astropy project supports and fosters the development of open-source and openly-developed Python packages that provide commonly-needed functionality to the astronomical community. A key element of the Astropy project is the core package Astropy, which serves as the foundation for more specialized projects and packages. In this article, we provide an overview of the organization of the Astropy project and summarize key features in the core package as of the recent major release, version 2.0. We then describe the project infrastructure designed to facilitate and support development for a broader ecosystem of inter-operable packages. We conclude with a future outlook of planned new features and directions for the broader Astropy project., Comment: Minor changes to author list and title. Comments and feedback welcome through the paper source repository: https://github.com/astropy/astropy-v2.0-paper For more information about Astropy, see http://www.astropy.org/

Starting in December 2014, Kepler K2 observed Neptune continuously for 49 days at a 1-minute cadence. The goals consisted of studying its atmospheric dynamics (Simon et al. 2016), detecting its global acoustic oscillations (Rowe et al., submitted), and those of the Sun, which we report on here. We present the first indirect detection of solar oscillations in intensity measurements. Beyond the remarkable technical performance, it indicates how Kepler would see a star like the Sun. The result from the global asteroseismic approach, which consists of measuring the oscillation frequency at maximum amplitude "nu_max" and the mean frequency separation between mode overtones "Delta nu", is surprising as the nu_max measured from Neptune photometry is larger than the accepted value. Compared to the usual reference nu_max_sun = 3100 muHz, the asteroseismic scaling relations therefore make the solar mass and radius appear larger by 13.8 +/- 5.8 % and 4.3 +/- 1.9 % respectively. The higher nu_max is caused by a combination of the value of nu_max_sun, being larger at the time of observations than the usual reference from SOHO/VIRGO/SPM data (3160 +/- 10 muHz), and the noise level of the K2 time series, being ten times larger than VIRGO's. The peak-bagging method provides more consistent results: despite a low signal-to-noise ratio (SNR), we model ten overtones for degrees l=0,1,2. We compare the K2 data with simultaneous SOHO/VIRGO/SPM photometry and BiSON velocity measurements. The individual frequencies, widths, and amplitudes mostly match those from VIRGO and BiSON within 1 sigma, except for the few peaks with lowest SNR., Comment: 8 pages, 4 figures, 1 table

As the interface between the Sun's photosphere and corona, the chromosphere and transition region play a key role in the formation and acceleration of the solar wind. Observations from the Interface Region Imaging Spectrograph reveal the prevalence of intermittent small-scale jets with speeds of 80-250 km/s from the narrow bright network lanes of this interface region. These jets have lifetimes of 20-80 seconds and widths of 300 km or less. They originate from small-scale bright regions, often preceded by footpoint brightenings and accompanied by transverse waves with ~20 km/s amplitudes. Many jets reach temperatures of at least ~100000 K and constitute an important element of the transition region structures. They are likely an intermittent but persistent source of mass and energy for the solar wind., Comment: Figs 1-4 & S1-S5; Movies S1-S8; published in Science, including the main text and supplementary materials. Reference: H. Tian, E. E. DeLuca, S. R. Cranmer, et al., Science 346, 1255711 (2014)

We present measurements of the microwave surface impedance of the single-layer cuprate Tl2201, deep in the overdoped regime, with Tc ~ 25 K. Measurements have been made using cavity perturbation of a dielectric resonator at 17 discrete frequencies ranging from 2.50 to 19.16 GHz, and at temperatures from 0.12 to 27.5 K. From the surface impedance we obtain the microwave conductivity, penetration depth and superfluid density. The superfluid density displays a strong linear temperature dependence from 2 to 14 K, indicative of line nodes in the energy gap. The microwave data are compared with theoretical predictions for a d-wave superconductor with point-like impurities, with the conclusion that disorder in Tl2201 acts predominantly in the weak-to-intermediate-strength scattering regime, and that small-angle scattering is important., Comment: 13 pages, 9 figures

We present measurements of the vortex-state surface impedance, Z_s = R_s + i X_s, of a high quality, ortho-II-ordered single crystal of the cuprate high temperature superconductor YBa2Cu3O6.52 (T_c = 59K). Measurements have been made at four microwave frequencies (\omega/2\pi = 2.64, 4.51, 9.12 and 13.97 GHz), for magnetic fields ranging from 0 to 7 T. From these data we obtain the field, frequency and temperature dependence of the vortex viscosity, pinning constant, depinning frequency and flux-flow resistivity. The vortex viscosity, \eta(\omega,T), has a surprisingly strong frequency dependence and bears a striking resemblance to the zero-field quasiparticle conductivity, \sigma_qp(\omega,T), suggesting that the dominant dissipative mechanism for the flux lines is induced electric fields coupling to bulk, long-lived d-wave quasiparticles outside the vortex cores. This is in sharp contrast to the conventional Bardeen-Stephen picture, in which dissipation takes place inside quasi-normal vortex cores. The strong frequency dependence of the vortex viscosity in the microwave range requires us to treat it as a complex response function, with an imaginary part that is predicted to contribute to the apparent pinning force on the vortices. Measurements of the frequency dependence of the pinning force confirm that this term is present, and in a form consistent with the requirements of causality. At low temperatures the flux-flow resistivity, \rho_ff \propto 1/\eta, has the form \rho_ff(T) = \rho_0 + \rho_1 \ln(1/T), reminiscent of the DC resistivity of cuprates in the pseudogap regime., Comment: 16 pages, 15 figures

CeCoIn5 is a heavy fermion superconductor with strong similarities to the high-Tc cuprates, including quasi-two-dimensionality, proximity to antiferromagnetism, and probable d-wave pairing arising from a non-Fermi-liquid normal state. Experiments allowing detailed comparisons of their electronic properties are of particular interest, but in most cases are difficult to realize, due to their very different transition temperatures. Here we use low temperature microwave spectroscopy to study the charge dynamics of the CeCoIn5 superconducting state. The similarities to cuprates, in particular to ultra-clean YBa2Cu3Oy, are striking: the frequency and temperature dependence of the quasiparticle conductivity are instantly recognizable, a consequence of rapid suppression of quasiparticle scattering below Tc; and penetration depth data, when properly treated, reveal a clean, linear temperature dependence of the quasiparticle contribution to superfluid density. The measurements also expose key differences, including prominent multiband effects and a temperature dependent renormalization of the quasiparticle mass., Comment: 9 pages, 6 figures

We present two-dimensional resistive magnetohydrodynamic simulations of line-tied asymmetric magnetic reconnection in the context of solar flare and coronal mass ejection current sheets. The reconnection process is made asymmetric along the inflow direction by allowing the initial upstream magnetic field strengths and densities to differ, and along the outflow direction by placing the initial perturbation near a conducting wall boundary that represents the photosphere. When the upstream magnetic fields are asymmetric, the post-flare loop structure is distorted into a characteristic skewed candle flame shape. The simulations can thus be used to provide constraints on the reconnection asymmetry in post-flare loops. More hard X-ray emission is expected to occur at the footpoint on the weak magnetic field side because energetic particles are more likely to escape the magnetic mirror there than at the strong magnetic field footpoint. The footpoint on the weak magnetic field side is predicted to move more quickly because of the requirement in two dimensions that equal amounts of flux must be reconnected from each upstream region. The X-line drifts away from the conducting wall in all simulations with asymmetric outflow and into the strong magnetic field region during most of the simulations with asymmetric inflow. There is net plasma flow across the X-line for both the inflow and outflow directions. The reconnection exhaust directed away from the obstructing wall is significantly faster than the exhaust directed towards it. The asymmetric inflow condition allows net vorticity in the rising outflow plasmoid which would appear as rolling motions about the flux rope axis., Comment: 33 pages, 8 figures, accepted to ApJ. Minor corrections since previous version

There are relatively few observations of UV emission during the impulsive phases of solar flares, so the nature of that emission is poorly known. Photons produced by solar flares can resonantly scatter off atoms and ions in the corona. Based on off-limb measurements by SOHO/UVCS, we derive the O VI $\lambda$1032 luminosities for 29 flares during the impulsive phase and the Ly$\alpha$ luminosities of 5 flares, and we compare them with X-ray luminosities from GOES measurements. The upper transition region and lower transition region luminosities of the events observed are comparable. They are also comparable to the luminosity of the X-ray emitting gas at the beginning of the flare, but after 10-15 minutes the X-ray luminosity usually dominates. In some cases we can use Doppler dimming to estimate flow speeds of the O VI emitting gas, and 5 events show speeds in the 40 to 80 $\rm km s^{-1}$ range. The O VI emission could originate in gas evaporating to fill the X-ray flare loops, in heated chromospheric gas at the footpoints, or in heated prominence material in the coronal mass ejection. All three sources may contribute in different events or even in a single event, and the relative timing of UV and X-ray brightness peaks, the flow speeds, and the total O VI luminosity favor each source in one or more events., Comment: 18 pages, 8 figures, 3 tables

We perform a time-dependent ionization analysis to constrain plasma heating requirements during a fast partial halo coronal mass ejection (CME) observed on 2000 June 28 by the Ultraviolet Coronagraph Spectrometer (UVCS) aboard the Solar and Heliospheric Observatory (SOHO). We use two methods to derive densities from the UVCS measurements, including a density sensitive O V line ratio at 1213.85 and 1218.35 Angstroms, and radiative pumping of the O VI 1032,1038 doublet by chromospheric emission lines. The most strongly constrained feature shows cumulative plasma heating comparable to or greater than the kinetic energy, while features observed earlier during the event show cumulative plasma heating of order or less than the kinetic energy. SOHO Michelson Doppler Imager (MDI) observations are used to estimate the active region magnetic energy. We consider candidate plasma heating mechanisms and provide constraints when possible. Because this CME was associated with a relatively weak flare, the contribution by flare energy (e.g., through thermal conduction or energetic particles) is probably small; however, the flare may have been partially behind the limb. Wave heating by photospheric motions requires heating rates significantly larger than those previously inferred for coronal holes, but the eruption itself could drive waves which heat the plasma. Heating by small-scale reconnection in the flux rope or by the CME current sheet is not significantly constrained. UVCS line widths suggest that turbulence must be replenished continually and dissipated on time scales shorter than the propagation time in order to be an intermediate step in CME heating., Comment: 14 pages, 7 figures, accepted for publication in ApJ, corrected values of kinetic energy in Table 4 with minor changes to text

Understanding the physical processes responsible for accelerating the solar wind requires detailed measurements of the collisionless plasma in the extended solar corona. Some key clues about these processes have come from instruments that combine the power of an ultraviolet (UV) spectrometer with an occulted telescope. This combination enables measurements of ion emission lines far from the bright solar disk, where most of the solar wind acceleration occurs. Although the UVCS instrument on SOHO made several key discoveries, many questions remain unanswered because its capabilities were limited. This white paper summarizes these past achievements and also describes what can be accomplished with next-generation instrumentation of this kind., Comment: 7 pages, 3 figures, white paper submitted to the NRC Solar/Space Physics Decadal Survey project

We test the usefulness of a generalized inverse participation ratio (GIPR) as a measure of Anderson localization. The GIPR differs from the usual inverse participation ratio in that it depends on the local density of states rather than on the single-electron wavefunctions. This makes it suitable for application to many-body systems. We benchmark the GIPR by performing a finite-size scaling analysis of a disordered, noninteracting, three-dimensional tight-binding lattice. We find values for the critical disorder and critical exponents that are in agreement with published values., Comment: 6 pages, 5 figures Accepted for publication in PRB

To investigate the impact of current sheet motion on the reconnection process, we perform resistive magnetohydrodynamic (MHD) simulations of two closely located reconnection sites which move apart from each other as reconnection develops. This simulation develops less quickly than an otherwise equivalent single perturbation simulation but eventually exhibits a higher reconnection rate. The unobstructed outflow jets are faster and longer than the outflow jets directed towards the magnetic island that forms between the two current sheets. The X-line and flow stagnation point are located near the trailing end of each current sheet very close to the obstructed exit. The speed of X-line retreat ranges from ~0.02-0.06 while the speed of stagnation point retreat ranges from ~0.03-0.07, in units of the initial upstream Alfven velocity. Early in time, the flow stagnation point is located closer to the center of the current sheet than the X-line, but later on the relative positions of these two points switch. Consequently, late in time there is significant plasma flow across the X-line in the opposite direction of X-line retreat. Throughout the simulation, the velocity at the X-line does not equal the velocity of the X-line. Motivated by these results, an expression for the rate of X-line retreat is derived in terms of local parameters at the X-point. This expression shows that X-line retreat is due to both advection by the bulk plasma flow and diffusion of the normal component of the magnetic field., Comment: 10 pages, 8 figures. To be published in Physics of Plasmas (http://pop.aip.org/). Typos corrected and references updated

Magnetic reconnection with asymmetry in the outflow direction occurs in the Earth's magnetotail, coronal mass ejections, flux cancellation events, astrophysical disks, spheromak merging experiments, and elsewhere in nature and the laboratory. A control volume analysis is performed for the case of steady antiparallel magnetic reconnection with asymmetric downstream pressure, which is used to derive scaling relations for the outflow velocity from each side of the current sheet and the reconnection rate. Simple relationships for outflow velocity are presented for the incompressible case and the case of symmetric downstream pressure but asymmetric downstream density. Asymmetry alone is not found to greatly affect the reconnection rate. The flow stagnation point and magnetic field null do not coincide in a steady state unless the pressure gradient is negligible at the flow stagnation point., Comment: 12 pages, 8 figures. Submitted to JGR. Any comments will be appreciated

The POLAR Investigation of the Sun (POLARIS) mission uses a combination of a gravity assist and solar sail propulsion to place a spacecraft in a 0.48 AU circular orbit around the Sun with an inclination of 75 degrees with respect to solar equator. This challenging orbit is made possible by the challenging development of solar sail propulsion. This first extended view of the high-latitude regions of the Sun will enable crucial observations not possible from the ecliptic viewpoint or from Solar Orbiter. While Solar Orbiter would give the first glimpse of the high latitude magnetic field and flows to probe the solar dynamo, it does not have sufficient viewing of the polar regions to achieve POLARIS' primary objective : determining the relation between the magnetism and dynamics of the Sun's polar regions and the solar cycle., Comment: 23 pages, 14 figures, 4 tables, Accepted by Experimental Astronomy

It is now well established that stellar winds of hot stars are fragmentary and that the X-ray emission from stellar winds has a strong contribution from shocks in winds. Chandra high spectral resolution observations of line profiles of O and B stars have shown numerous properties that had not been expected. Here we suggest explanations by considering the X-rays as arising from bow shocks that occur where the stellar wind impacts on spherical clumps in the winds. We use an accurate and stable numerical hydrodynamical code to obtain steady-state physical conditions for the temperature and density structure in a bow shock. We use these solutions plus analytic approximations to interpret some major X-ray features: the simple power-law distribution of the observed emission measure derived from many hot star X-ray spectra and the wide range of ionization stages that appear to be present in X-ray sources throughout the winds. Also associated with the adiabatic cooling of the gas around a clump is a significant transverse velocity for the hot plasma flow around the clumps, and this can help to understand anomalies associated with observed line widths, and the differences in widths seen in stars with high and low mass-loss rates. The differences between bow shocks and the planar shocks that are often used for hot stars are discussed. We introduce an ``on the shock'' (OTSh) approximation that is useful for interpreting the X-rays and the consequences of clumps in hot star winds and elsewhere in astronomy., Comment: to appear in the Astrophysical Journal

We report the results of a high angular resolution near-infrared survey of dusty Wolf-Rayet stars using the Keck-1 Telescope, including new multi-wavelength images of the pinwheel nebulae WR 98a, WR 104, and WR 112. Angular sizes were measured for an additional 8 dusty WR stars using aperture masking interferometry, allowing us to probe characteristics sizes down to ~20 milliarcseconds (~40 AU for typical sources). With angular sizes and specific fluxes, we can directly measure the wavelength-dependent surface brightness and size relations for our sample. We discovered tight correlations of these properties within our sample which could not be explained by simple spherically-symmetric dust shells or even the more realistic ``pinwheel nebula'' (3-D) radiative transfer model, when using optical constants of Zubko. While the tightly-correlated surface brightness relations we uncovered offer compelling indirect evidence of a shared and distinctive dust shell geometry amongst our sample, long-baseline interferometers should target the marginally-resolved objects in our sample in order to conclusively establish the presence or absence of the putative underyling colliding wind binaries thought to produce the dust shells around WC Wolf-Rayets., Comment: Accepted by Astrophysical Journal