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DOE OSTI2026

Scattering phase shift in quantum mechanics on quantum computers

Here, we investigate the feasibility of extracting infinite volume scattering phase shift on quantum computers in a simple one-dimensional quantum mechanical model, using the formalism established in the work by Guo and Gasparian [Phys. Rev. D 108, 074504 (2023)] that relates the integrated correlation functions for a trapped system to the infinite volume scattering phase shifts through a weighted integral. The system is first discretized in a finite box with periodic boundary conditions, and the formalism in real time is verified by employing a contact interaction potential with exact solutions. Quantum circuits are then designed and constructed to implement the formalism on current quantum computing architectures. To overcome the fast oscillatory behavior of the integrated correlation functions in real-time simulation, different methods of postdata analysis are proposed and discussed. Test results on IBM hardware show that good agreement can be achieved with two qubits, but complete failure ensues with three qubits due to two-qubit gate operation errors and thermal relaxation errors.

Guo, Peng [Dakota State Univ., Madison, SD (United↗

NASA NTRS2002

Calculation of Scattering Amplitude Without Partial Analysis: Inclusion of Exchange - II

There was a method for calculating the whole scattering amplitude, f(Omega(sub k)), directly. The idea was to calculate the complete wave function Psi numerically, and use it in an integral expression for f, which can be reduced to a 2 dimensional quadrature. The original application was for e-H scattering without exchange. There the Schrodinger reduces a 2-d partial differential equation (pde), which was solved using the finite element method (FEM). Here we extend the method to the exchange approximation. The S.E. can be reduced to a pair of coupled pde's, which are again solved by the FEM. The formal expression for f(Omega(sub k)) consists two integrals, f+/- = f(sub d) +/- f(sub e); f(sub d) is formally the same integral as the no-exchange f. We have also succeeded in reducing f(sub e) to a 2-d integral. Results will be presented at the meeting.

Temkin, Aaron↗

NASA NTRS1992

HDL to verification logic translator

The increasingly higher number of transistors possible in VLSI circuits compounds the difficulty in insuring correct designs. As the number of possible test cases required to exhaustively simulate a circuit design explodes, a better method is required to confirm the absence of design faults. Formal verification methods provide a way to prove, using logic, that a circuit structure correctly implements its specification. Before verification is accepted by VLSI design engineers, the stand alone verification tools that are in use in the research community must be integrated with the CAD tools used by the designers. One problem facing the acceptance of formal verification into circuit design methodology is that the structural circuit descriptions used by the designers are not appropriate for verification work and those required for verification lack some of the features needed for design. We offer a solution to this dilemma: an automatic translation from the designers' HDL models into definitions for the higher-ordered logic (HOL) verification system. The translated definitions become the low level basis of circuit verification which in turn increases the designer's confidence in the correctness of higher level behavioral models.

Gambles, J. W.↗

NASA NTRS1978

Radiative transfer calculated from a Markov chain formalism

The theory of Markov chains is used to formulate the radiative transport problem in a general way by modeling the successive interactions of a photon as a stochastic process. Under the minimal requirement that the stochastic process is a Markov chain, the determination of the diffuse reflection or transmission from a scattering atmosphere is equivalent to the solution of a system of linear equations. This treatment is mathematically equivalent to, and thus has many of the advantages of, Monte Carlo methods, but can be considerably more rapid than Monte Carlo algorithms for numerical calculations in particular applications. We have verified the speed and accuracy of this formalism for the standard problem of finding the intensity of scattered light from a homogeneous plane-parallel atmosphere with an arbitrary phase function for scattering. Accurate results over a wide range of parameters were obtained with computation times comparable to those of a standard 'doubling' routine. The generality of this formalism thus allows fast, direct solutions to problems that were previously soluble only by Monte Carlo methods. Some comparisons are made with respect to integral equation methods.

Esposito, L. W.↗

NASA NTRS2014

Combined Uncertainty and A-Posteriori Error Bound Estimates for General CFD Calculations: Theory and Software Implementation

This workshop presentation discusses the design and implementation of numerical methods for the quantification of statistical uncertainty, including a-posteriori error bounds, for output quantities computed using CFD methods. Hydrodynamic realizations often contain numerical error arising from finite-dimensional approximation (e.g. numerical methods using grids, basis functions, particles) and statistical uncertainty arising from incomplete information and/or statistical characterization of model parameters and random fields. The first task at hand is to derive formal error bounds for statistics given realizations containing finite-dimensional numerical error [1]. The error in computed output statistics contains contributions from both realization error and the error resulting from the calculation of statistics integrals using a numerical method. A second task is to devise computable a-posteriori error bounds by numerically approximating all terms arising in the error bound estimates. For the same reason that CFD calculations including error bounds but omitting uncertainty modeling are only of limited value, CFD calculations including uncertainty modeling but omitting error bounds are only of limited value. To gain maximum value from CFD calculations, a general software package for uncertainty quantification with quantified error bounds has been developed at NASA. The package provides implementations for a suite of numerical methods used in uncertainty quantification: Dense tensorization basis methods [3] and a subscale recovery variant [1] for non-smooth data, Sparse tensorization methods[2] utilizing node-nested hierarchies, Sampling methods[4] for high-dimensional random variable spaces.

CFD↗

NASA NTRS2016

ICAROUS - Integrated Configurable Algorithms for Reliable Operations Of Unmanned Systems

NASA's Unmanned Aerial System (UAS) Traffic Management (UTM) project aims at enabling near-term, safe operations of small UAS vehicles in uncontrolled airspace, i.e., Class G airspace. A far-term goal of UTM research and development is to accommodate the expected rise in small UAS traffic density throughout the National Airspace System (NAS) at low altitudes for beyond visual line-of-sight operations. This paper describes a new capability referred to as ICAROUS (Integrated Configurable Algorithms for Reliable Operations of Unmanned Systems), which is being developed under the UTM project. ICAROUS is a software architecture comprised of highly assured algorithms for building safety-centric, autonomous, unmanned aircraft applications. Central to the development of the ICAROUS algorithms is the use of well-established formal methods to guarantee higher levels of safety assurance by monitoring and bounding the behavior of autonomous systems. The core autonomy-enabling capabilities in ICAROUS include constraint conformance monitoring and contingency control functions. ICAROUS also provides a highly configurable user interface that enables the modular integration of mission-specific software components.

Consiglio, María↗

NASA NTRS2008

Safer Systems: A NextGen Aviation Safety Strategic Goal

The Joint Planning and Development Office (JPDO), is charged by Congress with developing the concepts and plans for the Next Generation Air Transportation System (NextGen). The National Aviation Safety Strategic Plan (NASSP), developed by the Safety Working Group of the JPDO, focuses on establishing the goals, objectives, and strategies needed to realize the safety objectives of the NextGen Integrated Plan. The three goal areas of the NASSP are Safer Practices, Safer Systems, and Safer Worldwide. Safer Practices emphasizes an integrated, systematic approach to safety risk management through implementation of formalized Safety Management Systems (SMS) that incorporate safety data analysis processes, and the enhancement of methods for ensuring safety is an inherent characteristic of NextGen. Safer Systems emphasizes implementation of safety-enhancing technologies, which will improve safety for human-centered interfaces and enhance the safety of airborne and ground-based systems. Safer Worldwide encourages coordinating the adoption of the safer practices and safer systems technologies, policies and procedures worldwide, such that the maximum level of safety is achieved across air transportation system boundaries. This paper introduces the NASSP and its development, and focuses on the Safer Systems elements of the NASSP, which incorporates three objectives for NextGen systems: 1) provide risk reducing system interfaces, 2) provide safety enhancements for airborne systems, and 3) provide safety enhancements for ground-based systems. The goal of this paper is to expose avionics and air traffic management system developers to NASSP objectives and Safer Systems strategies.

Darr, Stephen T.↗

NASA NTRS1976

Stabilization by modification of the Lagrangian

In order to reduce the error growth during a numerical integration, a method for stabilizing the differential equations of Keplerian motion is offered. It is characterized by the use of the eccentric anomaly as independent variable in such a way that the time transformation is given by a generalized Lagrange formalism. The control terms in the equations of motion obtained by this modified Lagrangian give immediately a completely Lyapunov-stable set of differential equations. The equation of time integration is modified by a control term which leads to an integral which defined the time element for the perturbed Keplerian motion.

Baumgarte, J. W.↗

NASA NTRS2013

Validation and Verification of LADEE Models and Software

The Lunar Atmosphere Dust Environment Explorer (LADEE) mission will orbit the moon in order to measure the density, composition and time variability of the lunar dust environment. The ground-side and onboard flight software for the mission is being developed using a Model-Based Software methodology. In this technique, models of the spacecraft and flight software are developed in a graphical dynamics modeling package. Flight Software requirements are prototyped and refined using the simulated models. After the model is shown to work as desired in this simulation framework, C-code software is automatically generated from the models. The generated software is then tested in real time Processor-in-the-Loop and Hardware-in-the-Loop test beds. Travelling Road Show test beds were used for early integration tests with payloads and other subsystems. Traditional techniques for verifying computational sciences models are used to characterize the spacecraft simulation. A lightweight set of formal methods analysis, static analysis, formal inspection and code coverage analyses are utilized to further reduce defects in the onboard flight software artifacts. These techniques are applied early and often in the development process, iteratively increasing the capabilities of the software and the fidelity of the vehicle models and test beds.

Gundy-Burlet, Karen↗

NASA NTRS2021

MBSE Validation and Verification: Case Study for LADEE

The Lunar Atmosphere Dust Environment Explorer (LADEE) mission orbited the moon in order to measure the density, composition, and time variability of the lunar dust environment. The successful mission launched September 7, 2013 and was de-orbited and impacted the moon's surface on April 17, 2014. The ground-side and onboard flight software for the mission was developed using a “Model-Based Software Engineering” (MBSE) methodology combined with strong reuse of Government and Commercial Off-The Shelf (G/COTS) components. Models of the spacecraft and flight software were developed in a graphical dynamics modeling package. Flight Software requirements were prototyped and refined using the simulated models. After the model was shown to work as desired in the simulation framework, C-code software was automatically generated from the models. The auto-generated software was then tested in real-time Processor-in-the-Loop and Hardware-in-the-Loop test beds. “Traveling Road Show” test beds were used for early integration tests with payloads and other subsystems. Traditional techniques for verifying computational sciences models were used to characterize the spacecraft simulation. A lightweight set of formal methods analysis, static analysis, formal inspection, and code coverage analyses were utilized to further reduce defects in the onboard flight software artifacts. These techniques were applied early and often in the development process, iteratively increasing the capabilities of software and fidelity of vehicle models and test beds.

Model-Based Software Engineering, Validation and V↗

NASA NTRS2016

ICAROUS: Integrated Configurable Architecture for Unmanned Systems

NASA's Unmanned Aerial System (UAS) Traffic Management (UTM) project aims at enabling near-term, safe operations of small UAS vehicles in uncontrolled airspace, i.e., Class G airspace. A far-term goal of UTM research and development is to accommodate the expected rise in small UAS traffic density throughout the National Airspace System (NAS) at low altitudes for beyond visual line-of-sight operations. This video describes a new capability referred to as ICAROUS (Integrated Configurable Algorithms for Reliable Operations of Unmanned Systems), which is being developed under the auspices of the UTM project. ICAROUS is a software architecture comprised of highly assured algorithms for building safety-centric, autonomous, unmanned aircraft applications. Central to the development of the ICAROUS algorithms is the use of well-established formal methods to guarantee higher levels of safety assurance by monitoring and bounding the behavior of autonomous systems. The core autonomy-enabling capabilities in ICAROUS include constraint conformance monitoring and autonomous detect and avoid functions. ICAROUS also provides a highly configurable user interface that enables the modular integration of mission-specific software components.

Consiglio, Maria C.↗

NASA NTRS1986

Aerodynamics via acoustics - Application of acoustic formulas for aerodynamic calculations

Prediction of aerodynamic loads on bodies in arbitrary motion is considered from an acoustic point of view, i.e., in a frame of reference fixed in the undisturbed medium. An inhomogeneous wave equation which governs the disturbance pressure is constructed and solved formally using generalized function theory. When the observer is located on the moving body surface there results a singular linear integral equation for surface pressure. Two different methods for obtaining such equations are discussed. Both steady and unsteady aerodynamic calculations are considered. Two examples are presented, the more important being an application to propeller aerodynamics. Of particular interest for numerical applications is the analytical behavior of the kernel functions in the various integral equations.

Farassat, F.↗

NASA NTRS1986

Aerodynamics Via Acoustics: Application of Acoustic Formulas for Aerodynamic Calculations

Farassat, F.↗

NASA NTRS2006

Simulated Data for High Temperature Composite Design

The paper describes an effective formal method that can be used to simulate design properties for composites that is inclusive of all the effects that influence those properties. This effective simulation method is integrated computer codes that include composite micromechanics, composite macromechanics, laminate theory, structural analysis, and multi-factor interaction model. Demonstration of the method includes sample examples for static, thermal, and fracture reliability for a unidirectional metal matrix composite as well as rupture strength and fatigue strength for a high temperature super alloy. Typical results obtained for a unidirectional composite show that the thermal properties are more sensitive to internal local damage, the longitudinal properties degrade slowly with temperature, the transverse and shear properties degrade rapidly with temperature as do rupture strength and fatigue strength for super alloys.

Chamis, Christos C.↗

NASA NTRS1975

Stabilization by modification of the Lagrangian

In order to reduce the error growth during a numerical integration, a method of stabilization of the differential equations of the Keplerian motion is offered. It is characterized by the use of the eccentric anomaly as an independent variable in such a way that the time transformation is given by a generalized Lagrange formalism. The control terms in the equations of motion obtained by this modified Lagrangian give immediately a completely Liapunov-stable set of differential equations. In contrast to other publications, here the equation of time integration is modified by a control term which leads to an integral which defined the time element for the perturbed Keplerian motion.

Baumgarte, J. W.↗

DOE OSTI2025

Finite-volume formalism for physical processes with an electroweak loop integral

This study investigates finite-volume effects in physical processes that involve the combination of long-range hadronic matrix elements with electroweak loop integrals. We adopt the approach of implementing the electroweak part as the infinite-volume version, which is denoted as the EW ∞ method in this work. A general approach is established for correcting finite-volume effects in cases where the hadronic intermediate states are dominated by either a single particle or two particles. For the single-particle case, this work derives the infinite volume reconstruction method from a new perspective. For the two-particle case, we provide the correction formulas for power-law finite-volume effects and unphysical terms with exponentially divergent time dependence. The finite-volume formalism developed in this study has broad applications, including the QED corrections in various processes and the two-photon exchange contribution in 𝐾 𝐿 → 𝜇 + ⁢𝜇 − or 𝜂 → 𝜇 + ⁢𝜇 − decays.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRS1984

Orbital stability of the unseen solar companion linked to periodic extinction events

Evidence from three-dimensional numerical modelling is presented that only cometary orbits with a limited range in inclination with respect to the galactic plane are formally stable for the length of time required to cause periodic extinction events. The calculations were done using Cowell's method employing a fourth-order Runge-Kutta integration scheme in an inertial reference frame in orbit about the Galaxy. Tidal perturbations in the radial direction due to the Galaxy and the Coriolis forces are included. The vertical component of the gravitational field of the galactic disk is superimposed on these forces. The results indicate that orbits for Nemesis that are inclined at more than 30 deg to the galactic plane are not allowed and suggests that the search for Nemesis should be concentrated toward the plane of the Galaxy. Perturbations by passing stars or molecular clouds may make even the low-inclination orbits unstable.

Torbett, M. V.↗

DOE OSTI2025

New charged-particle transport computational capability: the SIT code An L-4 milestone

We have developed a new high-fidelity code for direct transport of charged particles using the simple integral transport method. The code can be coupled to the outputs of any hydrodynamical simulation code in 1-D, 2-D or 3-D. In this report we summarize the formalism involved in treating complex transport problems. We present physical examples wherein we have used the code to calculate the transport of alpha particles. Future work is planned to study the sensitivity of hydrodynamical mix to charged-particle radiochemistry and reaction-in-flight neutrons for the complex inertial confinement fusion problems encountered at NIF and at the Z-machine.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗