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The performance of tactile and optical surface sensors for nano and micro coordinate measuring machines is currently limited by the lack of precisely characterised micro spheres, since established strategies have mainly been developed for spheres in the range of millimetres or above. We have, therefore, recently focused our research efforts towards a novel strategy for the characterisation of spheres in the sub-millimetre range. It is based on a set of atomic force microscope (AFM) surface scans in conjunction with a stitching algorithm. To obtain an uncertainty statement, the uncertainty about the shape of the reference surface needs to be propagated via the shape of the AFM tip to the actual measurement object. However, the sampling process of an AFM is non-linear and the processing of AFM scans requires complex algorithms. We have, therefore, recently begun to model the characterisation of micro spheres through simulations. In this contribution, this model is extended by the influence of the tip and reference surface. The influence of the tip's shape and reference surface is investigated through virtual and real experiments. The shape of the tip is varied by using tips with mean radii of 200 nm and 2 μm while sampling the same ruby sphere with a mean radius of 150 μm. In general, the simulation results imply that an uncertainty of less then 10 nm is achievable. However, an experimental validation of the model is still pending. The experimental investigations were limited by the lack of a suitable cleaning strategy for micro parts, which demonstrates the need for further investigations in this area. Although the characterisation of a full sphere has already been demonstrated, the investigations in this contribution are limited to equator measurements. [ABSTRACT FROM AUTHOR]

The microsphere profile of probe tips has to be measured and compensated to improve the measurement accuracy of micro-coordinate measuring machines (micro-CMMs) to less than several hundred nanometers. A high-precision radius and sphericity measurement method for the microsphere of the CMM probe tip is proposed in this article. Different circumferences of the tested microsphere are measured, and the true radius of any measuring point on the surface can be obtained after separating the runout errors. Then the sphericity of the tested microsphere can be evaluated by the minimum zone sphere method. A corresponding measuring system is developed based on the analysis of the primary error model and mechanical model, and verification experiments are conducted using a ruby microsphere (A-5000-7801, Renishaw Corporation) as the reference, whose claimed diameter and sphericity are 700 µm and 130 nm, respectively. Six groups of repeated experiments are performed, and 18 000 measurement points on 15 circumferences are recorded in each group of experiments. Results show that the average radius of the tested microsphere is 350.003 µm, and the average sphericity error is 208 nm with a standard deviation of 5.3 nm. Finally, the expanded uncertainty of the measurement results of the developed system is calculated as 209 nm (k = 1.96, normal distribution). The proposed method and system can be used in the precision measurements and compensations for probe tips of micro-CMMs and other parts, such as microspheres used in micro-bearings and micro-manufacturing machines. [ABSTRACT FROM AUTHOR]

Some observations, such as those presented in Walker et al., show that the observed entropy profiles of the intracluster medium (ICM) deviate from the power-law prediction of adiabatic simulations. This implies that nongravitational processes, which are absent in the simulations, may be important in the evolution of the ICM, and by quantifying the deviation, we may be able to estimate the feedback energy in the ICM and use it as a probe of the nongravitational processes. To address this issue, we calculate the ICM entropy profiles in a sample of 47 galaxy clusters and groups, which have been observed out to at least ∼r500 with Chandra, XMM-Newton, and/or Suzaku, by constructing a physical model to incorporate the effects of both gravity and nongravitational processes to fit the observed gas temperature and surface brightness profiles via Bayesian statistics. After carefully evaluating the effects of systematic errors, we find that the gas entropy profiles derived with best-fit results of our model are consistent with the simulation-predicted power-law profile near the virial radius, while the flattened profiles reported previously can be explained by introducing the gas clumping effect, the existence of which is confirmed in 19 luminous targets in our sample. We calculate the total feedback energy per particle and find that it decreases from ∼10 keV at the center to about zero at ∼0.35r200 and is consistent with zero outside ∼0.35r200, implying an upper limit of the feedback efficiency of ∼0.02 for the supermassive black holes hosted in the brightest cluster galaxies. [ABSTRACT FROM AUTHOR]

Rotation causes an increase in a neutron star’s mass and equatorial radius. The mass and radius depend sensitively on the unknown equation of state (EOS) of cold, dense matter. However, the increases in mass and radius due to rotation are almost independent of the EOS. The EOS independence leads to the idea of neutron star universality. In this paper, we compute sequences of rotating neutron stars with constant central density. We use a collection of randomly generated EOSs to construct simple correction factors to the mass and radius computed from the equations of hydrostatic equilibrium for nonrotating neutron stars. The correction factors depend only on the nonrotating star’s mass and radius and are almost independent of the EOS. This makes it computationally inexpensive to include observations of rotating neutron stars in EOS inference codes. We also construct a mapping from the measured mass and radius of a rotating neutron star to a corresponding nonrotating star. The mapping makes it possible to construct a zero-spin massâ€"radius curve if the masses and radii of many neutron stars with different spins are measured. We show that the changes in polar and equatorial radii are symmetric, in that the polar radius shrinks at the same rate in which the equatorial radius grows. This symmetry is related to the observation that the equatorial compactness (the ratio of mass to radius) is almost constant on one of the constant-density sequences. [ABSTRACT FROM AUTHOR]

The radio radiation mechanism is one of the open questions for pulsars. Multiband observations are very helpful to constrain pulsar radiation models. We observed PSR J1848-0123 at the 5 GHz band with the Shanghai Tianma 65 m radio telescope (TMRT). The 5 GHz observation together with the European Pulsar Network (EPN) and CSIRO ATNF Data Archives databases provides a broadband evolution property of the pulse profiles for this pulsar. We reprocessed these data sets to obtain the multiband pulse profiles. It was found that the pulse profile of PSR J1848-0123 narrows with increasing emission frequency. We separated the emission components of each pulse profile with a multi-Gaussian fitting method, and then calculated the beaming angle and emission radius of each component with the basic radiation geometry of pulsar. With the calculated beam angles and radiation radii, we simulated the radius-frequency mapping of this pulsar with an inverse Compton scatting model (ICS). It was found that the observed radio radiation could be generated in the core gap region above the polar cap of the pulsar. The beaming angle and emission radius versus frequency for PSR J1848-0123 can be explained well with the ICS model. [ABSTRACT FROM AUTHOR]

Micro coordinate measuring machines have been developed for the traceable characterization of small complex parts, due to the demand in research and industry. These machines require geometrically well characterized probing spheres of ever smaller radii. Currently, there is no established procedure for the measurement of such spheres below radii of 500 µm. In this paper we, therefore, propose and investigate an approach which is based on a set of atomic force microscope (AFM) surface scans in conjunction with a stitching algorithm. The strategy was implemented on a nano measuring machine and investigated on a ruby sphere with a radius of 150 µm. Although the strategy can generally be applied to the characterization of a full sphere, we limit ourselves to the measurement of one great circle (equator). The technique enables the measurement of micro spheres with a high lateral and vertical resolution. The mean radius of the ruby sphere was measured with a standard deviation of 3.7 nm over six repetitions. As our experiments have shown, the measurement procedure is at the moment mainly influenced by the shape of the AFM tip which requires further attention. [ABSTRACT FROM AUTHOR]

Interstellar Boundary Explorer (IBEX) observations of the "ribbon" of enhanced energetic neutral atom (ENA) fluxes show that it is a persistent feature that approximately forms a circle in the sky, likely formed from secondary ENAs whose source lies outside the heliopause. The IBEX ribbon's geometry (radius and center) depends on ENA energy and is believed to be influenced by the draping of the ISMF and the latitudinal structure of the SW. In this study, we demonstrate that the ribbon's geometry also depends on the pitch-angle scattering rate of ions outside the heliopause, which we simulate under strong and weak-scattering limits. The ribbon radius in the weak-scattering model is ∼4° larger than IBEX observations at most energies, and the strong-scattering model produces radii statistically consistent with IBEX at 1.1–2.7 keV. The simulated ribbon center is shifted between ∼2° and 5° along the B–V plane away from the IBEX center for the weak and strong limits, respectively, suggesting that the pristine ISMF far from the heliosphere is shifted ∼2°–5° away from our simulated ISMF toward the VLISM inflow direction. However, the magnitude needs to be decreased from ∼3 to 2 μG for the weak-scattering model to be consistent with the IBEX ribbon radius, which seems unlikely. We also find that the presence of interstellar He does not significantly affect the ribbon in the strong-scattering limit but yields weaker agreement with data in the weak limit. Our results slightly favor the strong-scattering limit for the ribbon's origin. [ABSTRACT FROM AUTHOR]

Measuring a spherical surface with small segment angle (e.g. 1°) precisely is a big challenge in scientific research and engineering applications. To fit sphere surfaces with small segment angles with high precision, a five-parameter constrained nonlinear least square fitting (CNLSF) method is presented in this work, where an Adam optimization algorithm with a prominent anti-interference ability is employed. We discuss various factors which influence the final uncertainty evaluation of the sphere's radius. A Monte Carlo simulation is conducted by superimposing Gaussian noise on the ideal spherical data to simulate practical instrument errors, then the relationship between the fitting bias of the sphere's radius and noise the level, the number of sampling points and the segment angle is investigated by comparing the performance of the linear least square fitting algorithm, the nonlinear least square fitting algorithm and the CNLSF algorithm. Finally, the simulated and experimental results show that the CNLSF method performs more precisely and robustly than the other algorithms, even when the corresponding segment angle approaches 1°, which illustrates that it is a promising and practical method in the real measurement world. [ABSTRACT FROM AUTHOR]

We present the distance-calibrated spectral energy distribution (SED) of the d/sdL7 SDSS J14162408+1348263A (J1416A) and an updated SED for SDSS J14162408+1348263B (J1416B). We also present the first retrieval analysis of J1416A using the Brewster retrieval code base and the second retrieval of J1416B. We find that the primary is best fit by a nongray cloud opacity with a power-law wavelength dependence but is indistinguishable between the type of cloud parameterization. J1416B is best fit by a cloud-free model, consistent with the results from Line et al. Most fundamental parameters derived via SEDs and retrievals are consistent within 1σ for both J1416A and J1416B. The exceptions include the radius of J1416A, where the retrieved radius is smaller than the evolutionary model-based radius from the SED for the deck cloud model, and the bolometric luminosity, which is consistent within 2.5σ for both cloud models. The pair's metallicity and carbon-to-oxygen ratio point toward formation and evolution as a system. By comparing the retrieved alkali abundances while using two opacity models, we are able to evaluate how the opacities behave for the L and T dwarf. Lastly, we find that relatively small changes in composition can drive major observable differences for lower-temperature objects. [ABSTRACT FROM AUTHOR]

The non-convex regularization is a new approach for sparse recovery. A minimizer of the regularized function can be computed by applying the ST-(αℓ1 − βℓ2) algorithm which is similar to the classical iterative soft thresholding algorithm (ISTA). It is known that ISTA converges quite slowly, and a faster alternative to ISTA is the projected gradient (PG) method. However, the conventional PG method is limited to solve problems with the classical ℓ1 sparsity regularization. In this paper, we present two accelerated alternatives to the ST-(αℓ1 − βℓ2) algorithm by extending the PG method to the non-convex sparsity regularization. Moreover, we discuss a strategy to determine the radius R of the ℓ1-ball constraint by Morozov's discrepancy principle. Numerical results are reported to illustrate the efficiency of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper presents a new approach for the regression of the center coordinates and radius of the solar disk in Hα solar full-disk images by using a Deep Convolutional Neural Network. We use ∼100,000 original Hα solar full-disk images obtained from Huairou Solar Observing Station as the experimental data set. The data set includes two parts: the original image and three numeric values (center coordinates and radius). In order to deal with the uneven distribution of the solar disk position in the original image, we randomly shift the solar disk during image preprocessing. Furthermore, data augmentation is also used to increase the robustness of the model. By evaluating the model with R-square and relative error, the center coordinates and the radius of the solar disk are proved to be effectively regressed. The data sets we constructed and source code are available as open source on GitHub. [ABSTRACT FROM AUTHOR]

In this paper, by making use of a new variational principle, we prove existence of nontrivial solutions for two different types of semilinear problems with Neumann boundary conditions in unbounded domains. Namely, we study elliptic equations and Hamiltonian systems on the unbounded domain where Br is a ball centred at the origin with radius r in. Our proofs consist of several new and novel ideas that can be used in broader contexts. [ABSTRACT FROM AUTHOR]

Using as references the posterior probability distribution functions of the equation of state (EOS) parameters inferred from the radii of canonical neutron stars (NSs) reported by the LIGO/VIRGO and NICER Collaborations based on their observations of GW170817 and PSR J0030+0451, we investigate how future radius measurements of more massive NSs will improve our current knowledge about the EOS of superdense neutron-rich nuclear matter, especially its symmetry energy term. Within the Bayesian statistical approach using an explicitly isospin-dependent parametric EOS for the core of NSs, we infer the EOS parameters of superdense neutron-rich nuclear matter from three sets of imagined mass–radius correlation data representing typical predictions by various nuclear many-body theories, that is, the radius stays the same, decreases, or increases with increasing NS mass within ±15% between 1.4 and 2.0 M⊙. The corresponding NS average density increases quickly or slowly or slightly decreases as the NS mass increases from 1.4 to 2.0 M⊙. While the EOSs of symmetric nuclear matter (SNM) inferred from the three data sets are approximately the same, the corresponding symmetry energies above about twice the saturation density of nuclear matter are very different, indicating that the radii of massive NSs carry important information about the high-density behavior of nuclear symmetry energy with little influence from the remaining uncertainties of the SNM EOS at suprasaturation densities. [ABSTRACT FROM AUTHOR]

The propagation of sidewall steps during the growth of nanowires is calculated in the frame of the Burton-Cabrera-Frank model. The stable shape of the nanowire comprises a cylinder section on top of a cone section: their characteristics are obtained as a function of the radius of the catalyst-nanowire area, the desorption-limited diffusion length of adatoms on the terraces, and the sticking of adatoms at step edges. The comparison with experimental data allows us to evaluate these last two parameters for InP and ZnTe nanowires; it reveals a different behavior for the two materials, related to a difference by an order of magnitude of the desorption-limited diffusion length. [ABSTRACT FROM AUTHOR]

The frequent flaring events in the X-ray and the near-IR (NIR) radiation of Sgr A* seem not to be periodic in time. However, statistical regularities, here termed "modulations by a pacemaker," are found in the recorded arrival times of both types of events. The characteristic time of the X-ray pacemaker is 149 minutes, and that of the NIR pacemaker is 40 minutes. Their reality as derived from observed data can be accepted at larger than 4.6σ and 3.8σ levels of statistical confidence, respectively. These results can be interpreted as evidence for a star that revolves around the black hole (BH) of Sgr A* in a slightly elliptical precessing orbit, at a distance of 3–3.5 Schwarzschild radii of the BH. The period of the X-ray pacemaker, which is not a periodicity of the flare occurrences themselves, is the epicyclic period of the star orbital motion. This is the time interval between two successive passages of the star through the pericenter of its orbit. The NIR pacemaker period is the mean sidereal binary period of the star revolution. The origin of the X-ray flares is in episodes of intense mass loss from the star that occur preferably near the pericenter phase of the binary revolution. The NIR flares originate or are triggered by processes that are internal to the star. The radiation emitted in the direction of Earth is slightly modulated by the changing aspect ratio of the two components of the BH/star binary to the line of sight from Earth at the sidereal binary frequency. [ABSTRACT FROM AUTHOR]

Given a probability vector x with its components sorted in non-increasing order, we consider the closed ball with p ⩾ 1 formed by the probability vectors whose ℓp-norm distance to the center x is less than or equal to a radius ϵ. Here, we provide an order-theoretic characterization of these balls by using the majorization partial order. Unlike the case p = 1 previously discussed in the literature, we find that the extremal probability vectors, in general, do not exist for the closed balls with 1 < p < ∞. On the other hand, we show that is a complete sublattice of the majorization lattice. As a consequence, this ball also has extremal elements. In addition, we give an explicit characterization of those extremal elements in terms of the radius and the center of the ball. This allows us to introduce some notions of approximate majorization and discuss its relation with previous results of approximate majorization given in terms of the ℓ1-norm. Finally, we apply our results to the problem of approximate conversion of resources within the framework of quantum resource theory of nonuniformity. [ABSTRACT FROM AUTHOR]

Recent work suggests that many short-period super-Earth and sub-Neptune planets may have significant spin axis tilts ("obliquities"). When planets are locked in high-obliquity states, the tidal dissipation rate may increase by several orders of magnitude. This intensified heat deposition within the planets' interiors should generate significant structural consequences, including atmospheric inflation leading to larger transit radii. Using up-to-date radius estimates from Gaia Data Release 2, we show evidence for ∼50% larger average radii of planets wide of first-order mean-motion resonances, a population of planets with a theorized frequent occurrence of high obliquities. We investigate whether this radius trend could be a signature of obliquity tides. Using an adaptation of the Modules for Experiments in Stellar Astrophysics (MESA) stellar evolution toolkit, we model the atmospheric evolution of sub-Neptune-mass planets in response to additional internal heat from obliquity tides. The degree of radius inflation predicted by the models is ∼10%–100% for tidal luminosities ≳10−5 of the incident stellar power; this degree of inflation is broadly consistent with the observations and can approximately be described by power-law relationships. We present a few case studies of very low density "super-puff" planets—Kepler-79 d, Kepler-31 c, and Kepler-27 b—and show that they are strong candidates for potentially having undergone tidally induced radius inflation. We also discuss how the discrepancy between the two populations of planets with masses derived from radial velocities and transit timing variations is connected to the radius distribution features we have identified. Altogether, the calculations in this work confirm that tidal dissipation has nonnegligible consequences for the structural properties of short-period sub-Neptunes. [ABSTRACT FROM AUTHOR]

A simple but accurate method for measuring the Earth’s radius using a video camera is described. A video camera was used to capture a shadow rising up the wall of a tall building at sunset. A free program called ImageJ was used to measure the time it took the shadow to rise a known distance up the building. The time, distance and length of the sidereal day were used to calculate the radius of the Earth. The radius was measured as 6394.3 ± 118 km, which is within 1.8% of the accepted average value of 6371 km and well within the experimental error. The experiment is suitable as a high school or university project and should produce a value for Earth’s radius within a few per cent at latitudes towards the equator, where at some times of the year the ecliptic is approximately normal to the horizon. [ABSTRACT FROM AUTHOR]

A measurement of the synchrotron self-absorption flux and frequency provides tight constraints on the physical size of the source and a robust lower limit on its energy. This lower limit is also a good estimate of the magnetic field and electrons' energy, if the two components are at equipartition. This well-known method was used for decades to study numerous astrophysical sources moving at non-relativistic (Newtonian) speeds. Here, we generalize the Newtonian equipartition theory to sources moving at relativistic speeds including the effect of deviation from spherical symmetry expected in such sources. As in the Newtonian case, minimization of the energy provides an excellent estimate of the emission radius and yields a useful lower limit on the energy. We find that the application of the Newtonian formalism to a relativistic source would yield a smaller emission radius, and would generally yield a larger lower limit on the energy (within the observed region). For sources where the synchrotron-self-Compton component can be identified, the minimization of the total energy is not necessary and we present an unambiguous solution for the parameters of the system. [ABSTRACT FROM AUTHOR]

Applying an equation of state (EOS) with its symmetric nuclear matter contribution and low-density symmetry energy Esym(ρ) constrained by heavy-ion reaction data, we calculate the dimensionless tidal deformability Λ of neutron stars in coalescing binary systems. Corresponding to the partially constrained EOS that previously predicted a radius of 11.5 km ≤ ≤ 13.6 km for canonical neutron-star configurations, Λ is found to be in the range of 292 ≤ ≤ 680, consistent with the very recent observation of the GW170817 event. We investigate the effect of the high-density behavior of Esym(ρ) on the tidal properties of neutron stars and find that while Λ depends strongly on the details of the symmetry energy, different trends of Esym(ρ) lead to very similar values of Λ. In particular, the transition from stiff/soft-to-soft/stiff Esym(ρ) could yield the same Λ. Thus, measuring Λ alone may not determine completely the density dependence of the symmetry energy. Coherent analyses of the dense neutron-rich nuclear matter EOS underlying both nuclear laboratory experiments and astrophysical observations are therefore necessary to break this degeneracy and determine precisely the details of the Esym(ρ). [ABSTRACT FROM AUTHOR]

The Kodaikanal Archive Program (India) is now available to the scientific community in digital form as daily digitized solar white light pictures, from 1923 to 2011. We present here the solar radius data, obtained after a painstaking effort to remove all effects that contribute to the error in their measurements (limb darkening, distortion of the objective lens, refraction, other instrumental effects, etc.). These data were analyzed to reveal any significant periodic variations, after applying a multi-taper method with red noise approximation and the Morlet wavelet transform analysis. After removing obvious periodic variations (such as solar rotation and Earth annual rotation), we found a possible cycle variation at 11.4 yr, quasi biennial oscillations at 1.5 and 3.8 yr, and Rieger-type periodicity at ≈159, 91, and 63 days. Another yr periodicity (as a mean) resulting from two other main periodicities detected at 6.3–7.8 yr can be identified as an atmospheric component. The detrending data show, over a mean radius of , a residual of less than ≈(−)1 mas over the time period of analysis: if not spurious, this estimate indicates a faint decline, but probably confirms more the constancy of the solar diameter during the considered ranging time, within instrumental and methodological limits. The Kodaikanal long quality observations contribute to international efforts to bring past solar data measurements to the community to further explore issues, for instance, those of the luminosity/radius properties that could be used to pinpoint the “seat of the solar cycle.” [ABSTRACT FROM AUTHOR]

Several models have been introduced in order to explain the radius distribution in exoplanet radii observed by Fulton et al. with one peak at , the other at , and the minimum at . In this paper we focus on the hypothesis that the exoplanet size distribution is caused by stellar X-ray and ultraviolet (XUV)-induced atmospheric loss. We evolve 106 synthetic exoplanets by exposing them to XUV irradiation from synthetic zero-age main-sequence stars. For each planet we set a different interior composition, which ranged from 100 wt% Fe (very dense), through to 100 wt% MgSiO3 (average density), and to 100 wt% ice (low density), with varying hydrogen envelope sizes that varied from 0 wt% (a negligible envelope) to 100 wt% (a negligible core). Our simulations were able to replicate the bimodal distribution in exoplanet radii. We argue that in order to reproduce the distribution by Fulton et al. it is mandatory for there to be a paucity of exoplanets with masses above . Furthermore, our best-fit result predicts an initial flat distribution in exoplanet occurrence for with a strong deficiency for planets with . Our results are consistent with the radius peak mostly encompassing denuded exoplanets, while the radius peak is mainly comprised of exoplanets with large hydrogen envelopes. [ABSTRACT FROM AUTHOR]

We search for evidence of the cause of the exoplanet radius gap, i.e., the dearth of planets with radii near 1.8 R⊕. If the cause were photoevaporation, the radius gap should trend with proxies for the early-life high-energy emission of the planet-hosting stars. If, alternatively, the cause were core-powered mass loss, no such trends should exist. Critically, spurious trends between the radius gap and stellar properties arise from an underlying correlation with instellation. After accounting for this underlying correlation, we find that no trends remain between the radius gap and stellar mass or present-day stellar activity as measured by near-UV emission. We dismiss the nondetection of a radius gap trend with near-UV emission because present-day near-UV emission is unlikely to trace early-life high-energy emission, but we provide a catalog of Galaxy Evolution Explorer near-UV and far-UV emission measurements for general use. We interpret the nondetection of a radius gap trend with stellar mass by simulating photoevaporation with mass-dependent evolution of stellar high-energy emission. The simulation produces an undetectable trend between the radius gap and stellar mass under realistic sources of error. We conclude that no evidence, from this analysis or others in the literature, currently exists that clearly favors either photoevaporation or core-powered mass loss as the primary cause of the exoplanet radius gap. However, repeating this analysis once the body of well-characterized <4 R⊕ planets has roughly doubled could confirm or rule out photoevaporation. [ABSTRACT FROM AUTHOR]

In this paper we show that X-ray spectral observations of the ATHENA mission, which is planned to launch in 2031, can constrain the equation of state (EOS) of superdense matter. We use our well-constrained continuum-fitting method to determine the mass and radius of a neutron star. Model spectra of the emission from a neutron star were calculated using the atmosphere code ATM24. In the next step, those models were fitted to simulated spectra of the neutron star calculated for ATHENA’s Wide Field Imager (WFI) detector, using satellite calibration files. To simulate the spectra we assumed three different values of effective temperature, surface gravity, and gravitational redshift. These cases relate to three different neutron star masses and radii. This analysis allows us to demonstrate both the precision of our method and the need for a fast detector onboard ATHENA. A large grid of theoretical spectra was calculated with various parameters and a hydrogen–helium–iron composition of solar proportions. These spectra were fitted to the simulated spectrum to estimate the precision of mass and radius determination. In each case, we obtained very precise values with errors in the range 3%–10% for mass and 2%–8% for radius within 1σ confidence. We show here that, with the ATHENA WFI detector, such a determination could be used to constrain the EOS of superdense neutron star matter. [ABSTRACT FROM AUTHOR]

We compare radii based on Gaia parallaxes to radii based on asteroseismic scaling relations for ∼300 dwarfs and subgiants and ∼3600 first-ascent giants from the Kepler mission. Systematics due to temperature, bolometric correction, extinction, asteroseismic radius, and the spatially correlated Gaia parallax zero-point contribute to a 2% systematic uncertainty on the agreement in Gaia–asteroseismic radius. We find that dwarf and giant scaling radii are on a parallactic scale at the level of −2.1% ± 0.5% (rand.) ± 2.0% (syst.) (dwarfs) and +1.7% ± 0.3% (rand.) ± 2.0% (syst.) (giants), supporting the accuracy and precision of scaling relations. In total, the 2% agreement that we find holds for stars spanning radii between 0.8 and 30 . We do, however, see evidence for relative errors in scaling radii between dwarfs and giants at the level of 4% ± 0.6%, and find evidence of departures from simple scaling relations for radii above 30 . Asteroseismic masses for very metal-poor stars are still overestimated relative to astrophysical priors, but at a reduced level. We see no trend with metallicity in radius agreement for stars with −0.5 < [Fe/H] < +0.5. We quantify the spatially correlated parallax errors in the Kepler field, which globally agree with the Gaia team’s published covariance model. We provide Gaia radii, corrected for extinction and the Gaia parallax zero-point, for our full sample of ∼3900 stars, including dwarfs, subgiants, and first-ascent giants. [ABSTRACT FROM AUTHOR]

A recipe based on physical principles employs the observed equivalent widths of 10 spectral lines to model the photosphere of a target star. Coupled with the visual magnitude and an absolute flux calibration, the recipe yields the angular radius, effective temperature, surface gravity, and metallicity. With the addition of a parallax, a linear radius and a mass estimate are added to the results. The method is applied to a sample of 26 G and K stars that span luminosity classes V to IIIa. The recipe-determined angular radii agree with the interferometer radii and have comparable errors. But unlike interferometers, the recipe is not limited to sizes ≳1 mas. The veracity of the other recipe-derived parameters is supported by numerous comparisons with previously published values. [ABSTRACT FROM AUTHOR]

Graze-and-merge collisions are common multi-step mergers occurring in low-velocity, off-axis impacts between similar-sized planetary bodies. The first impact happens at somewhat faster than the mutual escape velocity; for typical impact angles this does not result in immediate accretion, but the smaller body is slowed down so that it loops back around and collides again, ultimately accreting. The scenario changes in the presence of a third major body, i.e., planets accreting around a star, or satellites around a planet. We find that when the loop-back orbit remains inside roughly one third of the Hill radius from the target, then the overall process is not strongly affected. As the loop-back orbit increases in radius, the return velocity and angle of the second collision become increasingly random, with no record of the first collision’s orientation. When the loop-back orbit gets to about three quarters of the Hill radius, the path of smaller body is disturbed up to the point that it will usually escape the target. [ABSTRACT FROM AUTHOR]

By using the four-dimensional (4D) computer code of the time-dependent propagation of laser beams through atmospheric turbulence, the influence of atmospheric turbulence on the energy focusability of Gaussian beams with spherical aberration is studied in detail, where the mean-squared beam width, the power in the bucket (PIB), the β parameter and the energy Strehl ratio are taken as the characteristic parameters. It is shown that turbulence results in beam spreading, and the effect of spherical aberration on the beam spreading decreases due to turbulence. Gaussian beams with negative spherical aberration are more affected by turbulence than those with positive spherical aberration. For the negative spherical aberration case, the focus position moves to the source plane due to turbulence. It is mentioned that the influence of turbulence on the energy focusability defined by a certain energy (i.e. PIB�=�63%) is very heavy when the negative spherical aberration is very heavy. On the other hand, the influence of turbulence on the energy focusability defined by the energy within a given bucket radius (i.e. mean-squared beam width) is heaviest when a certain negative spherical aberration coefficient is adopted. [ABSTRACT FROM AUTHOR]

We study the basin of attraction of static extremal black holes, in the concrete setting of the STU model. By finding a connection to a decoupled Toda-like system and solving it exactly, we find a simple way to characterize the attraction basin via competing behaviors of certain parameters. The boundaries of attraction arise in the various limits where these parameters degenerate to zero. We find that these boundaries are generalizations of the recently introduced (extremal) subtracted geometry: the warp factors still exhibit asymptotic integer power law behaviors, but the powers can be different from one. As we cross over one of these boundaries (‘generalized subttractors’), the solutions turn unstable and start blowing up at finite radius and lose their asymptotic region. Our results are fully analytic, but we also solve a simpler theory where the attraction basin is lower dimensional and easy to visualize, and present a simple picture that illustrates many of the basic ideas. [ABSTRACT FROM AUTHOR]

We present the development of millimeter scale 3D hemispherical shell resonators fabricated from the polycrystalline diamond, a material with low thermoelastic damping and very high stiffness. These hemispherical wineglass resonators with 1.1 mm diameter are fabricated through a combination of micro-electro discharge machining (EDM) and silicon micromachining techniques. Using piezoelectric and electrostatic excitation and optical vibration measurement, the elliptical wineglass vibration mode is determined to be at 18.321 kHz, with the two degenerate wineglass modes having a relative frequency mismatch of 0.03%. A study on the effect of the size and misalignment of the anchor and resonator's radius variation on both the average frequency and frequency mismatch of the 2θ elliptical vibration modes is carried out. It is shown that the absolute frequency of a wineglass resonator will increase with the anchor size. It is also demonstrated that the fourth harmonic of radius variation is linearly related to the frequency mismatch. [ABSTRACT FROM AUTHOR]

As though to compensate for the rarity of multidimensional integrable systems, non-integrable spatial extensions of many of the well known dispersive equations on the line exhibit a remarkable variety of solitary patterns unavailable in 1D. In the present work we elaborate upon the ubiquity of this effect and find it to be even more pronounced in compacton admitting systems which admit new patterns otherwise unavailable, in both the real (the sublinear ZK) and the complex realm (the sublinear NLS and complex KG). In the planar complex case, in addition to a countable number of radial solutions, for every spin number m we find both analytical and numerical evidence of a countable number of multi-modal compact vortices which have a strictly finite radius and, depending on m, either extend to the origin or vanish identically in a disk around it. [ABSTRACT FROM AUTHOR]

The equation of the motion of a point charge q repelled by a fixed point-like charge Q is derived and studied. In solving this problem useful concepts in classical and relativistic kinematics, in Newtonian mechanics and in non-linear ordinary differential equations are revised. The validity of the approximations is discussed from the physical point of view. In particular the classical electron radius emerges naturally from the requirement that the initial distance is large enough for the non-relativistic approximation to be valid. The relevance of this topic for undergraduate physics teaching is pointed out. [ABSTRACT FROM AUTHOR]

We introduce the Vainshtein mechanism which plays a crucial role in massive gravities, as well as in related theories such as Galileons and their extensions. This mechanism, also known as k-mouflage, allows to hide via nonlinear effects—typically for source distances smaller than a so-called Vainshtein radius which depends on the source and on the theory considered—some degrees of freedom whose effects are then only left important at large distances, e.g. for cosmology. It is introduced here in nonlinear Fierz–Pauli theories (massive gravities), including the dRGT theories, in their decoupling limits, as well as in other models such as the DGP model or generalized Galileons. This presentation is self-contained, and before discussing the Vainshtein mechanism we introduce some useful results and concepts concerning massive gravity, such as the vDVZ discontinuity, the decoupling limits or the Boulware–Deser ghost. [ABSTRACT FROM AUTHOR]

Moons orbiting extrasolar planets are the next class of object to be observed and characterized for possible habitability. Like the host-planets to their host-star, exomoons have a limiting radius at which they may be gravitationally bound, or the Hill radius. In addition, they also have a distance at which they will become tidally locked and therefore in synchronous rotation with the planet. We have examined the flux phase profile of a simulated, hypothetical moon orbiting at a distant radius around the confirmed exoplanets μ Ara b, HD 28185 b, BD +14 4559 b, and HD 73534 b. The irradiated flux on a moon at its furthest, stable distance from the planet achieves its largest flux gradient, which places a limit on the flux ranges expected for subsequent (observed) moons closer in orbit to the planet. We have also analyzed the effect of planetary eccentricity on the flux on the moon, examining planets that traverse the habitable zone either fully or partially during their orbit. Looking solely at the stellar contributions, we find that moons around planets that are totally within the habitable zone experience thermal equilibrium temperatures above the runaway greenhouse limit, requiring a small heat redistribution efficiency. In contrast, exomoons orbiting planets that only spend a fraction of their time within the habitable zone require a heat redistribution efficiency near 100% in order to achieve temperatures suitable for habitability. This means that a planet does not need to spend its entire orbit within the habitable zone in order for the exomoon to be habitable. Because the applied systems comprise giant planets around bright stars, we believe that the transit detection method is most likely to yield an exomoon discovery. [ABSTRACT FROM AUTHOR]

There have been many proposed explanations for the larger-than-expected radii of some transiting hot Jupiters, including either stellar or orbital energy deposition deep in the atmosphere or deep in the interior. In this paper, we explore the important influences on hot-Jupiter radius evolution of (1) additional heat sources in the high atmosphere, the deep atmosphere, and deep in the convective interior; (2) consistent cooling of the deep interior through the planetary dayside, nightside, and poles; (3) the degree of heat redistribution to the nightside; and (4) the presence of an upper atmosphere absorber inferred to produce anomalously hot upper atmospheres and inversions in some close-in giant planets. In particular, we compare the radius expansion effects of atmospheric and deep-interior heating at the same power levels and derive the power required to achieve a given radius increase when night-side cooling is incorporated. We find that models that include consistent day/night cooling are more similar to isotropically irradiated models when there is more heat redistributed from the dayside to the nightside. In addition, we consider the efficacy of ohmic heating in the atmosphere and/or convective interior in inflating hot Jupiters. Among our conclusions are that (1) the most highly irradiated planets cannot stably have uB ≳ 10 km s-1 G over a large fraction of their daysides, where u is the zonal wind speed and B is the dipolar magnetic field strength in the atmosphere, and (2) that ohmic heating cannot in and of itself lead to a runaway in planet radius. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study the curvature of equilateral random walks and polygons that are confined in a sphere. Curvature is one of several basic geometric properties that can be used to describe random walks and polygons. We show that confinement affects curvature quite strongly, and in the limit case where the confinement diameter equals the edge length the unconfined expected curvature value doubles from π/2 to p. To study curvature a simple model of an equilateral random walk in spherical confinement in dimensions 2 and 3 is introduced. For this simple model we derive explicit integral expressions for the expected value of the total curvature in both dimensions. These expressions are functions that depend only on the radius R of the confinement sphere. We then show that the values obtained by numeric integration of these expressions agrees with numerical average curvature estimates obtained from simulations of random walks. Finally, we compare the confinement effect on curvature of random walks with random polygons. [ABSTRACT FROM AUTHOR]

Alternate contraction and drastic expansion, i.e., 'breathing' of electronic subshells, the effects of the fusion of two subshells into one subshell and its subsequent fission (splitting) into the original subshells, as well as multiple alteration of the order of subshells in confined semifilled shell atoms with a progressively narrowing confinement are theoretically discovered. The confinement is represented by a repulsive penetrable spherical potential of an inner radius r0. The effects are exemplified by calculated data for confined semifilled shell atoms from the second, third and fourth rows of Mendeleev's table--Li, N, P and Cr atoms with semifilled 2s¹, 2p³, 3p³ and 3d5 subshells, respectively--for the completeness of the study. The underlying physics behind the discovered effects is explained. [ABSTRACT FROM AUTHOR]

Whilst everyone is familiar with the process of blowing up a balloon, few of us have gone further to quantify the actual pressures involved at different stages in the inflation process. This paper seeks to describe experiments to fill some of those gaps and examine some of the apparently anomalous behaviour of connected balloons. [ABSTRACT FROM AUTHOR]

If the augmented density of a spherical anisotropic system is assumed to be multiplicatively separable into functions of the potential and the radius, the radial function, which can be completely specified by the behavior of the anisotropy parameter alone, also fixes the anisotropic ratios of every higher order velocity moment. It is inferred from this that the non- negativity of the distribution function necessarily limits the allowed behaviors of the radial function. This restriction is translated into the constraints on the behavior of the anisotropy parameter. We find that not all radial variations of the anisotropy parameter satisfy these constraints and thus anisotropy profiles exist that are not consistent with any separable augmented density. [ABSTRACT FROM AUTHOR]

The expressions of the radius and the surface tension of surface of tension Rs and γs in terms of the pressure distribution for nanoscale liquid threads are of great importance for molecular dynamics (MD) simulations of the interfacial phenomena of nanoscale fluids; these two basic expressions are derived in this paper. Although these expressions were derived first in the literature [Kim B G, Lee J S, Han M H, and Park S, 2006 Nanoscale and Microscale Thermophysical Engineering, 10, 283] and used widely thereafter, the derivation is wrong both in logical structure and physical thought. In view of the importance of these basic expressions, the logic and physical mistakes appearing in that derivation are pointed out. [ABSTRACT FROM AUTHOR]

Observations have revealed that a significant number of hot Jupiters have anomalously large radii. Layered convection induced by compositional inhomogeneity has been proposed to account for the radius anomaly of hot Jupiters. To reexamine the impact of the compositional inhomogeneity, we perform an evolutionary calculation by determining the convection regime at each evolutionary time step according to the criteria from linear analyses. It is shown that the impact is limited in the case of the monotonic gradient of heavy-element abundance. The layered convection is absent for the first 1 Gyr from the formation of hot Jupiters, and instead overturning convection develops. The superadiabaticity of the temperature gradient is limited by the neutrally stable state for the Ledoux stability criterion. The effect of the increased mass of heavy elements essentially compensates the effect of the delayed contraction on the planetary radius caused by compositional inhomogeneity. In addition, even in the case where the layered convection is artificially imposed, this mechanism requires extremely thin layers (∼101–103 cm) to account for the observed radius anomaly. The long-term stability of such thin layers remains to be studied. Therefore, if the criteria adopted in this paper are adequate, it might be difficult to explain the inflated radii of hot Jupiters by the monotonic gradient of heavy-element abundance alone. [ABSTRACT FROM AUTHOR]

The article discusses electric fire hazards that can occur in homes or in school laboratories and explores the minimum necessary radius of an electric wire to avoid such hazards. Topics covered include alternating currents (ACs), melting temperature of plastics, and electrical devices connected to plugs via metal wires.

Investigating the Gunn–Peterson (GP) trough of high-redshift quasars (QSOs) is a powerful way to reveal the cosmic reionization. As one of such attempts, we perform a series of analyses to examine the absorption lines observed with one of the highest-redshift QSOs, PSO J006.1240+39.2219, which we previously discovered at z = 6.62. Using the Subaru telescope, we obtained medium-resolution spectrum with a total exposure time of 7.5 hr. We calculate the Lyα transmission in different redshift bins to determine the near zone radius and the optical depth at 5.6 < z < 6.5. We find a sudden change in the Lyα transmission at 5.75 < z < 5.86, which is consistent with the result from the literature. The near zone radius of the QSO is 5.79 ± 0.09 pMpc, within the scatter of the near zone radii of other QSOs measured in previous studies. We also analyze the dark gap distribution to probe the neutral hydrogen fractions beyond the saturation limit of the GP trough. We extend the measurement of the dark gaps to 5.7 < z < 6.3. We find that the gap widths increase with increasing redshifts, suggesting more neutral universe at higher redshifts. However, these measurements strongly depend on the continuum modeling. As a continuum model-free attempt, we also perform the dark pixel counting analysis to find the upper limit of (0.8) at z < 5.8 (z > 5.8). All three analyses based on this QSO show increasingly neutral hydrogen toward higher redshifts, adding precious measurements up to z ∼ 6.5. [ABSTRACT FROM AUTHOR]

Here we give an observational method for measurements of the equatorial scattering region radius using variability in the polarized broad lines in Type 1 active galactic nuclei (AGNs). The polarization in broad lines of Type 1 AGNs is mostly caused by equatorial scattering, where specific features allow one to separate its contribution from the total polarized flux. We propose to monitor variability in the polarized line flux and find the time lag between the nonpolarized continuum and polarized broad line variability. The distance to the scattering screen can then be determined from the time delay. The method was, for the first time, applied to the observations of the Type 1 AGN Mrk 6, and we found that the size of the scattering region in this AGN is around 100 lt-days. That is significantly smaller than the dusty region size estimated by the infrared interferometric observations and also larger than known broad line region (BLR) size. This indicates that the scattering region lies between the BLR and the dusty region and could be used as a probe of the dust sublimation radius. [ABSTRACT FROM AUTHOR]

This paper presents a simple branch-and-bound (B&B) algorithm to compute the minimum zone circularity/sphericity error, which is formulated as the problem of finding the centers of two concentric circles/spheres that contain given points between them and have minimal difference in their radii. For any square domain of the center, a lower bound on the minimal radius difference attainable over the domain is proposed, and this monotonically increases as the domain is divided into square subdomains. Along with the branching operation, a domain will become infinitely small and provide only a center of concentric circles/spheres such that its lower bound is equal to the radius difference. Using such a lower bound, therefore, the B&B algorithm guarantees the computing of the exact circularity/sphericity error and it is proven that the accuracy of the computed result can be easily specified by the termination tolerance of the algorithm as needed. In addition, the algorithm is very efficient and easy to implement. [ABSTRACT FROM AUTHOR]

Neutron stars are formed in core-collapse supernova explosions, where a large number of neutrinos are emitted. In this paper, supernova neutrino light curves are computed for the cooling phase of protoneutron stars, which lasts a few minutes. In the numerical simulations, 90 models of the phenomenological equation of state with different incompressibilities, symmetry energies, and nucleon effective masses are employed for a comprehensive study. It is found that the cooling timescale is longer for a model with a larger neutron star mass and a smaller neutron star radius. Furthermore, a theoretical expression of the cooling timescale is presented as a function of the mass and radius and it is found to describe the numerical results faithfully. These findings suggest that diagnosing the mass and radius of a newly formed neutron star using its neutrino signal is possible. [ABSTRACT FROM AUTHOR]

Fresnel laws and the corresponding Fresnel reflection and transmission coefficients provide the quantitative information of the amount of reflected and transmitted (refracted) light in dependence on its angle of incidence. They are at the core of ray optics at planar interfaces. However, the well-known Fresnel formulae do not hold at curved interfaces and deviations are appreciable when the radius of curvature becomes of the order of several wavelengths of the incident light. This is of particular importance for optical microcavities that play a significant role in many modern research fields. Their convexly curved interfaces modify Fresnel’s law in a characteristic manner. Most notably, the onset of total internal reflection is shifted to angles larger than critical incidence (Martina and Henning 2002 Phys. Rev. E 65 045603). Here, we derive analytical Fresnel formulae for the opposite type of interface curvature, namely concavely curved refractive index boundaries, that have not been available so far. The accessibility of curvature-dependent Fresnel coefficients facilitates the analytical, ray-optics based description of light in complex mesoscopic optical structures that will be important in future nano- and microphotonic applications. [ABSTRACT FROM AUTHOR]

We develop a two-stage end-pumped Nd:YVO4 amplifier seeded by a passively Q-switched microchip laser. An average output power of 13.5 W with repetition rate up to 7 kHz and pulse duration of ∼1.24 ns is obtained, corresponding to a pump extraction efficiency of 16.1% (19.5% for the second stage) and peak power of ∼1.5 MW. The beam quality factors at maximum output power are measured to beand . We introduce an analytical model to estimate gain and beam quality after amplification. This model focuses on the influence of ratio of seed spot radius to pump spot radius when designing an amplifier. Moreover, our experiments reveal that the re-imaging system in the double-pass configuration can be used to enhance the beam quality. [ABSTRACT FROM AUTHOR]

The intermittent behavior of a quasi-coherent density fluctuation is observed in a laboratory plasma. The quasi-coherent fluctuation is localized but intermittent events are observed in the whole region of plasma. Conditional averaging shows the intermittent events propagate from the central region of the magnetized plasma column to the peripheral region. Auto-correlation function of fluctuations and Hurst analysis reveal the intermittency is highly auto-correlated and the Hurst parameter reaches to 0.8, indicating the existence of self-similar behavior and long-range time correlation, and self-organized criticality dynamics might be the mechanism. Cross-bicoherence between different radii shows the nonlinear coupling between the quasi-coherent fluctuation and ambient turbulence, which will contribute to the generation of intermittency of turbulence. [ABSTRACT FROM AUTHOR]