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At least 559 records · Page 31

Studies of superconducting materials with muon spin rotation

The muon spin rotation/relaxation technique was found to be an exceptionally effective means of measuring the magnetic properties of superconductors, including the new high temperature superconductor materials, at the microscopic level. The technique directly measures the magnetic penetration depth (type II superconductors (SC's)) and detects the presence of magnetic ordering (antiferromagnetism or spin-glass ordering were observed in some high temperature superconductor (HTSC's) and in many closely related compounds). Extensive studies of HTSC materials were conducted by the Virginia State University - College of William and Mary - Columbia University collaboration at Brookhaven National Laboratory and TRIUMF (Vancouver). A survey of LaSrCuO and YBaCaCuO systems shows an essentially linear relationship between the transition temperature T(sub c) and the relaxation rate. This appears to be a manifestation of the proportionality between T(sub c) and the Fermi energy, which suggests a high energy scale for the SC coupling, and which is not consistent with the weak coupling of phonon-mediated SC. Studies of LaCuO and YBaCuO parent compounds show clear evidence of antiferromagnetism. YBa2Cu(3-x)CO(x)O7 shows the simultaneous presence of spin-glass magnetic ordering and superconductivity. Three-dimensional SC, (Ba, K) BiO3, unlike the layered CuO-based compounds, shows no suggestion of magnetic ordering. Experimental techniques and theoretical implications are discussed.

Davis, Michael R.↗

Quasi-Equilibrium States in the Tropics Simulated by a Cloud-Resolving Model: Specific Features and Budget Analysis - Part 1

A series of long-term integrations using the two-dimensional Goddard Cumulus Ensemble (GCE) model were performed by altering imposed environmental components to produce various quasi-equilibrium thermodynamic states. Model results show that the genesis of a warm/wet quasi-equilibrium state is mainly due to either strong vertical wind shear (from nudging) or large surface fluxes (from strong surface winds), while a cold/dry quasi-equilibrium state is attributed to a remarkably weakened mixed-wind shear (from vertical mixing due to deep convection) along with weak surface winds. In general, latent heat flux and net large-scale temperature forcing, the two dominant physical processes, dominate in the beginning stage of the simulated convective systems, then considerably weaken in the final stage, which leads to quasi-equilibrium states. A higher thermodynamic regime is found to produce a larger rainfall amount, as convective clouds are the leading source of rainfall over stratiform clouds even though the former occupy much less area. Moreover, convective clouds are more likely to occur in the presence of strong surface winds (latent heat flux), while stratiform clouds (especially the well-organized type) are favored in conditions with strong wind shear (large-scale forcing). The convective systems, which consist of distinct cloud types due to the variation in horizontal winds, are also found to propagate differently. Accordingly, convective systems with mixed-wind shear generally propagate in the direction of shear, while the system with strong (multidirectional) wind shear propagates in a more complex way. Based on the results from the temperature (Q1) and moisture (Q2) budgets, cloud-scale eddies are found to act as a hydrodynamic 'vehicle' that cascades the heat and moisture vertically. Several other specific features such as atmospheric stability, CAPE, and mass fluxes are also investigated and found to be significantly different between diverse quasi-equilibrium states. Detailed comparisons between the various states are presented.

Shie, C.-L.↗

Modeling and Correcting the Time-Dependent ACS PSF

The ability to accurately measure the shapes of faint objects in images taken with the Advanced Camera for Surveys (ACS) on the Hubble Space Telescope (HST) depends upon detailed knowledge of the Point Spread Function (PSF). We show that thermal fluctuations cause the PSF of the ACS Wide Field Camera (WFC) to vary over time. We describe a modified version of the TinyTim PSF modeling software to create artificial grids of stars across the ACS field of view at a range of telescope focus values. These models closely resemble the stars in real ACS images. Using 10 bright stars in a real image, we have been able to measure HST s apparent focus at the time of the exposure. TinyTim can then be used to model the PSF at any position on the ACS field of view. This obviates the need for images of dense stellar fields at different focus values, or interpolation between the few observed stars. We show that residual differences between our TinyTim models and real data are likely due to the effects of Charge Transfer Efficiency (CTE) degradation. Furthermore, we discuss stochastic noise that is added to the shape of point sources when distortion is removed, and we present MultiDrizzle parameters that are optimal for weak lensing science. Specifically, we find that reducing the MultiDrizzle output pixel scale and choosing a Gaussian kernel significantly stabilizes the resulting PSF after image combination, while still eliminating cosmic rays/bad pixels, and correcting the large geometric distortion in the ACS. We discuss future plans, which include more detailed study of the effects of CTE degradation on object shapes and releasing our TinyTim models to the astronomical community.

Rhodes, Jason↗

Tidal Disruption of Phobos as the Cause of Surface Fractures

Phobos, the innermost satellite of Mars, displays an extensive system of grooves that are mostly symmetric about its sub-Mars point. Phobos is steadily spiraling inward due to the tides it raises on Mars lagging behind Phobos' orbital position and will suffer tidal disruption before colliding with Mars in a few tens of millions of years. We calculate the surface stress field of the deorbiting satellite and show that the first signs of tidal disruption are already present on its surface. Most of Phobos' prominent grooves have an excellent correlation with computed stress orientations. The model requires a weak interior that has very low rigidity on the tidal evolution time scale, overlain by an approximately 10-100 m exterior shell that has elastic properties similar to lunar regolith as described by Horvath et al. (1980).

Hurford, T. A.↗

On collisional disruption - Experimental results and scaling laws

Both homogeneous and inhomogeneous targets have been addressed by the present experimental consideration of the impact strengths, fragment sizes, and fragment velocities generated by cement mortar targets whose crushing strengths vary by an order of magnitude, upon impact of projectiles in the velocity range of 50-5700 m/sec. When combined with additional published data, dynamic impact strength is found to correlate with quasi-static material strengths for materials ranging in character from basalt to ice; two materials not following this trend, however, are weak mortar and clay targets. Values consistent with experimental results are obtainable with a simple scaling algorithm based on impact energy, material properties, and collisional strain rate.

Davis, Donald R.↗

Monsoon-Enso Relationships: A New Paradigm

This article is partly a review and partly a new research paper on monsoon-ENSO relationship. The paper begins with a discussion of the basic relationship between the Indian monsoon and ENSO dating back to the work of Sir Gilbert Walker up to research results in more recent years. Various factors that may affect the monsoon-ENSO, relationship, including regional coupled ocean-atmosphere processes, Eurasian snow cover, land-atmosphere hydrologic feedback, intraseasonal oscillation, biennial variability and inter-decadal variations, are discussed. The extreme complex and highly nonlinear nature of the monsoon-ENSO relationship is stressed. We find that for regional impacts on the monsoon, El Nino and La Nina are far from simply mirror images of each other. These two polarities of ENSO can have strong or no impacts on monsoon anomalies depending on the strength of the intraseasonal oscillations and the phases of the inter-decadal variations. For the Asian-Australian monsoon (AAM) as a whole, the ENSO impact is effected through a east-west shift in the Walker Circulation. For rainfall anomalies over specific monsoon areas, regional processes play important roles in addition to the shift in the Walker Circulation. One of the key regional processes identified for the boreal summer monsoon is the anomalous West Pacific Anticyclone (WPA). This regional feature has similar signatures in interannual and intraseasonal time scales and appears to determine whether the monsoon-ENSO relationship is strong or weak in a given year. Another important regional feature includes a rainfall and SST dipole across the Indian Ocean, which may have strong impact on the austral summer monsoon. Results are shown indicating that monsoon surface wind forcings may induce a strong biennial signal in ENSO and that strong monsoon-ENSO coupling may translate into pronounced biennial variability in ENSO. Finally, a new paradigm is proposed for the study of monsoon variability. This paradigm provides a unified framework in which monsoon predictability, the role of regional vs. basin-scale processes, its relationship with different climate subsystems, and causes of secular changes in monsoon-ENSO relationship can be investigated.

Lau, K. M.↗

On the dynamo generation of flux ropes in the Venus ionosphere

Small scale magnetic field structures or 'flux ropes' observed in the ionosphere of Venus can be interpreted as the result of a kinematic dynamo process acting on weak seed fields. The seed fields result from the prevailing downward convection of magnetic flux from the vicinity of the ionopause, while small scale fluctuations in the velocity of the ionospheric plasma, which can be caused by collisional coupling to gravity waves in the neutral atmosphere, provide the mechanism by which the field is twisted and redistributed into features of similar scale. This mechanism naturally explains some of the average properties of flux ropes such as the variation of their characteristics with altitude and solar zenith angle. It also elucidates the relationship between the large scale and small scale ionospheric magnetic fields.

Luhmann, J. G.↗

Liquid-free covalent reinforcement of carbon nanotube dry-spun yarns and free-standing sheets

Carbon nanotubes (CNTs) possess exceptional mechanical properties, surpassing stiffness and strength metrics of common materials such as steel alloys by 100× at the nanoscale. However, when myriads of individual CNTs are bundled together into macroscopic ensembles like fibers or sheets, the result is a 100-fold drop in strength compared to its individual components. Here we present a general strategy aimed to close this gap in property scaling. By using vapor-phase polymerization of a crosslinkable polymer, we reinforced the weak interlinkages among individual CNTs within both yarns and sheets to promote a better transference of mechanical load across the structure. Furthermore, after the treatment, dry-spun, low-density 2.3 μm thin yarns increased their elastic moduli by at least 300%, and free-standing CNT sheets exhibited a 10× boost. In-situ synchrotron small-angle X-ray scattering revealed that polymer-reinforced yarns undergo limited CNT bundle rearrangement when subjected to tensile loads compared to pristine yarns. This evidence supports the hypothesis that the polymer hinders CNTs slippage, the root cause of the poor scaling of mechanical properties in these materials. While we demonstrated this reinforcement method for CNT structures, it is not specific to CNTs and could be used in a wide variety of other hierarchical nanostructured ensembles.

36 MATERIALS SCIENCE↗

Using Multi-Scale Modeling Systems and Satellite Data to Study the Precipitation Processes

In recent years, exponentially increasing computer power has extended Cloud Resolving Model (CRM) integrations from hours to months, the number of computational grid points from less than a thousand to close to ten million. Three-dimensional models are now more prevalent. Much attention is devoted to precipitating cloud systems where the crucial 1-km scales are resolved in horizontal domains as large as 10,000 km in two-dimensions, and 1,000 x 1,000 km2 in three-dimensions. Cloud resolving models now provide statistical information useful for developing more realistic physically based parameterizations for climate models and numerical weather prediction models. It is also expected that NWP and mesoscale model can be run in grid size similar to cloud resolving model through nesting technique. Recently, a multi-scale modeling system with unified physics was developed at NASA Goddard. It consists of (l) a cloud-resolving model (Goddard Cumulus Ensemble model, GCE model), (2) a regional scale model (a NASA unified weather research and forecast, WRF), (3) a coupled CRM and global model (Goddard Multi-scale Modeling Framework, MMF), and (4) a land modeling system. The same microphysical processes, long and short wave radiative transfer and land processes and the explicit cloud-radiation, and cloud-land surface interactive processes are applied in this multi-scale modeling system. This modeling system has been coupled with a multi-satellite simulator to use NASA high-resolution satellite data to identify the strengths and weaknesses of cloud and precipitation processes simulated by the model. In this talk, the recent developments and applications of the multi-scale modeling system will be presented. In particular, the results from using multi-scale modeling system to study the precipitating systems and hurricanes/typhoons will be presented. The high-resolution spatial and temporal visualization will be utilized to show the evolution of precipitation processes. Also how to use of the multi-satellite simulator tqimproy~ precipitation processes will be discussed.

Tao, Wei-Kuo↗

Macro-scale Testing and Micromechanics Modeling of Fracture Behaviors for Boron Carbide Composites with Hierarchical Microstructures

With a unique combination of properties including high hardness, low density, wear and corrosion resistance, thermal stability, high neutron absorption, and semi-conductivity, boron carbide (B4C) is a candidate material for various engineering applications that involve extreme environment. The current applications of boron carbide, however, are limited by its intrinsic brittleness due to its strong covalent bonding. To toughen boron carbide, in this work hierarchical microstructure designs was used to provide multiple toughening mechanisms including crack deflection/bridging, micro-crack toughening, etc. Using field assisted sintering, B4C composites with hierarchical microstructure features including graphite platelets, micron and sub-micron sized TiB2 reinforcements were fabricated. The fracture toughness of fabricated B4C composites were previously measured at micro-scale using micro-indentation followed by post-testing microstructure inspection. However, questions including whether the fracture toughness enhancement measured at micro-scale can translate to macro-scale mechanical properties, and what are the fundamental mechanisms behind observed fracture toughness enhancement, remain to be answered. In this study, the fabricated B4C composites were tested using standardized four-point bending method to obtain fracture toughness at macro-scale. In addition, micromechanics modeling was conducted using MAC/GMC code and crack-band model to study the effect of residual stress and weak interphases on fracture behaviors of B4C composites reinforced with TiB2 particles. Through standardized four-point bending tests, fracture toughness enhancements up to 2.85, 3.32, and 3.65 MPa∙m(exp 1/2) (from 2.38 MPa∙m(exp 1/2)) were achieved for B4C composites with graphite platelets addition (micro/nano B4C), with TiB2 formation (micro B4C-TiB2), and with both graphite and TiB2 addition (micro/nano B4C-TiB2) respectively. Micromechanics modeling indicated that introduction of thermal residual stress and weak interphases caused enhanced micro-cracking behavior and resulted in the observed fracture toughness enhancement. These results furthered understanding about the mechanical behaviors at macro-scale and the mechanisms behind observed fracture toughness enhancement for B4C composites with hierarchical microstructures and can provide reference data for the future design of B4C composites with optimized microstructures for further fracture toughness enhancement.

Boron Carbide↗

Transitioning from Stage-III to Stage-IV: Cosmology from galaxy×CMB lensing and shear×CMB lensing (Final Report for Grant SC0021429 "Cosomology with Galaxy and CMB Surveys: Mitigating Systematic Effects Through Combining Datasets")

We examine the cosmological constraining power from two cross-correlation probes between galaxy and cosmic microwave background (CMB) surveys: the cross-correlation of lens galaxy density with CMB lensing convergence $\langle δ_g$$^κ\text{CMB}\rangle$, and source galaxy weak lensing shear with CMB lensing convergence $\langle^{γκ}$$_{\text{CMB}}\rangle$. These two cross-correlation probes provide an independent cross-check of other large-scale structure constraints and are insensitive to galaxy-only or CMB-only systematic effects. In addition, when combined with other large-scale structure probes, the cross-correlations can break degeneracies in cosmological and nuisance parameters, improving both the precision and robustness of the analysis. In this work, we study how the constraining power of $\langle δ_g$$^κ\text{CMB}\rangle + \langle^{γκ}$$_{\text{CMB}}\rangle$ changes from Stage-III (ongoing) to Stage-IV (future) surveys. Given the flexibility in selecting the lens galaxy sample, we also explore systematically the impact on cosmological constraints when we vary the redshift range and magnitude limit of the lens galaxies using mock galaxy catalogs. We find that in our setup, the contribution to cosmological constraints from $\langle δ_g$$^κ\text{CMB}\rangle$ and $\langle^{γκ}$$_{\text{CMB}}\rangle$ are comparable in the Stage-III data sets; but in Stage-IV surveys, the noise in$\langle δ_g$$^κ\text{CMB}\rangle$ becomes subdominant to cosmic variance, preventing $\langle δ_g$$^κ\text{CMB}\rangle$ to further improve the constraints. This implies that to maximize the cosmological constraints from future $\langle δ_g$$^κ\text{CMB}\rangle$ + $\langle^{γκ}$$_{\text{CMB}}\rangle$ analyses, we should focus more on the requirements on$^{γκ}$$_{\text{CMB}}\rangle$ instead of$\langle δ_g$$^κ\text{CMB}\rangle$. Furthermore, the selection of the lens sample should be optimized in terms of our ability to characterize its redshift or galaxy bias instead of its number density.

79 ASTRONOMY AND ASTROPHYSICS↗

Using Multi-Scale Modeling Systems to Study the Precipitation Processes

In recent years, exponentially increasing computer power has extended Cloud Resolving Model (CRM) integrations from hours to months, the number of computational grid points from less than a thousand to close to ten million. Three-dimensional models are now more prevalent. Much attention is devoted to precipitating cloud systems where the crucial 1-km scales are resolved in horizontal domains as large as 10,000 km in two-dimensions, and 1,000 x 1,000 km2 in three-dimensions. Cloud resolving models now provide statistical information useful for developing more realistic physically based parameterizations for climate models and numerical weather prediction models. It is also expected that NWP and mesoscale model can be run in grid size similar to cloud resolving model through nesting technique. Recently, a multi-scale modeling system with unified physics was developed at NASA Goddard. It consists of (1) a cloud-resolving model (Goddard Cumulus Ensemble model, GCE model), (2) a regional scale model (a NASA unified weather research and forecast, WRF), (3) a coupled CRM and global model (Goddard Multi-scale Modeling Framework, MMF), and (4) a land modeling system. The same microphysical processes, long and short wave radiative transfer and land processes and the explicit cloud-radiation, and cloud-land surface interactive processes are applied in this multi-scale modeling system. This modeling system has been coupled with a multi-satellite simulator to use NASA high-resolution satellite data to identify the strengths and weaknesses of cloud and precipitation processes simulated by the model. In this talk, a review of developments and applications of the multi-scale modeling system will be presented. In particular, the results from using multi-scale modeling system to study the interactions between clouds, precipitation, and aerosols will be presented. Also how to use of the multi-satellite simulator to improve precipitation processes will be discussed.

Tao, Wei-Kuo↗

Using Multi-Scale Modeling Systems and Satellite Data to Study the Precipitation Processes

In recent years, exponentially increasing computer power extended Cloud Resolving Model (CRM) integrations from hours to months, the number of computational grid points from less than a thousand to close to ten million. Three-dimensional models are now more prevalent. Much attention is devoted to precipitating cloud systems where the crucial 1-km scales are resolved in horizontal domains as large as 10,000 km in two-dimensions, and 1,000 x 1,000 sq km in three-dimensions. Cloud resolving models now provide statistical information useful for developing more realistic physically based parameterizations for climate models and numerical weather prediction models. It is also expected that NWP and mesoscale models can be run in grid size similar to cloud resolving models through nesting technique. Recently, a multi-scale modeling system with unified physics was developed at NASA Goddard. It consists of (1) a cloud-resolving model (Goddard Cumulus Ensemble model, GCE model). (2) a regional scale model (a NASA unified weather research and forecast, W8F). (3) a coupled CRM and global model (Goddard Multi-scale Modeling Framework, MMF), and (4) a land modeling system. The same microphysical processes, long and short wave radiative transfer and land processes and the explicit cloud-radiation and cloud-land surface interactive processes are applied in this multi-scale modeling system. This modeling system has been coupled with a multi-satellite simulator to use NASA high-resolution satellite data to identify the strengths and weaknesses of cloud and precipitation processes simulated by the model. In this talk, a review of developments and applications of the multi-scale modeling system will be presented. In particular, the results from using multi-scale modeling systems to study the interactions between clouds, precipitation, and aerosols will be presented. Also how to use the multi-satellite simulator to improve precipitation processes will be discussed.

Tao, Wei--Kuo↗

Microphysics in Multi-scale Modeling System with Unified Physics

Recently, a multi-scale modeling system with unified physics was developed at NASA Goddard. It consists of (1) a cloud-resolving model (Goddard Cumulus Ensemble model, GCE model), (2) a regional scale model (a NASA unified weather research and forecast, WRF), (3) a coupled CRM and global model (Goddard Multi-scale Modeling Framework, MMF), and (4) a land modeling system. The same microphysical processes, long and short wave radiative transfer and land processes and the explicit cloud-radiation, and cloud-land surface interactive processes are applied in this multi-scale modeling system. This modeling system has been coupled with a multi-satellite simulator to use NASA high-resolution satellite data to identify the strengths and weaknesses of cloud and precipitation processes simulated by the model. In this talk, a review of developments and applications of the multi-scale modeling system will be presented. In particular, the microphysics development and its performance for the multi-scale modeling system will be presented.

Tao, Wei-Kuo↗

Superclustering with the Atacama Cosmology Telescope and Dark Energy Survey. II. Anisotropic Large-scale Coherence in Hot Gas, Galaxies, and Dark Matter

Statistics that capture the directional dependence of the baryon distribution in the cosmic web enable unique tests of cosmology and astrophysical feedback. We use constrained oriented stacking of thermal Sunyaev–Zel’dovich (tSZ) maps to measure the anisotropic distribution of hot gas 2.5–40 Mpc away from galaxy clusters embedded in massive filaments and superclusters. The cluster selection and orientation (at a scale of ∼15 Mpc) use Dark Energy Survey (DES) Year 3 data, while expanded tSZ maps from the Atacama Cosmology Telescope Data Release 6 enable a ∼3× more significant measurement of the extended gas compared to the technique’s proof-of-concept. Decomposing stacks into cosine multipoles of order m , we detect a dipole ( m = 1) and quadrupole ( m = 2) at 8σ–10σ, as well as evidence for m = 4 signal at up to 6σ, indicating sensitivity to late-time non-Gaussianity. We compare to Cardinal simulations with spherical gas models pasted onto dark matter halos. The fiducial tSZ data can discriminate between two models that deplete pressure differently in low-mass halos (mimicking astrophysical feedback), preferring higher average pressure in extended structures. However, uncertainty in the amount of cosmic infrared background contamination reduces the constraining power. Additionally, we apply the technique to DES galaxy density and weak lensing to study for the first time their oriented relationships with tSZ. In the tSZ-to-lensing relation, averaged on 7.5 Mpc (transverse) scales, we observe dependence on redshift but not shape or radial distance. Thus, on large scales, the superclustering of gas pressure, galaxies, and total matter is coherent in shape and extent.

79 ASTRONOMY AND ASTROPHYSICS↗

Turbulent Concentration of Chondrules: Size Distribution and Multifractal Scaling

Size-selective concentration of particles in 3D turbulence may be related to collection of chondrules and other constituents into primitive bodies in a weakly turbulent protoplanetary nebula. In the terrestrial planet region, both the characteristic size and narrow size distribution of chondrules are explained, whereas "fluffier" particles would be concentrated in lower density, or more intensely turbulent, regions of the nebula. The spatial distribution of concentrated particle density obeys multifractal scaling, suggesting a dose tie to the turbulent cascade process. This scaling behavior allows predictions of the concentration probabilities to be made in the protoplanetary nebula, which are so large (> 10(exp 3) - 10(exp 4)) that further studies must be made of the role of mass loading.

Cuzzi, Jeffrey N.↗

Turbulent Transport in the Gray Zone: A Large Eddy Model Intercomparison Study of the CONSTRAIN Cold Air Outbreak Case

To quantify the turbulent transport at gray zone length scales between 1 and 10 km the Lagrangian evolution of the CONSTRAIN cold air outbreak (CAO) case was simulated with seven large eddy models. The case is characterized by rather large latent and sensible heat fluxes, and a rapid deepening rate of the boundary layer. In some models the entrainment velocity exceeds 4 cm/s. A significant fraction of this growth is attributed to a strong longwave radiative cooling of the inversion layer. The evolution and the timing of the breakup of the stratocumulus cloud deck differ significantly among the models. Sensitivity experiments demonstrate that a decrease in the prescribed cloud droplet number concentration, and the inclusion of ice microphysics, both act to speed up the thinning of the stratocumulus by enhancing the production of precipitation. In all models the formation of mesoscale fluctuations is clearly evident in the cloud fields but also in the horizontal wind velocity. Resolved vertical fluxes remain important for scales up to 10 km. The simulation results show that the resolved vertical velocity variance gradually diminishes with a coarsening of the horizontal mesh, but the total vertical fluxes of heat, moisture, and momentum are only weakly affected. This is a promising result as it demonstrates the potential use of a mesh size dependent turbulent length scale for convective boundary layers at gray zone model resolutions.

gray zone↗

Coronal density and temperature structure from coordinated observations associated with the total solar eclipse of 1988 March 18

This paper explores and compares diagnostics for temperature and density within large-scale structures of the inner corona based on cospatial and cotemporal spectrophotometric observations made at the time of the total solar eclipse of 1988 March 17/18. In the analysis a determination of plasma temperature T can be derived unambiguously from the intensity ratios Fe XIV/XUV or Fe XIV/Fe X since all the emission lines come from the ionized state of Fe and the ratios are only weakly dependent on density. These temperatures and the densities found in well-defined large-scale coronal structures are discussed. The emission-line temperature is found to be high (local maxima) in the coronal structures with enhanced white-light emission and associated with new cycle high-latitude magnetic fields separated from the old cycle polar field of opposite polarity. Also the average of the ratio of scale-height temperature/temperature over the entire range of position angle is roughly unity although the ratio is higher than unity (1.3-1.6) in the three most prominent streamers.

Guhathakurta, M.↗