Results for “Formal Methods” — Page 26

NASA NTRS1982

Improved perfect-fluid energy-momentum tensor with spin in Einstein-Cartan space-time

The description of the spin given here is classical in that it is intrinsic but not quantized. The approach in this matter is similar to, for example, the work of Bailey and Israel (1973, 1975, 1979), where the fluid particles, which have intrinsic spin, may be galaxies or clusters of galaxies. The elementary particles of these objects and the 'ferromagnetic alignment' of their quantum spins are not resorted to in order to describe a fluid with spin. Physically this means that the equation of motion for the spin tensor is a modified Fermi-Walker transport equation (Misner et al., 1973), arising as a direct result of the inclusion of spin as an intrinsic variable in the thermodynamic description of the internal energy. The variables in this description are classical variables throughout and are not microscopic fields. An improved perfect-fluid energy-momentum tensor that includes spin and torsion is presented. Use is made of a Lagrangian variational principle based on the tetrad formalism of Halbwach (1960) and the method od constraints of Ray (1972).

Ray, J. R.↗

NASA NTRS1987

Partial redistribution in high-density, highly ionized plasmas

The conditions for which partial redistribution functions must be used for radiation transport in high-Z, high-density, laser-produced plasmas are examined. A previously developed two-photon formalism based on the model microfield method is used to calculate redistribution functions including electron and ion Stark broadening with ion dynamic effects. The competition between the relaxation rates and spontaneous emission is shown to determine the conditions for partial redistribution. The discussion makes use of microfield fluctuation rates and broadening coefficients which can be determined from simulation calculations. The redistribution function for the Ly-alpha transition of Ar XVIII is presented for typical plasma conditions.

Talin, B.↗

NASA NTRS1993

A theory of nonlocal mixing-length convection. I - The moment formalism

A flexible and potentially powerful theory of convection, based on the mixing length picture, is developed to make unbiased self-consistent predictions about overshooting and other complicated phenomena in convection. The basic formalism is set up, and the method's power is demonstrated by showing that a simplified version of the theory reproduces all the standard results of local convection. The second-order equations of the theory are considered in the limit of a steady state and vanishing third moments, and it is shown that they reproduce all the standard results of local mixing-length convection. There is a particular value of the superadiabatic gradient, below which the only possible steady state of a fluid is nonconvecting. Above this critical value, a fluid is convectively unstable. Two distinct regimes of convection, which are identified as efficient and inefficient convection, are determined.

Grossman, Scott A.↗

NASA NTRS1997

The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems

In this paper, we study the Local Discontinuous Galerkin methods for nonlinear, time-dependent convection-diffusion systems. These methods are an extension of the Runge-Kutta Discontinuous Galerkin methods for purely hyperbolic systems to convection-diffusion systems and share with those methods their high parallelizability, their high-order formal accuracy, and their easy handling of complicated geometries, for convection dominated problems. It is proven that for scalar equations, the Local Discontinuous Galerkin methods are L(sup 2)-stable in the nonlinear case. Moreover, in the linear case, it is shown that if polynomials of degree k are used, the methods are k-th order accurate for general triangulations; although this order of convergence is suboptimal, it is sharp for the LDG methods. Preliminary numerical examples displaying the performance of the method are shown.

Cockburn, Bernardo↗

NASA NTRS2004

From Abstract to Concrete Norms in Agent Institutions

Norms specifying constraints over institutions are stated in such a form that allows them to regulate a wide range of situations over time without need for modification. To guarantee this stability, the formulation of norms need to abstract from a variety of concrete aspects, which are instead relevant for the actual operationalization of institutions. If agent institutions are to be built, which comply with a set of abstract requirements, how can those requirements be translated in more concrete constraints the impact of which can be described directly in the institution? In this work we make use of logical methods in order to provide a formal characterization of the translation rules that operate the connection between abstract and concrete norms. On the basis of this characterization, a comprehensive formalization of the notion of institution is also provided.

Grossi, Davide↗

NASA NTRS2016

Verification of Triple Modular Redundancy (TMR) Insertion for Reliable and Trusted Systems

We propose a method for TMR insertion verification that satisfies the process for reliable and trusted systems. If a system is expected to be protected using TMR, improper insertion can jeopardize the reliability and security of the system. Due to the complexity of the verification process, there are currently no available techniques that can provide complete and reliable confirmation of TMR insertion. This manuscript addresses the challenge of confirming that TMR has been inserted without corruption of functionality and with correct application of the expected TMR topology. The proposed verification method combines the usage of existing formal analysis tools with a novel search-detect-and-verify tool. Field programmable gate array (FPGA),Triple Modular Redundancy (TMR),Verification, Trust, Reliability,

Trust↗

NASA NTRSDate not supplied

NASA CARA Prelaunch Analysis and Process

NASA implemented an official Procedural Requirement (NPR) 8079.1 in June 2023, establishing the minimum collision avoidance requirements and associated operational protocols for NASA space flight programs, projects, and spacecraft to protect the space environment by reducing the risk of collision to an acceptable level. Part of the requirement employs a two-fold approach to analyze the satellite design process with conjunction assessment and risk mitigation in mind, during the pre-launch process, led by the Conjunction Assessment Risk Analysis (CARA) Program for non-Human Space Flight (HSF) Missions. This presentation outlines CARA coordination with missions, informed by the NPR, that spans early mission development to operations. CARA is an Agency-level resource that provides support to all NASA non-HSF missions. CARA protects the orbital environment from collision between NASA non-HSF missions and other tracked on-orbit objects. During the pre-formulation and formulation phases, NASA missions undergo a series of conjunction assessment analyses captured in the Orbital Collision Avoidance Plan (OCAP) prior to transitioning to the implementation phase (typically at the Preliminary Design Review (PDR) or equivalent). The OCAP analyses consist of a thorough review of the spacecraft(s) orbit selection and placement, deployment, cataloguing performance, trackability, ephemeris generation, conjunction mitigation options, autonomous maneuvering, and risk assessment parameters which are performed by a dedicated CARA Analysis Team. The results of these analyses, CARA’s formal recommendations, and the mission’s methods for implementing them, are documented in the OCAP. The intent of engaging in this process so early in the mission design phase, is to ensure that conjunction assessment is considered from the outset, thus mitigating costly design changes and operational risks down the road. NASA missions are also required to coordinate their operational processes and conjunction mitigation procedures with CARA in a Conjunction Assessment Operations Implementation Agreement (CAOIA). The aim of this process is to document the conjunction assessment screening process, conjunction risk assessment parameters, conjunction mitigation steps, flight dynamics operations concepts and maneuvers, and the communication and coordination process between the mission’s project manager and CARA. The intent of the CAOIA document is for it to be completed iteratively, and as missions update these elements, corresponding changes are made in the CAOIA. With this process in place, the engagement and coordination between the missions and CARA from early in the design process into mission operations, helps to ensure that missions not only have a robust conjunction assessment concept of operations to reduce conjunction risk for space sustainability, but are also able to achieve their science goals and have a successful mission.

conjunction assessment↗

NASA NTRSDate not supplied

NASA CARA Prelaunch Analysis and Process

NASA implemented an official Procedural Requirement (NPR) 8079.1 in June 2023, establishing the minimum collision avoidance requirements and associated operational protocols for NASA space flight programs, projects, and spacecraft to protect the space environment by reducing the risk of collision to an acceptable level. Part of the requirement employs a two-fold approach to analyze the satellite design process with conjunction assessment and risk mitigation in mind, during the pre-launch process, led by the Conjunction Assessment Risk Analysis (CARA) Program for non-Human Space Flight (HSF) Missions. This presentation outlines CARA coordination with missions, informed by the NPR, that spans early mission development to operations. CARA is an Agency-level resource that provides support to all NASA non-HSF missions. CARA protects the orbital environment from collision between NASA non-HSF missions and other tracked on-orbit objects. During the pre-formulation and formulation phases, NASA missions undergo a series of conjunction assessment analyses captured in the Orbital Collision Avoidance Plan (OCAP) prior to transitioning to the implementation phase (typically at the Preliminary Design Review (PDR) or equivalent). The OCAP analyses consist of a thorough review of the spacecraft(s) orbit selection and placement, deployment, cataloguing performance, trackability, ephemeris generation, conjunction mitigation options, autonomous maneuvering, and risk assessment parameters which are performed by a dedicated CARA Analysis Team. The results of these analyses, CARA’s formal recommendations, and the mission’s methods for implementing them, are documented in the OCAP. The intent of engaging in this process so early in the mission design phase, is to ensure that conjunction assessment is considered from the outset, thus mitigating costly design changes and operational risks down the road. NASA missions are also required to coordinate their operational processes and conjunction mitigation procedures with CARA in a Conjunction Assessment Operations Implementation Agreement (CAOIA). The aim of this process is to document the conjunction assessment screening process, conjunction risk assessment parameters, conjunction mitigation steps, flight dynamics operations concepts and maneuvers, and the communication and coordination process between the mission’s project manager and CARA. The intent of the CAOIA document is for it to be completed iteratively, and as missions update these elements, corresponding changes are made in the CAOIA. With this process in place, the engagement and coordination between the missions and CARA from early in the design process into mission operations, helps to ensure that missions not only have a robust conjunction assessment concept of operations to reduce conjunction risk for space sustainability, but are also able to achieve their science goals and have a successful mission.

conjunction assessment↗

DOE OSTI2024

Development of a Performance Portable Non-Equilibrium Plasma Fluid Solver on Adaptive Grids

This presentation will describe the numerical techniques, programming paradigms, verification, and performance of a non-equilibrium plasma fluid solver that can effectively utilize current and upcoming central processing and graphics processing unit (CPU+GPU) architectures. Our plasma fluid model solves the conservation equations for self-consistent electrostatic Poisson, electron and heavy species transport, and electron temperature on adaptive Cartesian grids. Our solver is written using performance portable adaptive mesh management library, AMReX (Zhang et al., JOSS, 4 (37) 1370, 2019), and can be built and run on widely available vendor specific GPU architectures (NVIDIA/AMD/Intel). We utilize a non-subcycled second order semi-implicit time-stepping method where all adaptive mesh refinement (AMR) levels are advanced with the same time step. The composite multi-level multigrid solver from within AMReX is used for each of the governing equations that are cast into a Helmholtz equation form. We have also developed a python based chemical mechanism parser framework that uses a similar format as CANTERA (Goodwin et al., Zenodo, 2018) yaml files as input. Our custom parser reads the yaml file and provides C++ files with transport and production rate functions that can be executed on both host (CPU) and device (GPU). We present verification of our solver using method of manufactured solutions that indicate formal second order accuracy with central diffusion and fifth order weighted-essentially-non-oscillatory (WENO) advection scheme. We also verify our solver with published literature on low-pressure capacitive and high-pressure streamer discharges. Our initial performance studies indicate 10X speed-up using 20 NVIDIA GPUs versus 200 CPUs for an atmospheric streamer discharge problem solved on a 512 x 1024 x 512 grid.

graphics processing units↗

NASA NTRS1976

K/S two-point-boundary-value problems

A method for developing the missing general K/S (Kustaanheimo/Stiefel) boundary conditions is presented, with use of the formalism of optimal control theory. As an illustrative example, the method is applied to the K/S Lambert problem to derive the missing terminal condition. The necessary equations are developed for a solution to this problem with the generalized eccentric anomaly, E, as the independent variable. This formulation, requiring the solution of only one nonlinear, well-behaved equation in one unknown, E, results in considerable simplification of the problem.

Jezewski, D. J.↗

NASA NTRS1993

Ab initio method for calculating total cross sections

A method for calculating total cross sections without formally including nonelastic channels is presented. The idea is to use a one channel T-matrix variational principle with a complex correlation function. The derived T matrix is therefore not unitary. Elastic scattering is calculated from T-parallel-squared, but total scattering is derived from the imaginary part of T using the optical theorem. The method is applied to the spherically symmetric model of electron-hydrogen scattering. No spurious structure arises; results for sigma(el) and sigma(total) are in excellent agreement with calculations of Callaway and Oza (1984). The method has wide potential applicability.

Bhatia, A. K.↗

DOE OSTI2024

Observables for scattering on targets with arbitrary spin

Starting from the Weinberg formalism for fields of arbitrary spin, we discuss a method for the decomposition of matrix elements of QCD operators (local currents, quark/gluon bilinears) for targets with arbitrary spin. This procedure is advantageous for the systematic study of the structure of hadrons and nuclei, particularly in the case of spin-dependent observables. As higher spin targets exhibit new features in their hadronic structure, the investigation of these properties can enhance our understanding of the strong force. The construction allows for a unified framework to discuss spin > 1/2 very similar to the spin 1/2 case, without subsidiary conditions for the wave functions. Different types of spinors (canonical, helicity, light-front helicity) can be easily accommodated. Its numerical implementation is simple and can be entirely reduced to objects familiar from the rotation group. A natural sl(2,C) multipole decomposition emerges, enabling a physical interpretation of non-perturbative objects that multiply spinor bilinears as Generalized Form Factors. To demonstrate the efficacy of this method, we apply it to the description of a spin 1 target, such as the deuteron. We discuss extensions of the formalism to hard exclusive processes on the deuteron and beyond.

Vera, Frank↗

DOE OSTI2025

The Transition Density Formalism in the First Compton Computation on $^4$He

The method and results of the first theory description of 4He Compton scattering at nuclear energies is presented, with a focus on figures. It uses the same Compton kernels familiar from proton, deuteron and 3He Compton scattering in Chiral Effective Field Theory with explicit Delta degrees of freedom, applicable between about 50 and 130MeV. The result compares well to data from HIγS, MAXlab and Illinois. The sensitivity of the cross section on the (static) scalar-isoscalar polarisabilities of the nucleon is explored. The project is part of the synergetic international effort of experimentalists and theorists in Compton scattering on one- and few-nucleon systems.

Griesshammer, Harald [The George Washington Univer↗

NASA NTRS1995

Using SCR methods to analyze requirements documentation

Software Cost Reduction (SCR) methods are being utilized to analyze and verify selected parts of NASA's EOS-DIS Core System (ECS) requirements documentation. SCR is being used as a spot-inspection tool. Through this formal and systematic approach of the SCR requirements methods, insights as to whether the requirements are internally inconsistent or incomplete as the scenarios of intended usage evolve in the OC (Operations Concept) documentation. Thus, by modelling the scenarios and requirements as mode charts using the SCR methods, we have been able to identify problems within and between the documents.

Callahan, John↗

NASA NTRS1989

A method for exponential propagation of large systems of stiff nonlinear differential equations

A new time integrator for large, stiff systems of linear and nonlinear coupled differential equations is described. For linear systems, the method consists of forming a small (5-15-term) Krylov space using the Jacobian of the system and carrying out exact exponential propagation within this space. Nonlinear corrections are incorporated via a convolution integral formalism; the integral is evaluated via approximate Krylov methods as well. Gains in efficiency ranging from factors of 2 to 30 are demonstrated for several test problems as compared to a forward Euler scheme and to the integration package LSODE.

Friesner, Richard A.↗

NASA NTRS2012

Hybrid Theory of P-Wave Electron-Hydrogen Elastic Scattering

We report on a study of electron-hydrogen scattering, using a combination of a modified method of polarized orbitals and the optical potential formalism. The calculation is restricted to P waves in the elastic region, where the correlation functions are of Hylleraas type. It is found that the phase shifts are not significantly affected by the modification of the target function by a method similar to the method of polarized orbitals and they are close to the phase shifts calculated earlier by Bhatia. This indicates that the correlation function is general enough to include the target distortion (polarization) in the presence of the incident electron. The important fact is that in the present calculation, to obtain similar results only 35-term correlation function is needed in the wave function compared to the 220-term wave function required in the above-mentioned previous calculation. Results for the phase shifts, obtained in the present hybrid formalism, are rigorous lower bounds to the exact phase shifts.

Bhatia, Anand↗

NASA NTRS1983

Three-dimensional inversion of satellite observed radiances A proposal

Fully three-dimensional temperature fields are obtained from observed satellite radiances through the use of variational methods which generalize the method of Wahba and Wendelberger (1980). This variational formalism allows a variety of different information types to contribute to the inversion process. Full use can be made of the horizontal smoothness of the temperature field in the calculation of three-dimensional retrievals. The present method facilitates the acquisition of maximum vertical resolution, accomplishes cloud effect filtering, and minimizes the effects of instrument noise, to yield horizontally coherent retrievals.

Hoffman, R. N.↗

DOE OSTI2026

Towards a Verifiable Domain-Specific Language for Hardware-Accelerated Stencils

Defining a domain-specific language (DSL) that supports vector-calculus abstractions eases the porting of partial differential equation (PDE) solvers to specialized architectures. Sufficiently high-level abstractions empower users to express universal laws with sufficient generality that the laws must always hold true within their domain of validity. A broad class of PDE solvers employs stencil-based algorithms, the target domain of Berkeley Lab's stencil accelerator chip co-design project. First released as open-source in January 2026, the Formal software framework lays a foundation for defining an embedded DSL based on composable operators that implement mimetic numerical methods -- stencil algorithms that guarantee satisfaction of discrete versions of important vector calculus theorems. The Formal DSL will be the frontend to a new class of stencil-PDE accelerators developed jointly by LBNL, UHCL, and UC Berkeley through the DOE Competitive Portfolios for Computer Science Project. This offers the potential of an order of magnitude acceleration for this important category of computational methods to serve the DOE mission. Future work on the Formal DSL will facilitate software verification via type-safe templates that enable problem-specific correctness proofs relying upon generic function theory and carefully crafted unit tests.

Rouson, Damian↗