Results for “Differentiable programming” — Page 19

DOE OSTI2025

First Differential Measurement of the Single 𝜋 + Production Cross Section in Neutrino Neutral-Current Scattering

Since its first observation in the 1970s, neutrino-induced neutral-current single positive pion production (NC⁢1⁢𝜋 + ) has remained an elusive and poorly understood interaction channel. This process is a significant background in neutrino oscillation experiments and studying it further is critical for the physics program of next-generation accelerator-based neutrino oscillation experiments. In this Letter, we present the first double-differential cross-section measurement of NC⁢1⁢𝜋 + interactions using data from the ND280 detector of the T2K experiment collected in 𝜈-beam mode. The measured flux-averaged integrated cross section is 𝜎 = (6.07 ± 1.22) × 10 −41 cm 2 /nucleon. We compare the results on a hydrocarbon target to the predictions of several neutrino interaction generators and final-state-interaction models. While model predictions agree with the differential results, the data show a weak preference for a cross-section normalization approximately 30% higher than predicted by most models studied in this Letter.

Neutrino detection↗

NASA NTRS1990

PAN AIR: A computer program for predicting subsonic or supersonic linear potential flows about arbitrary configurations using a higher order panel method. Volume 1: Theory document (version 3.0)

An outline of the derivation of the differential equation governing linear subsonic and supersonic potential flow is given. The use of Green's Theorem to obtain an integral equation over the boundary surface is discussed. The engineering techniques incorporated in the Panel Aerodynamics (PAN AIR) program (a discretization method which solves the integral equation for arbitrary first order boundary conditions) are then discussed in detail. Items discussed include the construction of the compressibility transformation, splining techniques, imposition of the boundary conditions, influence coefficient computation (including the concept of the finite part of an integral), computation of pressure coefficients, and computation of forces and moments. Principal revisions to version 3.0 are the following: (1) appendices H and K more fully describe the Aerodynamic Influence Coefficient (AIC) construction; (2) appendix L now provides a complete description of the AIC solution process; (3) appendix P is new and discusses the theory for the new FDP module (which calculates streamlines and offbody points); and (4) numerous small corrections and revisions reflecting the MAG module rewrite.

Epton, Michael A.↗

NASA NTRS1981

PAN AIR: A Computer Program for Predicting Subsonic or Supersonic Linear Potential Flows About Arbitrary Configurations Using a Higher Order Panel Method: Theory Document (Version 1.1) - Volume 1

An outline of the derivation of the differential equation governing linear subsonic and supersonic potential flow is given. The use of Green's Theorem to obtain an integral equation over the boundary surface is discussed. The engineering techniques incorporated in the PAN AIR (Panel Aerodynamics) program (a discretization method which solves the integral equation for arbitrary first order boundary conditions) are then discussed in detail. Items discussed include the construction of the compressibility transformations, splining techniques, imposition of the boundary conditions, influence coefficient computation (including the concept of the finite part of an integral), computation of pressure coefficients, and computation of forces and moments.

Magnus, Alfred E.↗

DOE OSTI2025

A mixed-integer PDE-constrained optimization formulation for constructing electromagnetic cloaks with multiple materials

We study the design of an electromagnetic cloak from multiple materials with an additional constraint on the mass of the cloak. Our problem is an example of a topology optimization problem, and we formulate this problem as a mixed-integer partial-differential equation constrained optimization (MIPDECO) problem, where Maxwell’s equation models the propagation of the wave through the cloak and surrounding medium. We use binary variables to model the assignment of the different materials, and their relevant properties (permittivity and density). The mass constraint adds a nontrivial constraint to this problem. We propose a two-phase strategy to solve this problem. In the first phase, we solve a continuous relaxation, and then propose a new variant of the feasibility pump that exploits the structure of the PDE to obtain an initial integral solution candidate. In the second phase, we use a trust-region approach to improve this incumbent. We also consider a continuation or mesh-sequencing approach to find better solutions faster on consecutively finer meshes. We present detailed numerical results to illustrate the effectiveness of our approaches for constructing multi-material cloaks with a mass constraint.

Calculus of Variations and Optimization↗

DOE OSTI2026

qsp4pde v1.0

The software program is a collection of Python implementations of quantum circuits for solving linear partial differential equations using quantum signal processing. The circuits are implemented using the qiskit SDK.

Kim, Hyeongjin [Lawrence Berkeley National Laborat↗

NASA NTRS1975

Study of viscous flow about airfoils by the integro-differential method

An integro-differential method was used for numerically solving unsteady incompressible viscous flow problems. A computer program was prepared to solve the problem of an impulsively started 9% thick symmetric Joukowski airfoil at an angle of attack of 15 deg and a Reynolds number of 1000. Some of the results obtained for this problem were discussed and compared with related work completed previously. Two numerical procedures were used, an Alternating Direction Implicit (ADI) method and a Successive Line Relaxation (SLR) method. Generally, the ADI solution agrees well with the SLR solution and with previous results are stations away from the trailing edge. At the trailing edge station, the ADI solution differs substantially from previous results, while the vorticity profiles obtained from the SLR method there are in good qualitative agreement with previous results.

Wu, J. C.↗

NASA NTRS1978

Efficient searching and sorting applications using an associative array processor

The purpose of this paper is to describe a method of searching and sorting data by using some of the unique capabilities of an associative array processor. To understand the application, the associative array processor is described in detail. In particular, the content addressable memory and flip network are discussed because these two unique elements give the associative array processor the power to rapidly sort and search. A simple alphanumeric sorting example is explained in hardware and software terms. The hardware used to explain the application is the STARAN (Goodyear Aerospace Corporation) associative array processor. The software used is the APPLE (Array Processor Programming Language) programming language. Some applications of the array processor are discussed. This summary tries to differentiate between the techniques of the sequential machine and the associative array processor.

Pace, W.↗

NASA NTRS1977

Discrete time modeling of heavy transport plane pilot behavior

The desire to improve flight safety leads to a classification of various flight troubles in three groups: (1) troubles from sensitivity to flight disturbances, (2) maneuverability troubles (whenever a correction maneuver induces an unexpected deviation on another parameter), and (3) pilot troubles (pilot overload when required attention is excessive or underload entailing a loss of vigilance). Sensitivity to disturbances and maneuverability of a given aircraft may be evaluated from the early design stage. Evaluation of the pilot behavior, however, may be realized only in actual flight or with a flight simulator, that is quite late in the development period. For this reason, it is desirable to have available, at the design stage, a model of the pilot behavior to command the differential system describing the envisioned aircraft. This aim implies two major requirements. First, the program must be compatible with a wide range of possible aircraft designs; ideally, the program should be self-learning. Second, mental load and overall pilot performance must be modeled.

Cavalli, D.↗

NASA NTRS1992

Systematic Disturbance Of Optimal Rotational Trajectory

Algorithm introduces systematic disturbance into otherwise optimal rotation of body from prescribed initial to prescribed final orientation. Disturbance introduced as deviation of actual axis of rotation from optimal one, like wobble of top. Algorithm effects rotational transformations and solves differential equations necessary to compute disturbed trajectory. Devised for use with motion-control program and three-dimensional computer-graphical display to study ability of observers to distinguish between optimal and suboptimal rotational trajectories.

Grunwald, Arthur J.↗

NASA NTRS2005

AutoChem

AutoChem is a suite of Fortran 90 computer programs for the modeling of kinetic reaction systems. AutoChem performs automatic code generation, symbolic differentiation, analysis, and documentation. It produces a documented stand-alone system for the modeling and assimilation of atmospheric chemistry. Given databases of chemical reactions and a list of constituents defined by the user, AutoChem automatically does the following: 1. Selects the subset of reactions that involve a user-defined list of constituents and automatically prepares a document listing the reactions; 2. Constructs the ordinary differential equations (ODEs) that describe the reactions as functions of time and prepares a document containing the ODEs; 3. Symbolically differentiates the time derivatives to obtain the Jacobian and prepares a document containing the Jacobian; 4. Symbolically differentiates the Jacobian to obtain the Hessian and prepares a document containing the Hessian; and 5. Writes all the required Fortran 90 code and datafiles for a stand-alone chemical modeling and assimilation system (implementation of steps 1 through 5). Typically, the time taken for steps 1 through 5 is about 3 seconds. The modeling system includes diagnostic components that automatically analyze each ODE at run time, the relative importance of each term, time scales, and other attributes of the model.

Lary, David John↗

NASA NTRS2014

Application of Fault Management Theory to the Quantitive Selection of a Launch Vehicle Abort Trigger Suite

SHM/FM theory has been successfully applied to the selection of the baseline set Abort Triggers for the NASA SLS center dot Quantitative assessment played a useful role in the decision process  M&FM, which is new within NASA MSFC, required the most "new" work, as this quantitative analysis had never been done before center dot Required development of the methodology and tool to mechanize the process center dot Established new relationships to the other groups  The process is now an accepted part of the SLS design process, and will likely be applied to similar programs in the future at NASA MSFC  Future improvements center dot Improve technical accuracy ‒Differentiate crew survivability due to an abort, vs. survivability even no immediate abort occurs (small explosion with little debris) ‒Account for contingent dependence of secondary triggers on primary triggers ‒Allocate "Δ LOC Benefit" of each trigger when added to the previously selected triggers. center dot Reduce future costs through the development of a specialized tool  Methodology can be applied to any manned/unmanned vehicle, in space or terrestrial

Lo, Yunnhon↗

NASA NTRS2021

A Study into Validating a Coupled Method of Characteristics and Direct Simulation Monte Carlo Method Against Empirical Data

The following will outline the methodology and results of validating a coupled Method of Characteristics (MOC) and Direct Simulation Monte Carlo (DSMC) method. This research focused specifically on modeling plume impingement, induced by Reaction Control System (RCS) thrusters that flew on the National Aeronautics and Space Administration’s (NASA’s) space shuttle Discovery. For each simulation, the continuum portion of the RCS thruster was simulated using MOC for solving hyperbolic Partial Differential Equations (PDEs) and computed with the NASA code, Reacting and Multi-phase Program (RAMP). The solution was then implemented as a starting condition into the NASA DSMC code, Direct Simulation and Monte Carlo Analysis Code (DAC). Typically, DSMC models rely on code-to-code validation for fidelity. The significance of this research is in its ability to validate its models against empirical data. Prior to computing solutions for these simulations, the mesh size and structure were optimized and many variants of DSMC input parameters were iterated on in order to acquire a reliable, mesh-independent, fully optimized numerical solution. This research will discuss the mathematical formulation of MOC for nozzle flow and DSMC for rarefied gases. Additionally, it will provide an explanation of how to implement these mathematical concepts into the two solvers: RAMP and DAC. Ultimately, this research will demonstrate that the overall process illustrated produces results in good agreement with empirical data. As a consequence, the methodology presented is granted an increased level of confidence and will greatly contribute to the aerospace industry and its effort in understanding and predicting rarefied flow fields.

Direct Simulation Monte Carlo Analysis Code↗

NASA NTRS2021

A Study into Validating A Coupled Method of Characteristics And Direct Simulation Monte Carlo Method Against Empirical Data

The following will outline the methodology and results of validating a coupled Method of Characteristics (MOC) and Direct Simulation Monte Carlo (DSMC) method. This research focused specifically on modeling plume impingement, induced by Reaction Control System (RCS) thrusters that flew on the National Aeronautics and Space Administration’s (NASA’s) space shuttle Discovery. For each simulation, the continuum portion of the RCS thruster was simulated using MOC for solving hyperbolic Partial Differential Equations (PDEs) and computed with the NASA code, Reacting and Multi-phase Program (RAMP). The solution was then implemented as a starting condition into the NASA DSMC code, Direct Simulation and Monte Carlo Analysis Code (DAC). Typically, DSMC models rely on code-to-code validation for fidelity. The significance of this research is in its ability to validate its models against empirical data. Prior to computing solutions for these simulations, the mesh size and structure were optimized and many variants of DSMC input parameters were iterated on in order to acquire a reliable, mesh-independent, fully optimized numerical solution. This research will discuss the mathematical formulation of MOC for nozzle flow and DSMC for rarefied gases. Additionally, it will provide an explanation of how to implement these mathematical concepts into the two solvers: RAMP and DAC. Ultimately, this research will demonstrate that the overall process illustrated produces results in good agreement with empirical data. As a consequence, the methodology presented is granted an increased level of confidence and will greatly contribute to the aerospace industry and its effort in understanding and predicting rarefied flow fields.

DAC↗

NASA NTRS2004

An Interactive Microsoft(registered tm) Excel Program for Tracking a Single Evaporating Droplet in Crossflow

Droplet interaction with a high temperature gaseous crossflow is important because of its wide application in systems involving two phase mixing such as in combustion requiring quick mixing of fuel and air with the reduction of pollutants and for jet mixing in the dilution zone of combustors. Therefore, the focus of this work is to investigate dispersion of a two-dimensional atomized and evaporating spray jet into a two-dimensional crossflow. An interactive Microsoft Excel program for tracking a single droplet in crossflow that has previously been developed will be modified to include droplet evaporation computation. In addition to the high velocity airflow, the injected droplets are also subjected to combustor temperature and pressure that affect their motion in the flow field. Six ordinary differential equations are then solved by 4th-order Runge-Kutta method using Microsoft Excel software. Microsoft Visual Basic programming and Microsoft Excel macrocode are used to produce the data and plot graphs describing the droplet's motion in the flow field. This program computes and plots the data sequentially without forcing the user to open other types of plotting programs. A user's manual on how to use the program is included.

Droplet↗

NASA NTRS1978

Multiplexer/demultiplexer flexibility enhancement program

This final report summarizes the accomplishments of the NASA/JSC MDM Flexibility Enhancement Program, Contract NAS9-15359 as carried out by Sperry Flight Systems from April through December 1977. Included are discussions of major statement of work tasks and the results, conclusions and recommended actions. All tasks called out in the amended SOW were carried out. Significant development tasks which were completed included the following: (1) Development, breadboard and test of a Pulse Output 28-volt Module. (2) Development and test of a 32-channel DC Analog Input (DCIN) Differential Module. (3) Development and test of a sequence memory module using an M2708 EPROM which can be programmed in the unit. (4) Development and test of a radiator top cover for a radiation-cooled Flexible MDM.

Source record↗

NASA NTRS1989

A method for solution of the Euler-Bernoulli beam equation in flexible-link robotic systems

An efficient numerical method for solving the partial differential equation (PDE) governing the flexible manipulator control dynamics is presented. A finite-dimensional model of the equation is obtained through discretization in both time and space coordinates by using finite-difference approximations to the PDE. An expert program written in the Macsyma symbolic language is utilized in order to embed the boundary conditions into the program, accounting for a mass carried at the tip of the manipulator. The advantages of the proposed algorithm are many, including the ability to (1) include any distributed actuation term in the partial differential equation, (2) provide distributed sensing of the beam displacement, (3) easily modify the boundary conditions through an expert program, and (4) modify the structure for running under a multiprocessor environment.

Tzes, Anthony P.↗

NASA NTRS1992

Domain-specific functional software testing: A progress report

Software Engineering is a knowledge intensive activity that involves defining, designing, developing, and maintaining software systems. In order to build effective systems to support Software Engineering activities, Artificial Intelligence techniques are needed. The application of Artificial Intelligence technology to Software Engineering is called Knowledge-based Software Engineering (KBSE). The goal of KBSE is to change the software life cycle such that software maintenance and evolution occur by modifying the specifications and then rederiving the implementation rather than by directly modifying the implementation. The use of domain knowledge in developing KBSE systems is crucial. Our work is mainly related to one area of KBSE that is called automatic specification acquisition. One example is the WATSON prototype on which our current work is based. WATSON is an automatic programming system for formalizing specifications for telephone switching software mainly restricted to POTS, i.e., plain old telephone service. Our current approach differentiates itself from other approaches in two antagonistic ways. On the one hand, we address a large and complex real-world problem instead of a 'toy domain' as in many research prototypes. On the other hand, to allow such scaling, we had to relax the ambitious goal of complete automatic programming, to the easier task of automatic testing.

Nonnenmann, Uwe↗

NASA NTRS1973

Marshall system for aerospace system simulation (MARSYAS), user's manual

The capabilities of the Marshall system for aerospace system simulation (MARSYAS) and how to use it are described. MARSYAS is a software system that allows easy setup and control of the simulation of the dynamics of large physical systems on a digital computer. The physical systems are modeled in the form of block diagrams or equations. The blocks can have multiple inputs and multiple outputs, and they can be nested to form hierarchies. The block diagrams can contain transfer functions, nonlinear and logical functions, equations, analog computer elements and FORTRAN programs. The input format of the equations can be combinations of nonlinear, time-varying differential equations and algebraic equations in their original format. MARSYAS could also serve as a storage and retrieval system for models as a basis for a model configuration control system on a central time-shared computer. The outputs of the simulation system can be not only time-responses but also other analysis data such as frequency response, power spectrum and stability parameters. The MARSYAS translator is written in FORTRAN running on the Univac 1108 computer under the EXEC 8 operating system.

Ventre, A.↗