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All sourcesNASA NTRSDOE OSTI
NASA NTRS1988

A mathematical model for spatial orientation from pictorial perspective displays

A previously formulated mathematical model, describing how observers reconstruct three-dimensional spatial layouts from perspective projections, has been extended to more complex situations. The model assumes that the observer has a priori knowledge of certain characteristics of the viewed objects, like size, shape, or parallelism or perpendicularity of lines or planes. These assumptions are used in a three-dimensional process to reconstruct a spatial layout that `best matches' the perceived lines of sight to the object coordinates. Sources of errors and biases in this process are specified and their effects on model outputs are discussed. An experiment, in which eight subjects judged the relative direction of one object with respect to another, has been conducted to validate the model. The model has been found to generally reproduce the systematic trends of the experimental results and also has provided an analytical explanation for them. The mathematical model is expected to be a useful tool in analyzing and developing pictorial perspective flight displays.

Grunwald, Arthur J.↗
NASA NTRS1995

An interpretation of a mysterious 3.0- to 4.6-kHz emission band observed on Voyager 2 near Neptune

A whistler mode interpretation is provided for the narrowband signal (f approx. 3 - 4.6 kHz, Delta f approx. 200 - 800 Hz) detected by the plasma wave instrument on Voyager 2 during its encounter with Neptune. Our analysis indicates that this signal may have been generated in a limited spatial region and that it propagated to other regions of the Neptunian magnetosphere in the nonducted whistler mode with wave normal vectors lying close to the whistler mode resonance cone. The observed frequency variation of the emission along the Voyager 2 trajectory is consistent with this interpretation. The source location is estimated to be near the magnetic equator at L approx. 4 and dipole longitude of 111 deg W (260 deg W longitude in Neptune coordinate system). The source frequency and bandwidth are estimated to be 3.6 kHz and 300 Hz, respectively. The waves most likely would have been generated by energetic electrons with 2- to 20-keV parallel energy via a gyroresonance mechanism. Our interpretation of the narrowband emissions places the following limits on the Neptunian thermal plasma density and temperature: (1) N(sub e, min) greater than 0.16 el/cu cm for 1.2 R(sub N) less than R less than 5 R(sub N), (2) N(sub e, max) = 597.5/cu cm at R - 1.3 R(sub N), (3) T(sub e, max) less than 500-1000 K at R approx. 5 R(sub N). It is also possible that the weak UV aurora observed near Neptune could have been caused by the precipitation of energetic particles by the narrowband emission as a result of wave particle interactions.

Sonwalkar, Vikas S.↗
NASA NTRS1999

New Approaches to HSCT Multidisciplinary Design and Optimization

New approaches to MDO have been developed and demonstrated during this project on a particularly challenging aeronautics problem- HSCT Aeroelastic Wing Design. To tackle this problem required the integration of resources and collaboration from three Georgia Tech laboratories: ASDL, SDL, and PPRL, along with close coordination and participation from industry. Its success can also be contributed to the close interaction and involvement of fellows from the NASA Multidisciplinary Analysis and Optimization (MAO) program, which was going on in parallel, and provided additional resources to work the very complex, multidisciplinary problem, along with the methods being developed. The development of the Integrated Design Engineering Simulator (IDES) and its initial demonstration is a necessary first step in transitioning the methods and tools developed to larger industrial sized problems of interest. It also provides a framework for the implementation and demonstration of the methodology. Attachment: Appendix A - List of publications. Appendix B - Year 1 report. Appendix C - Year 2 report. Appendix D - Year 3 report. Appendix E - accompanying CDROM.

Schrage, Daniel P.↗
NASA NTRS2014

America's Next Great Ship: Space Launch System Core Stage Transitioning from Design to Manufacturing

The Space Launch System (SLS) Program is essential to achieving the Nation's and NASA's goal of human exploration and scientific investigation of the solar system. As a multi-element program with emphasis on safety, affordability, and sustainability, SLS is becoming America's next great ship of exploration. The SLS Core Stage includes avionics, main propulsion system, pressure vessels, thrust vector control, and structures. Boeing manufactures and assembles the SLS core stage at the Michoud Assembly Facility (MAF) in New Orleans, LA, a historical production center for Saturn V and Space Shuttle programs. As the transition from design to manufacturing progresses, the importance of a well-executed manufacturing, assembly, and operation (MA&O) plan is crucial to meeting performance objectives. Boeing employs classic techniques such as critical path analysis and facility requirements definition as well as innovative approaches such as Constraint Based Scheduling (CBS) and Cirtical Chain Project Management (CCPM) theory to provide a comprehensive suite of project management tools to manage the health of the baseline plan on both a macro (overall project) and micro level (factory areas). These tools coordinate data from multiple business systems and provide a robust network to support Material & Capacity Requirements Planning (MRP/CRP) and priorities. Coupled with these tools and a highly skilled workforce, Boeing is orchestrating the parallel buildup of five major sub assemblies throughout the factory. Boeing and NASA are transforming MAF to host state of the art processes, equipment and tooling, the most prominent of which is the Vertical Assembly Center (VAC), the largest weld tool in the world. In concert, a global supply chain is delivering a range of structural elements and component parts necessary to enable an on-time delivery of the integrated Core Stage. SLS is on plan to launch humanity into the next phase of space exploration.

Birkenstock, Benjamin↗
DOE OSTI2026

Lab-Scale Cable-Driven Parallel Robot Prototype for Automated Prefabricated Component Manipulation

This paper presents the design and evaluation of a lab-scale cable-driven parallel robot (CDPR) developed as a flexible platform for automated installation of prefabricated components onto exterior building envelopes. Traditional manual installation methods for prefabricated components, which depend on scaffolding, cranes, cherry pickers, and verbal coordination, are not only labor-intensive and error-prone but also face significant limitations in dense urban environments due to site access constraints. To address these challenges, we developed a lab-scale CDPR platform capable of autonomously transporting building envelope components from a designated pickup zone to their target installation location, minimizing the need for human intervention. This study describes the system’s mechanical design, actuation architecture, real-time feedback system, and control strategy of the CDPR, and evaluates its performance in a laboratory environment. The robot’s actuation system uses torque control for end-effector manipulation. The robot’s real-time pose feedback comes from a construction-grade total station and a wireless inertial measurement unit (IMU), which together support precise end-effector control. Experimental results demonstrate the successful integration of the hardware, sensing, state estimation, and control subsystems. Preliminary tests showed that our lab-scale prototype can position the end effector with an error of less than 3 mm, which is a level of precision not previously achieved by existing CDPRs in construction applications. The key findings are twofold: (1) torque-only control is necessary but not sufficient for minimizing final pose error, and (2) incorporating real-time pose feedback can achieve the desired placement accuracy.

Liu, Yifang [Oak Ridge National Laboratory (ORNL),↗
NASA NTRSDate not supplied

Sparse Linear Algebra Toolkit for Computational Aerodynamics

Finding solutions to sparse linear systems of equations is an essential step in Computational Engineering applications of interest to NASA. Linear systems of equations are composed and solved in almost every computational engineering application. The characteristics of linear systems vary greatly from one application to another. Accordingly, there are a wide variety of methods for the solution of linear systems of equations. The operations and methods prepared by the authors are focused on linear systems of interest to NASA, primarily those associated with Computational Fluid Dynamics (CFD), Aeroelasticity, and Aeroacoustics. The Sparse Linear Algebra Toolkit (SLAT) is a coordinated collection of software featuring operations, methods, and data structures that are useful when solving sparse linear systems of equations on modern computer architectures. The implemented operations and methods are designed and tuned for parallelism in shared memory, in distributed memory, and across the hybrid combination of distributed-shared memory. The toolkit includes novel methods and implementations for modern architectures and facilitates development of new approaches for meeting NASA’s evolving computational engineering challenges using evolving computer architectures that are not available in vendor libraries. In this paper, significant features and interfaces within SLAT are presented and verified for simulations performed with NASA’s CFD solver, FUN3D. The runtime and scaling performance of the Generalized Minimum Residual (GMRES) method implemented in SLAT is analyzed for the linear subproblems within the solution of turbulent Navier-Stokes equations employed in the simulation of high-lift configurations. Prior to this work, the SPARSKIT GMRES implementation was the only Krylov subspace method available within FUN3D. A strong scaling study shows the SLAT GMRES implementation facilitates accurate Reynolds-averaged Navier-Stokes CFD solutions between 15% and 56% faster than the SPARSKIT GMRES implementation.

Stephen L Wood↗
NASA NTRSDate not supplied

Utilizing Gaps and Key Performance Parameters to Inform NASA Environmental Control and Life Support and Human Health and Performance Capability Technology Decisions

Human spaceflight is a complex endeavor requiring a multitude of capabilities for transportation, crew health, scientific goals, and safe return to Earth. The difference between spaceflight proven capabilities and those needed for a particular mission is defined as a capability gap. Capability gaps are not technology specific. Each capability gap is approachable with a wide array of technologies that have unique benefits and challenges. Determining what a capability’s relevant and distinguishing key performance parameters (KPPs) are for a mission is critical. Mass, power, and volume are always constrained and important, but defining these in a way normalized by performance is challenging. Additionally, KPP definition for reliability, dormancy, and integration needs are very important and still evolving. This paper provides the approach of the Environmental Control and Life Support – Crew Health and Performance (ECLSS-CHP) System Capability Leadership Team (SCLT) to defining gaps and KPPs in support of the NASA’s Capabilities Integration Team data call objectives. The nine ECLSS-CHP capability areas are decomposed to capabilities, gaps, and KPPs. Rather than defining very detailed gaps, ECLSS-CHP defines high-level gaps to be technology agnostic. Within a gap, detailed KPPs are defined to both compare technologies and measure progress within a technology over time. Ideally, KPPs are clearly defined, widely communicated both internally and externally, and provide a common nomenclature to describe the state of the art and the degree of improvement required for exploration missions. KPPs help define when the gap is closed and the core mission objectives can be accomplished. Further technology improvements to enhance the capability, as measured by improved KPPs, must then be weighed against investments in open capability gaps that prevent NASA from achieving its exploration missions. It is uncommon that a technology maturation to improve all the relevant KPPs simultaneously but using KPPs is a critical technology investment decision making component. In addition to traditional technology selections, KPPs are informing how investments in ground testing prior to and in parallel with ISS technology demonstrations are required to improve reliability KPPs. The collection of all major technology activities within a capability area are captured on technology roadmaps to communicate how diverse program activities are coordinated to close gaps and infuse into exploration mission needs. A selection of ECLSS-CHP gaps and KPPs and their formulation, current state, and how they inform capability roadmap planning are discussed. The paper will contain a summary of the approximately 60 gaps. Gaps are classified as to their type (architecture, knowledge, technology, developmental, or engineering) depending on the magnitude of the gap. The paper will provide brief overviews of a few major technology challenges and the technologies being considered, but will reference detailed papers for a more thorough treatment of the challenges and state of the art. Data analysis of the gaps is in work and results are not currently available for this abstract. It is anticipated the paper will include examples of select KPPs with descriptions as to why these are the relevant measures. Additionally some KPPs will be graphically presented over time to show progress to date and when performance targets need to be achieved to support exploration missions. Graphical summaries of how gaps closures with near term mission elements support follow-on mission elements will be provided.

Life Support↗
NASA NTRSDate not supplied

Utilizing Gaps and Key Performance Parameters to Inform NASA Environmental Control and Life Support and Human Health and Performance Capability Technology Decisions

Human spaceflight is a complex endeavor requiring multiple capabilities for transportation, crew health, scientific goals, and safe return to Earth. The difference between spaceflight proven capabilities and those needed for future exploration architectures is defined as a capability gap. Capability gaps are not technology specific. Each capability gap is approachable with a wide array of technologies that have unique benefits and challenges. Determining what a capability’s relevant and distinguishing key performance parameters (KPPs) are for a mission is critical. Mass, power, and volume are always constrained and important, but defining these in a way normalized by performance is challenging. Additionally, KPP definition for reliability, dormancy, and integration needs are very important and still evolving. This paper provides the approach of the Environmental Control and Life Support – Crew Health and Performance (ECLSS-CHP) System Capability Leadership Team (SCLT) has used to define gaps and KPPs in support of the NASA’s Capabilities Integration Team data call objectives. The nine ECLSS-CHP capability areas are decomposed to capabilities with ~76 gaps and supported with KPPs. Rather than defining very detailed gaps, ECLSS-CHP defines high-level gaps to be technology agnostic. Within a gap, detailed KPPs are defined to both compare technologies and measure progress within a technology over time. Ideally, KPPs are clearly defined, widely communicated both internally and externally, and provide a common nomenclature to describe the state of the art and the degree of improvement required for exploration missions. KPPs help define when the gap is closed, and the core mission objectives can be accomplished. Further technology improvements to enhance the capability, as measured by improved KPPs, must then be weighed against investments in open capability gaps that prevent NASA from achieving its exploration missions. It is uncommon that a technology maturation to improve all the relevant KPPs simultaneously but using KPPs is a critical technology investment decision making component. In addition to traditional technology selections, KPPs are informing how investments in ground testing prior to and in parallel with ISS technology demonstrations are required to improve reliability KPPs. The collection of all major technology activities within a capability area are captured on technology roadmaps to communicate how diverse program activities are coordinated to close gaps and infuse into exploration mission needs. A selection of ECLSS-CHP gaps and KPPs and their formulation, current state, and how they inform capability roadmap planning are discussed.

Life Support↗
NASA NTRS1999

Parallel Grid Manipulations in Earth Science Calculations

The National Aeronautics and Space Administration (NASA) Data Assimilation Office (DAO) at the Goddard Space Flight Center is moving its data assimilation system to massively parallel computing platforms. This parallel implementation of GEOS DAS will be used in the DAO's normal activities, which include reanalysis of data, and operational support for flight missions. Key components of GEOS DAS, including the gridpoint-based general circulation model and a data analysis system, are currently being parallelized. The parallelization of GEOS DAS is also one of the HPCC Grand Challenge Projects. The GEOS-DAS software employs several distinct grids. Some examples are: an observation grid- an unstructured grid of points at which observed or measured physical quantities from instruments or satellites are associated- a highly-structured latitude-longitude grid of points spanning the earth at given latitude-longitude coordinates at which prognostic quantities are determined, and a computational lat-lon grid in which the pole has been moved to a different location to avoid computational instabilities. Each of these grids has a different structure and number of constituent points. In spite of that, there are numerous interactions between the grids, e.g., values on one grid must be interpolated to another, or, in other cases, grids need to be redistributed on the underlying parallel platform. The DAO has designed a parallel integrated library for grid manipulations (PILGRIM) to support the needed grid interactions with maximum efficiency. It offers a flexible interface to generate new grids, define transformations between grids and apply them. Basic communication is currently MPI, however the interfaces defined here could conceivably be implemented with other message-passing libraries, e.g., Cray SHMEM, or with shared-memory constructs. The library is written in Fortran 90. First performance results indicate that even difficult problems, such as above-mentioned pole rotation- a sparse interpolation with little data locality between the physical lat-lon grid and a pole rotated computational grid- can be solved efficiently and at the GFlop/s rates needed to solve tomorrow's high resolution earth science models. In the subsequent presentation we will discuss the design and implementation of PILGRIM as well as a number of the problems it is required to solve. Some conclusions will be drawn about the potential performance of the overall earth science models on the supercomputer platforms foreseen for these problems.

Sawyer, W.↗
NASA NTRS1991

Linear magnetic spring and spring/motor combination

A magnetic spring, or a spring and motor combination, providing a linear spring force characteristic in each direction from a neutral position, in which the spring action may occur for any desired coordinate of a typical orthogonal coordinate system. A set of magnets are disposed, preferably symmetrically about a coordinate axis, poled orthogonally to the desired force direction. A second set of magnets, respectively poled opposite the first set, are arranged on the sprung article. The magnets of one of the sets are spaced a greater distance apart than those of the other, such that an end magnet from each set forms a pair having preferably planar faces parallel to the direction of spring force, the faces being offset so that in a neutral position the outer edge of the closer spaced magnet set is aligned with the inner edge of the greater spaced magnet set. For use as a motor, a coil can be arranged with conductors orthogonal to both the magnet pole directions and the direction of desired spring force, located across from the magnets of one set and fixed with respect to the magnets of the other set. In a cylindrical coordinate system having axial spring force, the magnets are radially poled and motor coils are concentric with the cylinder axis.

Patt, Paul J.↗
NASA NTRS1989

Algorithmic considerations of integrated design for CSI on a hypercube architecture

An approach is presented to the integrated design problem for actively controlled large, flexible mechanical systems for which Control Structure Interaction (CSI) problems are of concern. The two coupled design problems were identified as the optimal Structural Design problem the optimal Controller Design problem. These two problems can be addressed within a decision making loop that would consider each separately, and then sequentially analyze the effects of one on the other. Embedded in such a loop would be the simulation and coordination tasks as part of the decision tools required in a total (software) package. All of the above are compute-intensive tasks. In any such task, possible decompositions and gains due to the inherent parallelism have to be exploited. The problems under consideration, as applied to large flexible mechanical structures, are particularly suited to be mapped onto multicomputer systems in a hypercube topology.

Oezguener, UE.↗
NASA NTRS1992

Stability investigations of airfoil flow by global analysis

As the result of global, non-parallel flow stability analysis the single value of the disturbance growth-rate and respective frequency is obtained. This complex value characterizes the stability of the whole flow configuration and is not referred to any particular flow pattern. The global analysis assures that all the flow elements (wake, boundary and shear layer) are taken into account. The physical phenomena connected with the wake instability are properly reproduced by the global analysis. This enhances the investigations of instability of any 2-D flows, including ones in which the boundary layer instability effects are known to be of dominating importance. Assuming fully 2-D disturbance form, the global linear stability problem is formulated. The system of partial differential equations is solved for the eigenvalues and eigenvectors. The equations, written in the pure stream function formulation, are discretized via FDM using a curvilinear coordinate system. The complex eigenvalues and corresponding eigenvectors are evaluated by an iterative method. The investigations performed for various Reynolds numbers emphasize that the wake instability develops into the Karman vortex street. This phenomenon is shown to be connected with the first mode obtained from the non-parallel flow stability analysis. The higher modes are reflecting different physical phenomena as for example Tollmien-Schlichting waves, originating in the boundary layer and having the tendency to emerge as instabilities for the growing Reynolds number. The investigations are carried out for a circular cylinder, oblong ellipsis and airfoil. It is shown that the onset of the wake instability, the waves in the boundary layer, the shear layer instability are different solutions of the same eigenvalue problem, formulated using the non-parallel theory. The analysis offers large potential possibilities as the generalization of methods used till now for the stability analysis.

Morzynski, Marek↗
DOE OSTI2021

Generalizable coordination of large multiscale workflows: challenges and learnings at scale

The advancement of machine learning techniques and the heterogeneous architectures of most current supercomputers are propelling the demand for large multiscale simulations that can automatically and autonomously couple diverse components and map them to relevant resources to solve complex problems at multiple scales. Nevertheless, despite the recent progress in workflow technologies, current capabilities are limited to coupling two scales. In the first-ever demonstration of using three scales of resolution, we present a scalable and generalizable framework that couples pairs of models using machine learning and in situ feedback. We expand upon the massively parallel Multiscale Machine-Learned Modeling Infrastructure (MuMMI), a recent, award-winning workflow, and generalize the framework beyond its original design. We discuss the challenges and learnings in executing a massive multiscale simulation campaign that utilized over 600,000 node hours on Summit and achieved more than 98% GPU occupancy for more than 83% of the time. We present innovations to enable several orders of magnitude scaling, including simultaneously coordinating 24,000 jobs, and managing several TBs of new data per day and over a billion files in total. Finally, we describe the generalizability of our framework and, with an upcoming open-source release, discuss how the presented framework may be used for new applications.

Bhatia, Harsh↗
NASA NTRS1980

Asynchronous interactive control systems

A class of interactive control systems is derived by generalizing interactive manipulator control systems. The general structural properties of such systems are discussed and an appropriate general software implementation is proposed. This is based on the fact that tasks of interactive control systems can be represented as a network of a finite set of actions which have specific operational characteristics and specific resource requirements, and which are of limited duration. This has enabled the decomposition of the overall control algorithm into a set of subalgorithms, called subcontrollers, which can operate simultaneously and asynchronously. Coordinate transformations of sensor feedback data and actuator set-points have enabled the further simplification of the subcontrollers and have reduced their conflicting resource requirements. The modules of the decomposed control system are implemented as parallel processes with disjoint memory space communicating only by I/O. The synchronization mechanisms for dynamic resource allocation among subcontrollers and other synchronization mechanisms are also discussed in this paper. Such a software organization is suitable for the general form of multiprocessing using computer networks with distributed storage.

Vuskovic, M. I.↗
DOE OSTI2024

The inviscid incompressible limit of Kelvin–Helmholtz instability for plasmas

The Kelvin–Helmholtz Instability (KHI) is an interface instability that develops between two fluids or plasmas flowing with a common shear layer. KHI occurs in astrophysical jets, solar atmosphere, solar flows, cometary tails, planetary magnetospheres. Two applications of interest, encompassing both space and fusion applications, drive this study: KHI formation at the outer flanks of the Earth’s magnetosphere and KHI growth from non-uniform laser heating in magnetized direct-drive implosion experiments. Here, we study 2D KHI with or without a magnetic field parallel to the flow. We use both the GAMERA code, which solves the compressible Euler equations, and the STRATOSPEC code, which solves the Navier-Stokes equations under the Boussinesq approximation, coupled with the magnetic field dynamics. GAMERA is a global three-dimensional MHD code with high-order reconstruction in arbitrary nonorthogonal curvilinear coordinates, which is developed for a large range of astrophysical applications. STRATOSPEC is a three-dimensional pseudo-spectral code with an accuracy of infinite order (no numerical diffusion). Magnetized KHI is a canonical case for benchmarking hydrocode simulations with extended MHD options. An objective is to assess whether or not, and under which conditions, the incompressibility hypothesis allows to describe a dynamic compressible system. For comparing both codes, we reach the inviscid incompressible regime, by decreasing the Mach number in GAMERA, and viscosity and diffusion in STRATOSPEC. Here, we specifically investigate both single-mode and multi-mode initial perturbations, either with or without magnetic field parallel to the flow. The method relies on comparisons of the density fields, 1D profiles of physical quantities averaged along the flow direction, and scale-by-scale spectral densities. We also address the triggering, formation and damping of filamentary structures under varying Mach number or Atwood number, with or without a parallel magnetic field. Comparisons show very satisfactory results between the two codes. The vortices dynamics is well reproduced, along with the breaking or damping of small-scale structures. We end with the extraction of growth rates of magnetized KHI from the compressible regime to the incompressible limit in the linear regime assessing the effects of compressibility under increasing magnetic field. The observed differences between the two codes are explained either from diffusion or non-Boussinesq effects.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1974

The influence of the direction of the geomagnetic dipole on the position of the neutral sheet

An analysis of neutral sheet crossings detected by the NASA-Goddard Space Flight Center magnetometer on the Explorer 34 satellite has shown that the diurnal wobble of the geomagnetic dipole measurably influences the position of the neutral sheet at 30 earth radii. Viewed in the solar-ecliptic coordinate system, the dipole wobble originates from the 11 deg angle between the earth's spin axis and the dipole axis, has a period of 24 hours, and can be resolved into components of motion perpendicular and parallel to the earth-sun line. The perpendicular component exerts a torque on the magnetotail and causes the neutral sheet to pivot about an axis approximately parallel to the solar wind direction. The parallel component encourages the neutral sheet to move above and below the solar-magnetospheric equatorial plane with an amplitude of 1 earth radius. This latter motion is consistent with the neutral sheet's being hinged at a geocentric distance of 5.25 earth radii.

Bowling, S. B.↗
NASA NTRS1991

VLSI architectures for geometrical mapping problems in high-definition image processing

This paper explores a VLSI architecture for geometrical mapping address computation. The geometric transformation is discussed in the context of plane projective geometry, which invokes a set of basic transformations to be implemented for the general image processing. The homogeneous and 2-dimensional cartesian coordinates are employed to represent the transformations, each of which is implemented via an augmented CORDIC as a processing element. A specific scheme for a processor, which utilizes full-pipelining at the macro-level and parallel constant-factor-redundant arithmetic and full-pipelining at the micro-level, is assessed to produce a single VLSI chip for HDTV applications using state-of-art MOS technology.

Kim, K.↗
DOE OSTI2024

Galaxy bispectrum in the spherical Fourier-Bessel basis

The bispectrum, the three-point correlation in Fourier space, is a crucial statistic for studying many effects targeted by the next-generation galaxy surveys, such as primordial non-Gaussianity (PNG) and general relativistic (GR) effects on large scales. In this work we develop a formalism for the bispectrum in the spherical Fourier-Bessel (SFB) basis—a natural basis for computing correlation functions on the curved sky, as it diagonalizes the Laplacian operator in spherical coordinates. Working in the SFB basis allows for line-of-sight effects such as redshift space distortions and GR to be accounted for exactly, i.e., without having to resort to perturbative expansions to go beyond the plane-parallel approximation. Only analytic results for the SFB bispectrum exist in the literature given the intensive computations needed. We numerically calculate the SFB bispectrum for the first time, enabled by a few techniques: We implement a template decomposition of the redshift-space kernel Z 2 into Legendre polynomials, and separately treat the PNG and velocity-divergence terms. We derive an identity to integrate a product of three spherical harmonics connected by a Dirac delta function as a simple sum and use it to investigate the limit of a homogeneous and isotropic Universe. Furthermore, we present a formalism for convolving the signal with separable window functions and use a toy spherically symmetric window to demonstrate the computation and give insights into the properties of the observed bispectrum signal. While our implementation remains computationally challenging, it is a step toward a feasible full extraction of information on large scales via a SFB bispectrum analysis.

79 ASTRONOMY AND ASTROPHYSICS↗