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All sources NASA NTRS DOE OSTI

DOE OSTI2026

Implementing the finite-volume three-pion scattering formalism across all non-maximal isospins

We present a numerical exploration of the relativistic-field-theory (RFT) formalism for three pions with all possible values of non-maximal isospin, I πππ = 2, 1 and 0. Using the generic-isospin extension of the RFT formalism [1] and applying our open-source Python library to implement the framework, we predict a range of three-pion energies for illustrative values of the two-to-two scattering amplitudes for various finite-volume irreps also with non-zero total momentum P in the finite-volume frame. The results restrict attention to the case of a vanishing intrinsic three-body interaction so that the spectra can be understood as a baseline. In future lattice QCD calculations, deviations from these values will be translated into evidence for intrinsic three-body effects in the various scattering channels.

hadronic spectroscopy↗

NASA NTRS1998

A Framework for a Supervisory Expert System for Robotic Manipulators with Joint-Position Limits and Joint-Rate Limits

This report addresses the problem of path planning and control of robotic manipulators which have joint-position limits and joint-rate limits. The manipulators move autonomously and carry out variable tasks in a dynamic, unstructured and cluttered environment. The issue considered is whether the robotic manipulator can achieve all its tasks, and if it cannot, the objective is to identify the closest achievable goal. This problem is formalized and systematically solved for generic manipulators by using inverse kinematics and forward kinematics. Inverse kinematics are employed to define the subspace, workspace and constrained workspace, which are then used to identify when a task is not achievable. The closest achievable goal is obtained by determining weights for an optimal control redistribution scheme. These weights are quantified by using forward kinematics. Conditions leading to joint rate limits are identified, in particular it is established that all generic manipulators have singularities at the boundary of their workspace, while some have loci of singularities inside their workspace. Once the manipulator singularity is identified the command redistribution scheme is used to compute the closest achievable Cartesian velocities. Two examples are used to illustrate the use of the algorithm: A three link planar manipulator and the Unimation Puma 560. Implementation of the derived algorithm is effected by using a supervisory expert system to check whether the desired goal lies in the constrained workspace and if not, to evoke the redistribution scheme which determines the constraint relaxation between end effector position and orientation, and then computes optimal gains.

Mutambara, Arthur G. O.↗

NASA NTRS2009

Deriving Safety Cases for the Formal Safety Certification of Automatically Generated Code

We present an approach to systematically derive safety cases for automatically generated code from information collected during a formal, Hoare-style safety certification of the code. This safety case makes explicit the formal and informal reasoning principles, and reveals the top-level assumptions and external dependencies that must be taken into account; however, the evidence still comes from the formal safety proofs. It uses a generic goal-based argument that is instantiated with respect to the certified safety property (i.e., safety claims) and the program. This will be combined with a complementary safety case that argues the safety of the framework itself, in particular the correctness of the Hoare rules with respect to the safety property and the trustworthiness of the certification system and its individual components. Keywords: Automated code generation, Hoare logic, formal code certification, safety case, Goal Structuring Notation.

Basir, Nurlida↗

DOE OSTI2024

How to Partition a Quantum Observable

We present a partition of quantum observables in an open quantum system that is inherited from the division of the underlying Hilbert space or configuration space. It is shown that this partition leads to the definition of an inhomogeneous continuity equation for generic, non-local observables. This formalism is employed to describe the local evolution of the von Neumann entropy of a system of independent quantum particles out of equilibrium. Crucially, we find that all local fluctuations in the entropy are governed by an entropy current operator, implying that the production of entanglement entropy is not measured by this partitioned entropy. For systems linearly perturbed from equilibrium, it is shown that this entropy current is equivalent to a heat current, provided that the system-reservoir coupling is partitioned symmetrically. Finally, we show that any other partition of the coupling leads directly to a divergence of the von Neumann entropy. Thus, we conclude that Hilbert-space partitioning is the only partition of the von Neumann entropy that is consistent with the laws of thermodynamics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS2013

A Formal Basis for Safety Case Patterns

By capturing common structures of successful arguments, safety case patterns provide an approach for reusing strategies for reasoning about safety. In the current state of the practice, patterns exist as descriptive specifications with informal semantics, which not only offer little opportunity for more sophisticated usage such as automated instantiation, composition and manipulation, but also impede standardization efforts and tool interoperability. To address these concerns, this paper gives (i) a formal definition for safety case patterns, clarifying both restrictions on the usage of multiplicity and well-founded recursion in structural abstraction, (ii) formal semantics to patterns, and (iii) a generic data model and algorithm for pattern instantiation. We illustrate our contributions by application to a new pattern, the requirements breakdown pattern, which builds upon our previous work

Formal Methods↗

NASA NTRS2015

Kodiak: An Implementation Framework for Branch and Bound Algorithms

Recursive branch and bound algorithms are often used to refine and isolate solutions to several classes of global optimization problems. A rigorous computation framework for the solution of systems of equations and inequalities involving nonlinear real arithmetic over hyper-rectangular variable and parameter domains is presented. It is derived from a generic branch and bound algorithm that has been formally verified, and utilizes self-validating enclosure methods, namely interval arithmetic and, for polynomials and rational functions, Bernstein expansion. Since bounds computed by these enclosure methods are sound, this approach may be used reliably in software verification tools. Advantage is taken of the partial derivatives of the constraint functions involved in the system, firstly to reduce the branching factor by the use of bisection heuristics and secondly to permit the computation of bifurcation sets for systems of ordinary differential equations. The associated software development, Kodiak, is presented, along with examples of three different branch and bound problem types it implements.

Smith, Andrew P.↗

NASA NTRS1986

Design criteria for expert systems

Knowledge based expert systems are applicable to a wide range of engineering problems ranging from formation to derivation. At the formation end of the spectrum, design, planning and prediction have been identified as generic tasks with similar issues that are dealt with by experts, and need to be formalized for successful expert system implementation. At the derivation end, diagnosis, interpretation and monitoring have been identified as generic tasks with similar subproblems with which experts must cope. At theimplementation level, four levels of programming have been identified: logic programming, production system programming, object oriented programming and hybrid programming.

Allen, R.↗

DOE OSTI2025

Bounding entanglement entropy with Clifford double cosets

Following on our previous work studying the orbits of quantum states under Clifford circuits via reachability graphs, we introduce contracted graphs whose vertices represent classes of quantum states with the same entropy vector. These contracted graphs represent the double cosets of the Clifford group, where the left cosets are built from the stabilizer subgroup of the starting state and the right cosets are built from the entropy-preserving operators. We study contracted graphs for stabilizer states, as well as 𝑊 states and Dicke states, discussing how the diameter of a state's contracted graph constrains the entropic diversity of its two-qubit Clifford orbit. We derive an upper bound on the number of entropy vectors that can be generated using any 𝑛-qubit Clifford circuit, for any quantum state. Here, we speculate on the holographic implications for the relative proximity of gravitational duals of states within the same Clifford orbit. Although we concentrate on how entropy evolves under the Clifford group, our double-coset formalism, and thus the contracted graph picture, is extendable to generic gate sets and generic state properties.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1994

User Interface Technology for Formal Specification Development

Formal specification development and modification are an essential component of the knowledge-based software life cycle. User interface technology is needed to empower end-users to create their own formal specifications. This paper describes the advanced user interface for AMPHION1 a knowledge-based software engineering system that targets scientific subroutine libraries. AMPHION is a generic, domain-independent architecture that is specialized to an application domain through a declarative domain theory. Formal specification development and reuse is made accessible to end-users through an intuitive graphical interface that provides semantic guidance in creating diagrams denoting formal specifications in an application domain. The diagrams also serve to document the specifications. Automatic deductive program synthesis ensures that end-user specifications are correctly implemented. The tables that drive AMPHION's user interface are automatically compiled from a domain theory; portions of the interface can be customized by the end-user. The user interface facilitates formal specification development by hiding syntactic details, such as logical notation. It also turns some of the barriers for end-user specification development associated with strongly typed formal languages into active sources of guidance, without restricting advanced users. The interface is especially suited for specification modification. AMPHION has been applied to the domain of solar system kinematics through the development of a declarative domain theory. Testing over six months with planetary scientists indicates that AMPHION's interactive specification acquisition paradigm enables users to develop, modify, and reuse specifications at least an order of magnitude more rapidly than manual program development.

Lowry, Michael↗

NASA NTRS1991

The linear Boltzmann equation in slab geometry - Development and verification of a reliable and efficient solution

The linear Boltzmann equation can be cast in a form mathematically identical to the radiation-transport equation. A multigroup procedure is used to reduce the energy (or velocity) dependence of the transport equation to a series of one-speed problems. Each of these one-speed problems is equivalent to the monochromatic radiative-transfer problem, and existing software is used to solve this problem in slab geometry. The numerical code conserves particles in elastic collisions. Generic examples are provided to illustrate the applicability of this approach. Although this formalism can, in principle, be applied to a variety of test particle or linearized gas dynamics problems, it is particularly well-suited to study the thermalization of suprathermal particles interacting with a background medium when the thermal motion of the background cannot be ignored. Extensions of the formalism to include external forces and spherical geometry are also feasible.

Stamnes, K.↗

NASA NTRS2012

A Systems Modeling Approach for Risk Management of Command File Errors

The main cause of commanding errors is often (but not always) due to procedures. Either lack of maturity in the processes, incompleteness of requirements or lack of compliance to these procedures. Other causes of commanding errors include lack of understanding of system states, inadequate communication, and making hasty changes in standard procedures in response to an unexpected event. In general, it's important to look at the big picture prior to making corrective actions. In the case of errors traced back to procedures, considering the reliability of the process as a metric during its' design may help to reduce risk. This metric is obtained by using data from Nuclear Industry regarding human reliability. A structured method for the collection of anomaly data will help the operator think systematically about the anomaly and facilitate risk management. Formal models can be used for risk based design and risk management. A generic set of models can be customized for a broad range of missions.

probabilistic risk↗

DOE OSTI2023

Peculiarities of beta functions in sigma models

In this paper we consider perturbation theory in generic two-dimensional sigma models in the so-called first-order formalism, using the coordinate regularization approach. Our goal is to analyze the first-order formalism in application to β functions and compare its results with the standard geometric calculations. Already in the second loop, we observe deviations from the geometric results that cannot be explained by the regularization/renormalization scheme choices. Moreover, in certain cases the first-order calculations produce results that are not symmetric under the classical diffeomorphisms of the target space. Although we could not present the full solution to this remarkable phenomenon, we found some indirect arguments indicating that an anomaly similar to that established in supersymmetric Yang-Mills theory might manifest itself starting from the second loop. We discuss why the difference between two answers might be an infrared effect, similar to that in β functions in supersymmetric Yang-Mills theories.

Sigma Models↗

NASA NTRS1991

Diskoseismology: Probing accretion disks. I - Trapped adiabatic oscillations

The normal modes of acoustic oscillations within thin accretion disks which are terminated by an innermost stable orbit around a slowly rotating black hole or weakly magnetized compact neutron star are analyzed. The dominant relativistic effects which allow modes to be trapped within the inner region of the disk are approximated via a modified Newtonian potential. A general formalism is developed for investigating the adiabatic oscillations of arbitrary unperturbed disk models. The generic behavior is explored by way of an expansion of the Lagrangian displacement about the plane of symmetry and by assuming separable solutions with the same radial wavelength for the horizontal and vertical perturbations. The lowest eigenfrequencies and eigenfunctions of a particular set of radial and quadrupole modes which have minimum motion normal for the plane are obtained. These modes correspond to the standard dispersion relation of disk theory.

Nowak, Michael A.↗

NASA NTRS2013

V and V of Lexical, Syntactic and Semantic Properties for Interactive Systems Through Model Checking of Formal Description of Dialog

During early phases of the development of an interactive system, future system properties are identified (through interaction with end users in the brainstorming and prototyping phase of the application, or by other stakehold-ers) imposing requirements on the final system. They can be specific to the application under development or generic to all applications such as usability principles. Instances of specific properties include visibility of the aircraft altitude, speed… in the cockpit and the continuous possibility of disengaging the autopilot in whatever state the aircraft is. Instances of generic properties include availability of undo (for undoable functions) and availability of a progression bar for functions lasting more than four seconds. While behavioral models of interactive systems using formal description techniques provide complete and unambiguous descriptions of states and state changes, it does not provide explicit representation of the absence or presence of properties. Assessing that the system that has been built is the right system remains a challenge usually met through extensive use and acceptance tests. By the explicit representation of properties and the availability of tools to support checking these properties, it becomes possible to provide developers with means for systematic exploration of the behavioral models and assessment of the presence or absence of these properties. This paper proposes the synergistic use two tools for checking both generic and specific properties of interactive applications: Petshop and Java PathFinder. Petshop is dedicated to the description of interactive system behavior. Java PathFinder is dedicated to the runtime verification of Java applications and as an extension dedicated to User Interfaces. This approach is exemplified on a safety critical application in the area of interactive cockpits for large civil aircrafts.

human-computer interface↗

DOE OSTI2024

Three-particle formalism for multiple channels: the ηππ + $ K\overline{K}\pi $ system in isosymmetric QCD

We generalize previous three-particle finite-volume formalisms to allow for multiple three-particle channels. For definiteness, we focus on the two-channel ηππ and $ K\overline{K}\pi $ system in isosymmetric QCD, considering the positive G parity sector of the latter channel, and neglecting the coupling to modes with four or more particles. The formalism we obtain is thus appropriate to study the b 1 (1235) and η(1295) resonances. The derivation is made in the generic relativistic field theory approach using the time-ordered perturbation theory method. We study how the resulting quantization condition reduces to that for a single three-particle channel when one drops below the upper ($ K\overline{K}\pi $) threshold. We also present parametrizations of the three-particle K matrices that enter into the formalism.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

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↗

NASA NTRS1994

Open architectures for formal reasoning and deductive technologies for software development

The objective of this project is to develop an open architecture for formal reasoning systems. One goal is to provide a framework with a clear semantic basis for specification and instantiation of generic components; construction of complex systems by interconnecting components; and for making incremental improvements and tailoring to specific applications. Another goal is to develop methods for specifying component interfaces and interactions to facilitate use of existing and newly built systems as 'off the shelf' components, thus helping bridge the gap between producers and consumers of reasoning systems. In this report we summarize results in several areas: our data base of reasoning systems; a theory of binding structures; a theory of components of open systems; a framework for specifying components of open reasoning system; and an analysis of the integration of rewriting and linear arithmetic modules in Boyer-Moore using the above framework.

Mccarthy, John↗

DOE OSTI2022

Hidden Sectors from Multiple Line Bundles for the B−L$B-L$ MSSM

Abstract We give a formalism for constructing hidden sector bundles as extensions of sums of line bundles in heterotic M‐theory. Although this construction is generic, we present it within the context of the specific Schoen threefold that leads to the physically realistic MSSM model. We discuss the embedding of the line bundles, the existence of the extension bundle, and a number of necessary conditions for the resulting bundle to be slope‐stable and thus supersymmetric. An explicit example is presented, where two line bundles are embedded into the factor of the maximal subgroup of the hidden sector E 8 gauge group, and then enhanced to a non‐Abelian bundle by extension. For this example, there are in fact six inequivalent extension branches, significantly generalizing that space of solutions compared with hidden sectors constructed from a single line bundle.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗