SEARCH · Engineering Papers

Results for “covariance constraints”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 145 records · Page 8

All sources NASA NTRS DOE OSTI

NASA NTRS1994

Echo mapping of active galactic nuclei broad-line regions: Fundamental algorithms

We formulate and test a series of algorithms for echo mapping the emission-line regions near active galactic nuclei from measurements of correlated variability in their line and continuum light curves. The linear regularization method (LRM) employs a direct inversion of evenly spaced light-curve data, with a regularization parameter that can be used to control the trade-off between noise and resolution. Matrix formulas express the formal solution as well as its variance and covariance in terms of uncertainties in the measurements. Unlike the maximum-entropy method (MEM), LRM applies to kernels with both positive and negative values, but the results are somewhat limited by ringing effects. A positivity constraint proves effective in controlling the ringing. MEM combines regularization and positivity in a natural way, but similar results are also found using positivity constraints with nonentropic regularization functions. Direct inversions of unevenly sampled light curves require interpolating the noisy data. In this case better results are found by solving for both the continuum light curve and kernel function in a simultaneous fit to the data. Our conclusion is that while echo mapping currently gives ambiguous results, the algorithms are not the limiting factor. Progress depends on efforts to increase the accuracy and completeness of sampling of the observed light curves.

Vio, Roberto↗

NASA NTRS2012

An Iterated Global Mascon Solution with Focus on Land Ice Mass Evolution

Land ice mass evolution is determined from a new GRACE global mascon solution. The solution is estimated directly from the reduction of the inter-satellite K-band range rate observations taking into account the full noise covariance, and formally iterating the solution. The new solution increases signal recovery while reducing the GRACE KBRR observation residuals. The mascons are estimated with 10-day and 1-arc-degree equal area sampling, applying anisotropic constraints for enhanced temporal and spatial resolution of the recovered land ice signal. The details of the solution are presented including error and resolution analysis. An Ensemble Empirical Mode Decomposition (EEMD) adaptive filter is applied to the mascon solution time series to compute timing of balance seasons and annual mass balances. The details and causes of the spatial and temporal variability of the land ice regions studied are discussed.

Luthcke, S. B.↗

NASA NTRS2013

Antarctica, Greenland and Gulf of Alaska Land-ice Evolution from an Iterated GRACE Global Mascon Solution

We have determined the ice mass evolution of the Antarctica and Greenland ice sheets (AIS and GIS) and Gulf of Alaska (GOA) glaciers from a new GRACE global solution of equal-area surface mass concentration parcels (mascons) in equivalent height of water. The mascons were estimated directly from the reduction of the inter-satellite K-band range-rate (KBRR) observations, taking into account the full noise covariance, and formally iterating the solution. The new solution increases signal recovery while reducing the GRACE KBRR observation residuals. The mascons were estimated with 10 day and 1 arc degree equal-area sampling, applying anisotropic constraints. An ensemble empirical mode decomposition adaptive filter was applied to the mascon time series to compute annual mass balances. The details and causes of the spatial and temporal variability of the land-ice regions studied are discussed. The estimated mass trend over the total GIS, AIS and GOA glaciers for the time period 1 December 2003 to 1 December 2010 is -380 plus or minus 31 Gt a(exp -1), equivalent to -1.05 plus or minus 0.09 mma(exp -1) sea-level rise. Over the same time period we estimate the mass acceleration to be -41 plus or minus 27 Gt a(exp -2), equivalent to a 0.11 plus or minus 0.08 mm a(exp -2) rate of change in sea level. The trends and accelerations are dependent on significant seasonal and annual balance anomalies.

MASCON↗

DOE OSTI2021

The first Hubble diagram and cosmological constraints using superluminous supernovae

In this work, we present the first Hubble diagram of superluminous supernovae (SLSNe) out to a redshift of two, together with constraints on the matter density, Ω M , and the dark energy equation-of-state parameter, w(≡p/ρ). We build a sample of 20 cosmologically useful SLSNe I based on light curve and spectroscopy quality cuts. We confirm the robustness of the peak–decline SLSN I standardization relation with a larger data set and improved fitting techniques than previous works. We then solve the SLSN model based on the above standardization via minimization of the χ2 computed from a covariance matrix that includes statistical and systematic uncertainties. For a spatially flat Λ cold dark matter (ΛCDM) cosmological model, we find $\Omega _{\rm M}=0.38^{+0.24}_{-0.19}$, with an rms of 0.27 mag for the residuals of the distance moduli. For a w 0 w a CDM cosmological model, the addition of SLSNe I to a ‘baseline’ measurement consisting of Planck temperature together with Type Ia supernovae, results in a small improvement in the constraints of w 0 and wa of 4 per cent. We present simulations of future surveys with 868 and 492 SLSNe I (depending on the configuration used) and show that such a sample can deliver cosmological constraints in a flat ΛCDM model with the same precision (considering only statistical uncertainties) as current surveys that use Type Ia supernovae, while providing a factor of 2–3 improvement in the precision of the constraints on the time variation of dark energy, w 0 and w a . This paper represents the proof of concept for superluminous supernova cosmology, and demonstrates they can provide an independent test of cosmology in the high-redshift (z > 1) universe.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS2002

Site Distribution and Aliasing Effects in the Inversion for Load Coefficients and Geocenter Motion from GPS Data

Precise GPS measurements of elastic relative site displacements due to surface mass loading offer important constraints on global surface mass transport. We investigate effects of site distribution and aliasing by higher-degree (n greater than or equal 2) loading terms on inversion of GPS data for n = 1 load coefficients and geocenter motion. Covariance and simulation analyses are conducted to assess the sensitivity of the inversion to aliasing and mismodeling errors and possible uncertainties in the n = 1 load coefficient determination. We found that the use of center-of-figure approximation in the inverse formulation could cause 10- 15% errors in the inverted load coefficients. n = 1 load estimates may be contaminated significantly by unknown higher-degree terms, depending on the load scenario and the GPS site distribution. The uncertainty in n = 1 zonal load estimate is at the level of 80 - 95% for two load scenarios.

global positioning system↗

DOE OSTI2020

Functional methods for Heavy Quark Effective Theory

We use functional methods to compute one-loop effects in Heavy Quark Effective Theory. The covariant derivative expansion technique facilitates the efficient extraction of matching coefficients and renormalization group evolution equations. This paper pro- vides the first demonstration that such calculations can be performed through the algebraic evaluation of the path integral for the class of effective field theories that are (i) constructed using a non-trivial one-to-many mode decomposition of the UV theory, and (ii) valid for non-relativistic kinematics. We discuss the interplay between operators that appear at intermediate steps and the constraints imposed by the residual Lorentz symmetry that is encoded as reparameterization invariance within the effective description. The tools presented here provide a systematic approach for computing corrections to higher order in the heavy mass expansion; precision applications include predictions for experimental data and connections to theoretical tests via lattice QCD. A set of pedagogical appendices comprehensively reviews modern approaches to performing functional calculations algebraically, and derives contributions from a term with open covariant derivatives for the first time.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2026

Emergent constraints on future methane emissions from global wetlands

Future methane (CH 4 ) emissions from natural wetlands are predicted to increase due to global warming, leading to positive feedback on climate change. However, the magnitude of this increase remains highly uncertain. Here we present novel ensemble simulations of seven state-of-the-art terrestrial biosphere models to estimate wetland CH 4 emissions (eCH 4 ) during the twenty-first century. Our estimates suggest that for every 1 °C increase in global land surface temperature, there is a 24 ± 10 Tg CH 4 yr −1 increase in eCH 4 . We also identify an emergent relationship between contemporary temperature dependence and projected eCH 4 . When constrained by 163 site-year eddy-covariance measurements of eCH 4 , we show that wetland emissions can increase by 50–60% by the 2090s relative to the 2010s under a high-warming scenario. The projected decadal increase in eCH 4 from the 2010–2019 baseline to the 2030s would very likely (90% probability) offset an amount equivalent in scale to 8–10% of anthropogenic eCH 4 at the 2020 level, comparable to the reductions committed under the Global Methane Pledge. However, the constraint is dominated by mid- and high-latitude observations, with limited tropical coverage, and uncertainties in projected wetland inundation contribute substantially to uncertainty in eCH 4 . Our findings reduce the uncertainty in projected wetland methane–climate feedback and highlight its potential impacts on methane mitigation efforts to slow global warming.

Zhang, Zhen [Chinese Academy of Sciences (CAS), Be↗

DOE OSTI2025

Dark Energy Survey Year 3 Results: Cosmological constraints from second- and third-order shear statistics

Here, we present a cosmological analysis of the third-order aperture mass statistic using Dark Energy Survey Year 3 (DES Y3) data. We perform a complete tomographic measurement of the three-point correlation function of the Y3 weak lensing shape catalog with the four fiducial source redshift bins. Building upon our companion methodology paper, we apply a pipeline that combines the two-point function ξ ± with the mass aperture skewness statistic ⟨ M ap 3 ⟩ , which is an efficient compression of the full shear three-point function. We use a suite of simulated shear maps to obtain a joint covariance matrix. By jointly analyzing ξ ± and ⟨ M ap 3 ⟩ measured from DES Y3 data with a Λ CDM model, we find S 8 = 0.780 ± 0.015 and Ω m = 0.26 6 - 0.040 + 0.039 , yielding 111% of figure-of-merit improvement in the Ω m - S 8 plane relative to ξ ± alone, consistent with expectations from simulated likelihood analyses. With a w CDM model, we find S 8 = 0.74 9 - 0.026 + 0.027 and w 0 = - 1.39 ± 0.31 , which gives an improvement of 22% on the joint S 8 - w 0 constraint. Our results are consistent with w 0 = - 1 . Our new constraints are compared to CMB data from the Planck satellite, and we find that with the inclusion of ⟨ M ap 3 ⟩ the existing tension between the datasets is at the level of 2.3 σ . We show that the third-order statistic enables us to self-calibrate the mean photometric redshift uncertainty parameter of the highest redshift bin with little degradation in the figure of merit. Our results demonstrate the constraining power of higher-order lensing statistics and establish ⟨ M ap 3 ⟩ as a practical observable for joint analyses in current and future surveys.

Gomes, R. C. H. [University of Pennsylvania] (ORCI↗

DOE OSTI2023

Practical Guide to Measuring Wetland Carbon Pools and Fluxes

Abstract Wetlands cover a small portion of the world, but have disproportionate influence on global carbon (C) sequestration, carbon dioxide and methane emissions, and aquatic C fluxes. However, the underlying biogeochemical processes that affect wetland C pools and fluxes are complex and dynamic, making measurements of wetland C challenging. Over decades of research, many observational, experimental, and analytical approaches have been developed to understand and quantify pools and fluxes of wetland C. Sampling approaches range in their representation of wetland C from short to long timeframes and local to landscape spatial scales. This review summarizes common and cutting-edge methodological approaches for quantifying wetland C pools and fluxes. We first define each of the major C pools and fluxes and provide rationale for their importance to wetland C dynamics. For each approach, we clarify what component of wetland C is measured and its spatial and temporal representativeness and constraints. We describe practical considerations for each approach, such as where and when an approach is typically used, who can conduct the measurements (expertise, training requirements), and how approaches are conducted, including considerations on equipment complexity and costs. Finally, we review key covariates and ancillary measurements that enhance the interpretation of findings and facilitate model development. The protocols that we describe to measure soil, water, vegetation, and gases are also relevant for related disciplines such as ecology. Improved quality and consistency of data collection and reporting across studies will help reduce global uncertainties and develop management strategies to use wetlands as nature-based climate solutions.

Bansal, Sheel (ORCID:0000000312331707)↗

NASA NTRS2021

Satellite Constraints on the Latitudinal Distribution and Temperature Sensitivity of Wetland Methane Emissions

Wetland methane (CH4) emissions comprise about one-third of the global CH4 source. The latitudinal distribution and climate sensitivity of wetland CH4 fluxes are the key determinants of the global CH4-climate feedback. However, large differences exist between bottom-up estimates, informed by ground-based flux measurements, and top-down estimates derived from spaceborne total column CH4. Despite the extensive coverage of satellite CH4 concentration observations, challenges remain with using top-down estimates to test bottom-up models, mainly because of the uncertainties in the satellite retrievals, the model representation errors, the variable prior emissions, and the confounding role of the posterior error covariance structures. Here, we use satellite-based top-down CH4 flux estimates (2010–2012) to test and refine 42 bottom-up estimates of wetland emissions that use a range of hypothesized wetland extents and process controls. Our comparison between bottom-up models and satellite-based fluxes innovatively accounts for cross-correlations and spatial uncertainties typically found in top-down inverse estimates, such that only the information from satellite observations and the atmospheric transport model is kept as a constraint. We present a satellite-constrained wetland CH4 ensemble product derived from assembling the highest-performance bottom-up models, which estimates global wetland CH4 emissions of 148 (117–189, 5th–95th percentile) Tg CH4 yr−1. We find that tropical wetland emissions contribute 72% (63%–85%) to the global wetland total. We also find that a lower-than-expected temperature sensitivity agrees better with atmospheric CH4 measurements. Overall, our approach demonstrates the potential for using satellites to quantitatively refine bottom-up wetland CH4 emission estimates, their latitudinal distributions, and their sensitivity to climate.

wetland ch4↗

DOE OSTI2025

Detection of supernova magnitude fluctuations induced by large-scale structure

The peculiar velocities of supernovae and their host galaxies are correlated with the large-scale structure of the Universe, and can be used to constrain the growth rate of structure and test the cosmological model. In this work, we measure the correlation statistics of the large-scale structure traced by the Dark Energy Spectroscopic Instrument Bright Galaxy Survey Data Release 1 sample, and magnitude fluctuations of type Ia supernova from the Pantheon+ compilation across redshifts z < 0.1. We find a detection of the cross-correlation signal between galaxies and type Ia supernova magnitudes. Fitting the normalised growth rate of structure f sigma_8 to the auto- and cross-correlation function measurements we find f sigma_8 = 0.384 +0.094 -0.157, which is consistent with the Planck LambdaCDM model prediction, and indicates that the supernova magnitude fluctuations are induced by peculiar velocities. Using a large ensemble of N-body simulations, we validate our methodology, calibrate the covariance of the measurements, and demonstrate that our results are insensitive to supernova selection effects. We highlight the potential of this methodology for measuring the growth rate of structure, and forecast that the next generation of type Ia supernova surveys will improve f sigma_8 constraints by a further order of magnitude.

Nguyen, A. [Swinburne U., Ctr. Astrophys. Supercom↗

NASA NTRS1983

Kinematics of velocity and vorticity correlations in turbulent flow

The kinematic problem of calculating second-order velocity moments from given values of the vorticity covariance is examined. Integral representation formulas for second-order velocity moments in terms of the two-point vorticity correlation tensor are derived. The special relationships existing between velocity moments in isotropic turbulence are expressed in terms of the integral formulas yielding several kinematic constraints on the two-point vorticity correlation tensor in isotropic turbulence. Numerical evaluation of these constraints suggests that a Gaussian curve may be the only form of the longitudinal velocity correlation coefficient which is consistent with the requirement of isotropy. It is shown that if this is the case, then a family of exact solutions to the decay of isotropic turbulence may be obtained which contains Batchelor's final period solution as a special case. In addition, the computed results suggest a method of approximating the integral representation formulas in general turbulent shear flows.

Bernard, P. S.↗

NASA NTRS2007

Salinity Remote Sensing and the Study of the Global Water Cycle

The SMOS and AquariusISAC-D satellite missions will begin a new era to map the global sea surface salinity (SSS) field and its variability from space within the next twothree years. They will provide critical data needed to study the interactions between the ocean circulation, global water cycle and climate. Key scientific issues to address are (1) mapping large expanses of the ocean where conventional SSS data do not yet exist, (2) understanding the seasonal and interannual SSS variations and the link to precipitation, evaporation and sea-ice patterns, (3) links between SSS and variations in the oceanic overturning circulation, (4) air-sea coupling processes in the tropics that influence El Nino, and (4) closing the marine freshwater budget. There is a growing body of oceanographic evidence in the form of salinity trends that portend significant changes in the hydrologic cycle. Over the past several decades, highlatitude oceans have become fresher while the subtropical oceans have become saltier. This change is slowly spreading into the subsurface ocean layers and may be affecting the strength of the ocean's therrnohaline overturning circulation. Salinity is directly linked to the ocean dynamics through the density distribution, and provides an important signature of the global water cycle. The distribution and variation of oceanic salinity is therefore attracting increasing scientific attention due to the relationship to the global water cycle and its influence on circulation, mixing, and climate processes. The oceans dominate the water cycle by providing 86% of global surface evaporation (E) and receiving 78% of global precipitation (P). Regional differences in E-P, land runoff, and the melting or freezing of ice affect the salinity of surface water. Direct observations of E-P over the ocean have large uncertainty, with discrepancies between the various state-of-the-art precipitation analyses of a factor of two or more in many regions. Quantifying the climatic influence of the oceanic water cycle requires more accurately resolving the net air-sea water flux. Measuring global SSS trends on seasonal to interannual timescales by satellite is fundamental to this problem because the SSS trends represent detectable time-integrated signals of the variable marine hydrological cycle. Satellite measurements, coupled with an array of in situ observations, will provide global synoptic SSS fields for the first time history. These data will provide a strong constraint on climate models and data assimilation efforts, which must properly represent the freshwater budget in terms of E-P, ocean advection and surface layer mixing in order to accurately simulate the true ocean state. The SSS fields will allow us to quantify the covariability between the SSS and the strong seasonal E-P cycle in the tropics and high latitudes. Field measurement campaigns to exploit satellite and in situ measurements to close the seasonal E-P cycle over an ocean region are being considered. Lastly the satellite systems will monitor and trace the large long-lived SSS anomalies from year to year that have the potential to influence El Nino and the large scale ocean circulation.

Lagerloef, G. S. E.↗

NASA NTRS1986

Plate motions and deformations from geologic and geodetic data

Research effort on behalf of the Crustal Dynamics Project focused on the development of methodologies suitable for the analysis of space-geodetic data sets for the estimation of crustal motions, in conjunction with results derived from land-based geodetic data, neo-tectonic studies, and other geophysical data. These methodologies were used to provide estimates of both global plate motions and intraplate deformation in the western U.S. Results from the satellite ranging experiment for the rate of change of the baseline length between San Diego and Quincy, California indicated that relative motion between the North American and Pacific plates over the course of the observing period during 1972 to 1982 were consistent with estimates calculated from geologic data averaged over the past few million years. This result, when combined with other kinematic constraints on western U.S. deformation derived from land-based geodesy, neo-tectonic studies, and other geophysical data, places limits on the possible extension of the Basin and Range province, and implies significant deformation is occurring west of the San Andreas fault. A new methodology was developed to analyze vector-position space-geodetic data to provide estimates of relative vector motions of the observing sites. The algorithm is suitable for the reduction of large, inhomogeneous data sets, and takes into account the full position covariances, errors due to poorly resolved Earth orientation parameters and vertical positions, and reduces baises due to inhomogeneous sampling of the data. This methodology was applied to the problem of estimating the rate-scaling parameter of a global plate tectonic model using satellite laser ranging observations over a five-year interval. The results indicate that the mean rate of global plate motions for that interval are consistent with those averaged over several million years, and are not consistent with quiescent or greatly accelerated plate motions. This methodology was also used to provide constraints on deformation in the western U.S. using very long baseline interferometry observations over a two-year period.

Jordan, T. H.↗

DOE OSTI2020

Holographic Space-Time and Quantum Information

The formalism of Holographic Space-time (HST) is a translation of the principles of Lorentzian geometry into the language of quantum information. Intervals along time-like trajectories, and their associated causal diamonds, completely characterize a Lorentzian geometry. The Bekenstein-Hawking-Gibbons-’t Hooft-Jacobson-Fischler-Susskind-Bousso Covariant Entropy Principle, equates the logarithm of the dimension of the Hilbert space associated with a diamond to one quarter of the area of the diamond’s holographic screen, measured in Planck units. The most convincing argument for this principle is Jacobson’s derivation of Einstein’s equations as the hydrodynamic expression of this entropy law. In that context, the null energy condition (NEC) is seen to be the analog of the local law of entropy increase. The quantum version of Einstein’s relativity principle is a set of constraints on the mutual quantum information shared by causal diamonds along different time-like trajectories. The implementation of this constraint for trajectories in relative motion is the greatest unsolved problem in HST. The other key feature of HST is its claim that, for non-negative cosmological constant or causal diamonds much smaller than the asymptotic radius of curvature for negative c.c., the degrees of freedom localized in the bulk of a diamond are constrained states of variables defined on the holographic screen. This principle gives a simple explanation of otherwise puzzling features of BH entropy formulae, and resolves the firewall problem for black holes in Minkowski space. It motivates a covariant version of the CKN [1] bound on the regime of validity of quantum field theory (QFT) and a detailed picture of the way in which QFT emerges as an approximation to the exact theory

tensor network↗

NASA NTRS2021

Optimizing GRACE/GRACE-FO Data and A priori Hydrological Knowledge for Improved Global Terrestial Water Storage Component Estimates

The comprehensive information of global terrestrial water storage (TWS) components (soil moisture, groundwater, snow, surface water) is essential for effective assessment of water resource availability, climate variation, and disaster mitigation measures. Observational data provided by the Gravity Recovery And Climate Experiment (GRACE) and GRACE Follow-On satellite missions offer global TWS variation (ΔTWS) in terms of an integrated water column. However, GRACE spatial resolution is relatively coarse (i.e., 3°), and the vertically integrated value cannot be separated into ΔTWS components directly. This study demonstrates the feasibility to estimate ΔTWS components at any desired spatial-vertical resolution by effectively maintaining the native resolution of the employed hydrological knowledge. It utilizes a least-squares with constraints (LSC) approach to rigorously incorporate GRACE and GRACE-FO data and a priori hydrological knowledge, with the aim to improve global ΔTWS components’ accuracy and spatial resolution. The 3°×3° GRACE mascon derived ΔTWS data is disaggregated into the 0.5°×0.5° anomalous soil moisture storage (ΔSMS), groundwater storage (ΔGWS), snow water equivalent (ΔSWE), and surface water storage (ΔSWS) based on the covariance information obtained from the Community Atmosphere Biosphere Land Exchange (CABLE) and the PCRaster Global Water Balance (PCR-GLOBWB) models. Evaluation with different ground measurements and satellite products between 2002 and 2019 exhibits significantly improved accuracy in all individual ΔTWS components. This improvement is of particular note in ΔGWS and ΔSWS, where the LSC approach increases the globally averaged correlation values by approximately 0.13 and 0.05, respectively. Reliable prior knowledge leads to a more accurate ΔTWS component estimate, and the use of ensemble-mean knowledge yields the best result.

GRACE↗

NASA NTRS1994

Truncated Gaussians as tolerance sets

This work focuses on the use of truncated Gaussian distributions as models for bounded data measurements that are constrained to appear between fixed limits. The authors prove that the truncated Gaussian can be viewed as a maximum entropy distribution for truncated bounded data, when mean and covariance are given. The characteristic function for the truncated Gaussian is presented; from this, algorithms are derived for calculation of mean, variance, summation, application of Bayes rule and filtering with truncated Gaussians. As an example of the power of their methods, a derivation of the disparity constraint (used in computer vision) from their models is described. The authors' approach complements results in Statistics, but their proposal is not only to use the truncated Gaussian as a model for selected data; they propose to model measurements as fundamentally in terms of truncated Gaussians.

Cozman, Fabio↗

DOE OSTI2020

GW190814: Impact of a 2.6 solar mass neutron star on the nucleonic equations of state

Is the secondary component of GW190814 the lightest black hole or the heaviest neutron star ever discovered in a double compact-object system? This is the central question animating this paper. Covariant density functional theory provides a unique framework to investigate both the properties of finite nuclei and neutron stars, while enforcing causality at all densities. By tuning existing energy density functionals we were able to: (i) account for a 2.6 M ⊙ neutron star, (ii) satisfy the original constraint on the tidal deformability of a 1.4 M ⊙ neutron star, and (iii) reproduce ground-state properties of finite nuclei. Yet, for the class of models explored in this work, we find that the stiffening of the equation of state required to support supermassive neutron stars is inconsistent with either constraints obtained from energetic heavy-ion collisions or from the low deformability of medium-mass stars. Furthermore, we speculate that the maximum neutron star mass can not be significantly higher than the existing observational limit and that the 2.6 M ⊙ compact object is likely to be the lightest black hole ever discovered.

79 ASTRONOMY AND ASTROPHYSICS↗