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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Progress Towards NQA-1 for Cardinal in FY25

Cardinal is a wrapping of the GPU-oriented spectral element Computational Fluid Dynamics (CFD) code NekRS and the Monte Carlo particle transport code OpenMC within the Multiphysics Object-Oriented Simulation Environment (MOOSE). Cardinal provides high-resolution thermal-hydraulics and/or radiation transport feedback to MOOSE multiphysics simulations. Multiphysics feedback is implemented in a geometry-agnostic manner which eliminates the need for rigid one-to-one mappings. A generic data transfer implementation also allows NekRS and OpenMC to couple to any MOOSE application, enabling a broad set of multiphysics capabilities. Cardinal simulations can also leverage combinations of MPI, OpenMP, and GPU resources. Cardinal continuous development and improvement efforts have led to the software being considered as a high-fidelity design and licensing tool for key areas of nuclear reactor relevant physics, including neutron transport, fluid flow, heat transfer, and mechanical processes. The fast development and expansion of the software from a pure R&D framework towards its application in the nuclear industry and regulation require a focus on developing, enhancing,and maintaining Cardinal’s software quality through strict adherence to a Software Quality Assurance (SQA) framework and SQA program. To facilitate compliance with SQA standards, the Cardinal SQA Program was initiated during Fiscal Year 2023 (FY23). During the development of the Cardinal SQA Program, multiple gaps have been identified. These gaps are primarily related to model verification and code pedigree as they relate to the use of Cardinal as an analysis tool. These gaps were captured in a report published in 2023. A second report highlighted the progress made during Fiscal Year 2024 (FY24) and described Argonne’s effort to document and integrate software verification within Cardinal’s software development process. This report documents the progress made towards NQA-1 for Cardinal in the Fiscal Year 2025 (FY25). All cases in the expanded Continuous Integration (CI) suite of NekRS are included in this report which test the solvers and modules available in NekRS exhaustively. The NekRS tests are integrated with the Cardinal CI suite and made available in publicly accessible Github documentation. Following the CI practice permits integrating of source code changes frequently and ensuring that the integrated codebase clears the verification testing for the software. Also in this report is a brief overview of the development of the Cardinal Software Quality Assurance Plan (SQAP) that was done in FY25, though it should be noted that the rest of the documentation for the SQA program needs to be developed in a future step of this task.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Software Quality Assurance for the MOOSE-Based Open-Source Multiphysics Code Cardinal - An Expanded CI Testing Suite

Cardinal is a wrapping of the GPU-oriented spectral element Computational Fluid Dynamics (CFD) code NekRS and the Monte Carlo particle transport code OpenMC within the Multiphysics Object-Oriented Simulation Environment (MOOSE). Cardinal provides high-resolution thermal-hydraulics and/or radiation transport feedback to MOOSE multiphysics simulations. Multiphysics feedback is implemented in a geometry-agnostic manner which eliminates the need for rigid one-to-one mappings. A generic data transfer implementation also allows NekRS and OpenMC to couple to any MOOSE application, enabling a broad set of multiphysics capabilities. Cardinal simulations can also leverage combinations of MPI, OpenMP, and GPU resources. Cardinal continuous development and improvement efforts have led to the software being considered as a high-fidelity design and licensing tool for key areas of nuclear reactor relevant physics, including neutron transport, fluid flow, heat transfer, and mechanical processes. The fast development and expansion of the software from a pure R&D framework towards its application in the nuclear industry and regulation require a focus on developing, enhancing and, maintaining Cardinal’s software quality through strict adherence to a Software Quality Assurance (SQA) framework and SQA program. To facilitate compliance with SQA standards, the Cardinal SQA Program has been initiated during Fiscal Year 2023 (FY23). During the development of the Cardinal SQA Program, multiple gaps have been identified. These gaps are primarily related to model verification and code pedigree as they relate to the use of Cardinal as a safety analysis tool. These gaps have been captured in a report published in 2023. A second report highlighted the progress made during Fiscal Year 2024 (FY24) and described Argonne’s effort to document and integrate software verification within Cardinal’s software development process. This report documents a snapshot of the verification test cases currently available for Cardinal and NekRS in their assimilation into a Continuous Integration (CI) platform. Following the CI practice permits the integrating of source code changes frequently and ensuring that the integrated codebase clears the verification testing for the software. It should be noted that the SQA program itself, including the program plans, procedures, configuration management, and testing strategies, need to be developed in a future step of this task.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2020

An Update on Cardinal: Toward Full Core Pebble Simulations

The new DOE-NE Center of Excellence for Thermal-fluids applications in Nuclear Energy inaugurated in April 2018 considers and researches novel new solution strategies for historically challenging flow issues that still plague the current fleet of deployed Light Water nuclear Reactors (LWRs) as well as predicting various fluid flow and fluid related issues with advanced reactor technologies. Our advanced thermal-fluids research and development approach synergistically combines three natural, though overlapping, length and time scales in a hierarchal multi-scale approach to avoid the temptation and pitfalls of attempting to develop a single solve-all algorithm for physical fluid flow problems that will span nine orders of magnitude in spatial and temporal scales. To demonstrate the multi-scale philosophy of the center we focus on Fluoride Cooled High Temperature Reactors (FHRs), and in particular on the Berkley’s PB-FHR Mark-I design. The Fluoride salt cooled High temperature Reactor (FHR) is a class of advanced nuclear reactors that combine the robust coated particle fuel form from high temperature gas cooled reactors, direct reactor auxiliary cooling system (DRACS) passive decay removal of liquid metal fast reactors, and the transparent, high volumetric heat capacitance liquid Fluoride salt working fluids - such as Flibe - from molten salt reactors. This combination of fuel and coolant enables FHRs to operate in a high-temperature low-pressure design space that has beneficial safety and economic implications. The PB-FHR reactor relies on a pebble bed approach and pebble bed reactors are in a sense the poster child for multi-scale analysis. The lower length-scale simulator for pebble reactor cores comprises three physics: neutronics (OpenMC), thermal-fluids (Nek5000/NekRS) and fuel performance (BISON). As part of Center of Excellence ongoing research efforts we have developed Cardinal, a new tool platform for lower length-scale simulation. Cardinal tightly couples all three physics and leverages advances in MOOSE such as the MultiApp system and the concept of MOOSE-wrapped Apps. The present report provides an update on the development of Cardinal with an extension of Cardinal to GPUs. We also perform a first-of-a-kind demonstration simulation on Summit representing a 10x capability increase in terms of pebble count for Cardinal.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2021

Cardinal: A Lower-Length-Scale Multiphysics Simulator for Pebble-Bed Reactors

This paper demonstrates a multiphysics solver for pebble-bed reactors, in particular, for Berkeley’s pebble-bed -fluoride-salt-cooled high-temperature reactor (PB-FHR) (Mark I design). The FHR is a class of advanced nuclear reactors that combines the robust coated particle fuel form from high-temperature gas-cooled reactors, the direct reactor auxiliary cooling system passive decay removal of liquid-metal fast reactors, and the transparent, high-volumetric heat capacitance liquid-fluoride salt working fluids (e.g., FLiBe) from molten salt reactors. This fuel and coolant combination enables FHRs to operate in a high-temperature, low-pressure design space that has beneficial safety and economic implications. The PB-FHR relies on a pebble-bed approach, and pebble-bed reactors are, in a sense, the poster child for multiscale analysis. Relying heavily on the MultiApp capability of the Multiphysics Object-Oriented Simulation Environment (MOOSE), we have developed Cardinal, a new platform for lower-length-scale simulation of pebble-bed cores. The lower-length-scale simulator comprises three physics: neutronics (OpenMC), thermal fluids (Nek5000/NekRS), and fuel performance (BISON). Cardinal tightly couples all three physics and leverages advances in MOOSE, such as the MultiApp system and the concept of MOOSE-wrapped applications. Moreover, Cardinal can utilize graphics processing units for accelerating solutions. In this paper, we discuss the development of Cardinal and the verification and validation and demonstration simulations.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2019

Cardinal: A Lower Length-scale Simulator for Fluoride Cooled High Temperature Reactors

The new DOE-NE “Center of Excellence for Thermal-fluids applications in Nuclear Energy” inaugurated in April 2018 considers and researches novel new solution strategies for historically challenging flow issues that still plague the current fleet of deployed Light Water Reactor (LWR) nuclear reactors as well as predicting various fluid flow and fluid related issues with advanced reactor technologies. Our advanced thermal-fluids research and development approach synergistically combines three natural, though overlapping, length and time scales in a hierarchal multi-scale approach to avoid the temptation and pitfalls of attempting to develop a single “solve all” algorithm for physical fluid flow problems that will span 109 in spatial and temporal scales. The demonstrate the multi-scale philosophy of the center we focus first on Fluoride Cooled High Temperature Reactors (FHRs), and in particular on the Berkeley’s PB-FHR design Mark-I design. The Fluoride salt cooled High temperature Reactor (FHR) is a class of advanced nuclear reactors that combine the robust coated particle fuel form from high temperature gas cooled reactors, direct reactor auxiliary cooling system (DRACS) passive decay removal of liquid metal fast reactors, and the transparent, high volumetric heat capacitance liquid fluoride salt working fluids - Flibe - from molten salt reactors. This combination of fuel and coolant enables FHRs to operate in a high-temperature low-pressure design space that has beneficial safety and economic implications. The PB-FHR reactor relies on a pebble bed approach and pebble bed reactors are in a sense the poster child for multiscale analysis. The lower length-scale simulator for pebble reactor cores comprises three physics: neutronics (OpenMC), thermal-fluids (Nek5000) and fuel performance (BISON). As part of center of excellence ongoing research efforts we have developed “Cardinal”, a new tool platform for lower length-scale simulation. Cardinal tightly couples all three physics and leverages advances in MOOSE such as the MultiApp system and the concept of MOOSE-wrapped Apps. Moreover it is designed from the ground-up to scale on massively parallel architectures and perform well on world-class super-computing architectures. In this report we describe the design of Cardinal and present a demo of the application of Cardinal to an FHR.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2024

Buzzard to Cardinal: Improved Mock Catalogs for Large Galaxy Surveys

Abstract We present the Cardinal mock galaxy catalogs, a new version of the Buzzard simulation that has been updated to support ongoing and future cosmological surveys, including the Dark Energy Survey (DES), DESI, and LSST. These catalogs are based on a one-quarter sky simulation populated with galaxies out to a redshift of z = 2.35 to a depth of m r = 27. Compared to the Buzzard mocks, the Cardinal mocks include an updated subhalo abundance matching model that considers orphan galaxies and includes mass-dependent scatter between galaxy luminosity and halo properties. This model can simultaneously fit galaxy clustering and group–galaxy cross-correlations measured in three different luminosity threshold samples. The Cardinal mocks also feature a new color assignment model that can simultaneously fit color-dependent galaxy clustering in three different luminosity bins. We have developed an algorithm that uses photometric data to further improve the color assignment model and have also developed a novel method to improve small-scale lensing below the ray-tracing resolution. These improvements enable the Cardinal mocks to accurately reproduce the abundance of galaxy clusters and the properties of lens galaxies in the DES data. As such, these simulations will be a valuable tool for future cosmological analyses based on large sky surveys.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Coupled Monte Carlo and thermal-fluid modeling of high temperature gas reactors using Cardinal

Cardinal is an open-source application that couples OpenMC Monte Carlo transport and NekRS computa-tional fluid dynamics to the Multiphysics Object-Oriented Simulation Environment (MOOSE), closing neutronics and thermal-fluid gaps in conducting high-resolution multiscale and multiphysics analyses of nuclear systems. Here, we provide an introduction to Cardinal's software design, data mapping, and multi -physics coupling strategy to highlight our approach to overcoming common challenges in multiphysics simulation. We then describe an application of Cardinal to prismatic High Temperature Gas Reactors (HTGRs) with various combinations of NekRS, OpenMC, BISON, and THM. A high-resolution coupling of NekRS, OpenMC, and BISON provides a reference solution at the unit cell level and shows excellent agree-ment with a lower-resolution coupling of THM, OpenMC, and BISON. A full core coupling of THM, OpenMC, and BISON resolving the three-dimensional conjugate heat transfer and sub-pin power distri-bution then provides detailed predictions of HTGR temperatures and the fission distribution.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2022

Coupled Monte Carlo and thermal-hydraulics modeling of a prismatic gas reactor fuel assembly using Cardinal

Cardinal is a MOOSE application that couples OpenMC Monte Carlo transport and NekRS computational fluid dynamics to the MOOSE framework, closing the neutronics and thermal-fluid gaps in conducting tightly-coupled, high-resolution multiscale and multiphysics analyses. By leveraging MOOSE's interfaces for wrapping external codes, Cardinal overcomes many challenges encountered in earlier multiphysics coupling works, such as file-based I/O or overly-restrictive geometry mapping requirements. In this work, we leverage a subset of the multiphysics interfaces in Cardinal to perform coupling of OpenMC neutron transport, MOOSE heat conduction, and THM thermal-fluids for steady-state modeling of a prismatic gas reactor fuel assembly.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2023

Software Quality Assurance, Software Requirements and Gap Analysis for the MOOSE-Based Open-Source Multiphysics Code Cardinal

Cardinal continuous development and improvement efforts have led to the software being considered as a high-fidelity design and licensing tool for key areas of nuclear reactor relevant physics, including neutron transport, fluid flow, heat transfer, and mechanical processes. The fast development and expansion of the software from a pure R&D framework towards its application in the nuclear industry and regulation require a focus on maintaining and enhancing Cardinal’s software quality through strict adherence to a Software Quality Assurance (SQA) framework. To facilitate compliance with SQA standards, the Cardinal SQA Program has been initiated during Fiscal Year 2023 (FY23).

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2005

Expansion of direction space around the cardinal axes revealed by smooth pursuit eye movements

It is well established that perceptual direction discrimination shows an oblique effect; thresholds are higher for motion along diagonal directions than for motion along cardinal directions. Here, we compare simultaneous direction judgments and pursuit responses for the same motion stimuli and find that both pursuit and perceptual thresholds show similar anisotropies. The pursuit oblique effect is robust under a wide range of experimental manipulations, being largely resistant to changes in trajectory (radial versus tangential motion), speed (10 versus 25 deg/s), directional uncertainty (blocked versus randomly interleaved), and cognitive state (tracking alone versus concurrent tracking and perceptual tasks). Our data show that the pursuit oblique effect is caused by an effective expansion of direction space surrounding the cardinal directions and the requisite compression of space for other directions. This expansion suggests that the directions around the cardinal directions are in some way overrepresented in the visual cortical pathways that drive both smooth pursuit and perception.

Visual Pathways/physiology↗
DOE OSTI2025

Thermomechanics coupling to Monte Carlo particle transport on unstructured mesh geometries using Cardinal

Geometry deformation due to thermal expansion influences neutron transport in many systems. Studying this phenomenon involves coupling models for neutronics, thermal hydraulics, and solid mechanics. To enable high fidelity modeling of these coupled physics, new capabilities were introduced in Cardinal, coupling OpenMC Monte Carlo particle transport models with MOOSE thermomechanical physics on unstructured moving-mesh geometries. In this work, we present a fully open-source capability leveraging on-the-fly mesh skinning to automatically regenerate OpenMC geometry, which allows multiphysics feedback from temperature, density, and geometry changes. The new capability is verified using an analytic benchmark slab problem, which couples S 2 neutron transport with thermal conduction, convective boundary conditions, Doppler-broadened cross sections, and nonlinear thermal expansion effects along the heated slab. Cardinal reproduces the analytic solutions for the neutron flux, heating, k eff , and temperature with demonstrated convergence in various error terms including mesh resolution and cross section temperature library spacing. For the nominal benchmark conditions and with a fine mesh, maximum relative errors for neutron flux, temperature, and heating are lower than 1%, while errors in integral quantities such as k eff and slab length are within 1 pcm and 48 µm, respectively. This work (i) presents a new numerical approach to thermomechanics coupling with OpenMC models, (ii) is the first (to our knowledge) to utilize a mechanical partial differential equation (PDE) solution to solve the (Griesheimer and Kooreman, 2022) analytic benchmark, and (iii) develops this verified capability within an open-source package.

97 - MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Cardinal: Seismic and Geoacoustic Array Processing

Data collected via seismic and infrasound array deployments are leveraged in the geosciences to detect and characterize a myriad of natural and anthropogenic sources. These deployments consist of numerous sensors placed in a predetermined configuration to amplify signal strength and improve the efficacy of array processing techniques used to measure signal directionality and waveform coherence. High‐fidelity feature extraction is often predicated on interstation distance as well as the frequency content and wavelength of an incident signal. Numerous array processing softwares analyze data in sequential frequency bands to obtain a more detailed characterization of a signal. However, current algorithms are limited in their ability to determine optimal array configuration for each band. We introduce an open‐source Python code, called Cardinal, to process seismic and infrasound array data in discretized time–frequency space with the option of applying an adaptive array design to determine optimal subarray configuration for each frequency band. To reduce computational time, the array processing step can be run in parallel using multithreading. Furthermore, the software has the capability to aggregate array processing results from different time–frequency pixels to produce separate sets of detections, or families, with added utility via the application of an adaptive semblance threshold, which aids in isolating signals‐of‐interest from coherent background noise. Upon appropriate configuration, Cardinal exhibits the potential to combine distinct seismic and infrasound phases into separate families.

Adaptive Array↗
DOE OSTI2021

CARDINAL

Cardinal is a code that automates the workflow for iteratively solving neutral particle transport via the OpenMC code and computational fluid dynamics via the NekRS code within the Multiphysics Object Oriented Simulation Environment (MOOSE), a finite element framework for solving general partial differential equations. Cardinal establishes a mapping between the Monte Carlo geometry representation used in OpenMC and the spectral element mesh used in NekRS to other physics applications built upon the MOOSE framework, allowing high-resolution particle transport and fluid dynamics physics feedback to the MOOSE application ecosystem. Heat generation rates as solved by OpenMC are used as heat sources in MOOSE, while the temperature and density fields from NekRS are used as conjugate heat transfer boundary conditions and/or source fields in MOOSE. OpenMC, Nek5000, and MOOSE are open source, community-developed simulation codes.

NOVAK, APRILJEAN RODGERS↗
DOE OSTI2020

Active Betweenness Cardinality: Algorithms and Applications

Centrality rankings such as degree, closeness, betweenness, Katz, PageRank, etc. are commonly used to identify critical nodes in a graph. These methods are based on two assumptions that restrict their wider applicability. First, they assume the exact topology of the network is available. Secondly, they do not take into account the activity over the network and only rely on its topology. However, in many applications, the network is autonomous, vast, and distributed, and it is hard to collect the exact topology. At the same time, the underlying pairwise activity between node pairs is not uniform and node criticality strongly depends on the activity on the underlying network. In this paper, we propose active betweenness cardinality, as a new measure, where the node criticalities are based on not the static structure, but the activity of the network. We show how this metric can be computed efficiently by using only local information for a given node and how we can find the most critical nodes starting from only a few nodes. We also show how this metric can be used to monitor a network and identify failed nodes. We present experimental results to show effectiveness by demonstrating how the failed nodes can be identified by measuring active betweenness cardinality of a few nodes in the system.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Simulation and Analysis on Reactor Pressure Vessel (RPV) subjected to Pressurized Thermal Shock (PTS) under SBLOCA scenario by using Cardinal to support the fracture mechanics analyses

The structural components that comprise nuclear reactors and their supporting structures are subjected to harsh operating environments that can challenge their integrity, especially after exposure for extended durations or under accident condition. As one of the most significant components of a Reactor, the Reactor Pressure Vessel (RPV) is exposed to an aggressive environment during the operation time (e.g. more than 40 years). Ageing degradation mechanisms (e.g. thermos-fatigue) could grow initial defects up to a critical size, increasing the susceptibility to failure in the RPV. The conventional methods are mostly based on simple crack and structure geometries. Very limited studies consider the real conditions of the RPV subjected to a thermal shock due to a Loss of Coolant Accident (LOCA). During a LOCA event, the most severe conditions take place when the emergency core cooling (ECC) water is injected inside the cold legs filled initially with hotter water and/or steam. The rapid cooling of the down-comer and the internal RPV surface followed probably by re-pressurization of the RPV causes large temperature gradients and variation of pressure which induces thermal-mechanical stresses. In order to develop the model for integrity assessment of a reactor pressure vessel (RPV) subjected to pressurized thermal shock (PTS), a multi-physics simulation, which includes the thermo-hydraulic, thermo-mechanical and fracture mechanics analyses is necessary. The multi-physics simulations are performed using Cardinal, a wrapping of the GPU-oriented spectral element Computational Fluid Dynamics (CFD) code NekRS and other multi-physics sub-modules within the MOOSE framework. Cardinal now fully supports MOOSE stochastic perturbations of NekRS models with varying boundary conditions, initial conditions, material properties, and any other quantity which is defined by a kernel (such as coefficients in a momentum source model). The implementation is designed in a flexible manner so that scalar values are sent from MOOSE into a user scratch space in NekRS, which can then be applied for any purpose within the NekRS case files (both on the host and device). When modeling PTS, several factors can impact the results significantly. In this report, the impacts of the geometry of the model, Reynolds number and buoyancy effect are investigated. Two geometry, i.e., a simplified model and a realistic RPV model, with both laminar and turbulent flow condition are adopted for the PTS simulation with and without buoyancy effect. The purpose of the investigation is to understand the impact of these factors on the prediction of temperature history of RPV. The accurate prediction on the temperature evolution, which will be exported to Grizzly code for further analyses on the progression of aging mechanisms and their effects on the integrity of RPV structures, is very crucial. Based on the understanding of these factors, a more sophisticated model is built to analysis the PTS under SBLOCA scenario. A literature survey is conducted to pick the SBLOCA scenario for the multi-physics simulation. The analysis helps to explain the form and the transformation of the cold plum when the ECC is activated under SBLOCA. This model can be can be applied to study the PTS effect for different RPV configurations. The results can help to assess structural component degradation for advanced reactors.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Software Quality Assurance Plan: Cardinal

The Cardinal Software Quality Assurance (SQA) Program aims to provide the controls and processes necessary to enable continuous, high-quality software development while meeting user and program sponsor requirements. This SQA Plan (SQAP) delineates the SQA Program framework for Cardinal by describing the Program activities, organization, and documentation, and by clearly defining the interconnection of all Program items. It should be noted that this SQAP is aligned with the current version of the Argonne Quality Assurance Program Plan, which was designed to align with DOE O 414.1D. This SQAP is also aligned with the revision 10 of the SQAP for MOOSE and MOOSE-based applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Cardinality-Regularized Hawkes-Granger Model

We propose a new sparse Granger-causal learning framework for temporal event data. We focus on a specific class of point processes called the Hawkes process. We begin by pointing out that most of the existing sparse causal learning algorithms for the Hawkes process suffer from a singularity in maximum likelihood estimation. As a result, their sparse solutions can appear only as numerical artifacts. In this paper, we propose a mathematically well-defined sparse causal learning framework based on a cardinality-regularized Hawkes process, which remedies the pathological issues of existing approaches. We leverage the proposed algorithm for the task of instance-wise causal event analysis, where sparsity plays a critical role. We validate the proposed framework with two real use-cases, one from the power grid and the other from the cloud data center management domain.

Ide, Tsuyoshi↗
NASA NTRS1974

Flight test data for a Cessna Cardinal

The results of a flight test analysis of the performance of a standard Cessna 177B Cardinal airplane are presented. The airplane was fully instrumented to obtain steady state performance, stick-fixed dynamic stability characteristics, and roll response data. Results obtained include graphs of C sub L versus alpha, C sub D versus C sub L, and speed-power relationships. Dynamic data include Phugoid and Dutch characteristics, and roll response characteristics.

Kohlman, D. L.↗