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At least 1,153 records · Page 64
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Power Flow Geometry and Approximation

Here, the power flow equations are important in numerous power systems problems of practical interest which consider alternating current power flow (ACPF) physics. Perhaps the most well studied being the alternating current optimal power flow problem (ACOPF), seeking to optimize the operation of an electric power system. Due to their non-linearity, problems which include the power flow equations are typically challenging, particularly in optimization. Interestingly, the set of solutions to the power flow equations forms a smooth manifold. As a result, differential geometry can be used to describe and analyze this set of equations. This approach has proven effective in several engineering applications (e.g., solving ACOPF and analyzing the solution space boundary). Central to the success of this approach is an understanding of the power flow manifold's geometry. In this work, we develop the geometric and topological properties of this manifold using concepts from differential geometry. After demonstrating the convenience of this manifold's representation as a function's graph, computational methods are emphasized: we develop retractions, error bounds for linear approximation, and formulas for evaluating the Riemannian metric (including associated objects such as geodesics and the curvature tensor). Scalar curvature and the second fundamental form play a new role in quantifying the quality of linear approximations, like the popular direct current approximation. All functions are implemented in Julia and available in an online repository. Proofs are included for completeness.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2023

Simultaneous Momentum and Position Measurement and the Instrumental Weyl-Heisenberg Group

The canonical commutation relation, [Q,P]=iℏ, stands at the foundation of quantum theory and the original Hilbert space. The interpretation of P and Q as observables has always relied on the analogies that exist between the unitary transformations of Hilbert space and the canonical (also known as contact) transformations of classical phase space. Now that the theory of quantum measurement is essentially complete (this took a while), it is possible to revisit the canonical commutation relation in a way that sets the foundation of quantum theory not on unitary transformations but on positive transformations. This paper shows how the concept of simultaneous measurement leads to a fundamental differential geometric problem whose solution shows us the following. The simultaneous P and Q measurement (SPQM) defines a universal measuring instrument, which takes the shape of a seven-dimensional manifold, a universal covering group we call the instrumental Weyl-Heisenberg (IWH) group. The group IWH connects the identity to classical phase space in unexpected ways that are significant enough that the positive-operator-valued measure (POVM) offers a complete alternative to energy quantization. Five of the dimensions define processes that can be easily recognized and understood. The other two dimensions, the normalization and phase in the center of the IWH group, are less familiar. The normalization, in particular, requires special handling in order to describe and understand the SPQM instrument.

47 OTHER INSTRUMENTATION↗
DOE OSTI2023

(U) A General-Purpose Code for Correlated Sampling Using Batch Statistics with MCNP6 for Fixed-Source Problems

Correlated sampling can be used to reduce the uncertainty of a difference of tallies by taking advantage of the negative covariance term in the sandwich formula. Booth first showed how correlated sampling can be applied with batch statistics using MCNP’s tally fluctuation chart (TFC) to reduce the uncertainty of a difference of tallies in fixed-source problems. Booth presented a problem in which a 1273% uncertainty in a difference was reduced to 8% by accounting for correlations. Researchers He and Su recently studied correlated sampling using the TFC in MCNP version 5. They determined that the code did not print enough digits in the TFC tally means for accurate batch statistics in some cases. After modifying the source code, they concluded that “correlated sampling can yield a standard deviation of about one magnitude smaller than that predicted by the direct, un-correlated simulation when the changes in system response are small (say about 1%), which is equivalent to saving in CPU time by a factor of 100. Such saving [sic] becomes less significant as the change in system response becomes larger.” He and Su provided the formulas needed to apply batch statistics to compute the correlated uncertainty of a difference of tallies. In this report, we follow up on their work by providing the formulas needed to apply batch statistics to compute the correlated uncertainty of a ratio of tallies and of a difference of two tallies divided by a third tally. We extend these formulas to differences and ratios of ratios. These formulas are applied to reduce the uncertainty associated with calculating a relative sensitivity. He and Su did not investigate the accuracy of their correlated sampling uncertainty estimates. We use their test problems and evaluate the accuracy of the uncertainty estimates by comparing with results obtained from random sampling, and, in simple cases, with theoretical values of the “exact” uncertainties. We find that the uncertainties obtained from batch statistics are accurate as long as at least 100 batches are used. We present a new computer code, COSUBS (COrrelated Sampling Using Batch Statistics), that reads MCNP6 TFCs and applies correlated sampling using batch statistics for the tally combinations that the user specifies. COSUBS is a very general tool that compares all TFCs for a base case and one or two perturbed cases. It computes uncertainties for ratios if given only a base case. This report is organized as follows. The equations to apply batch statistics to the difference of random tallies are reviewed in Sec. II. Section III presents the equations for applying batch statistics to a ratio of random tallies; this is useful for computing relative sensitivities using a one-sided finite difference and the relative sensitivity using the differential operator method. Section IV presents the equations for applying batch statistics to a difference of two random tallies divided by a third; this is useful for computing a relative sensitivities using a central difference. Section V presents the equations for applying batch statistics to a difference of two ratios with four random tallies. Section VI presents the equations for applying batch statistics to a one-sided finite difference estimate of the relative sensitivity of a ratio (this uses four random tallies). Section VII presents the equations for applying batch statistics to a central difference estimate of the relative sensitivity of a ratio (this uses six random tallies). Section VIII presents the equations for applying batch statistics to a sum of random tallies. Section IX discusses how to apply batch statistics using MCNP6. Section X presents COSUBS, describing its command-line options and logic. Sections XI through XVI present numerical results for various test problems. Section XVII is a summary and conclusions. Appendix A derives the theoretical Monte Carlo tally variance given certain assumptions; these variances are used to verify the batch statistics for some of the problems. Appendix B lists the MCNP6 input for the unperturbed example problem. Appendix C presents modifications made to MCNP6.3 to support this work.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

End-exclusion zones in strongly stretched, molten polymer brushes of arbitrary shape

Theories of strongly stretched polymer brushes, particularly the parabolic brush theory, are valuable for providing analytically tractable predictions for the thermodynamic behavior of surface-grafted polymers in a wide range of settings. Furthermore, the parabolic brush limit fails to describe polymers grafted to convex curved substrates, such as the surfaces of spherical nanoparticles or the interfaces of strongly segregated block copolymers. It has previously been shown that strongly stretched curved brushes require a boundary layer devoid of free chain ends, requiring modifications of the theoretical analysis. While this “end-exclusion zone” has been successfully incorporated into the descriptions of brushes grafted onto the outer surfaces of cylinders and spheres, the behavior of brushes on surfaces of arbitrary curvature has not yet been studied. We present a formulation of the strong-stretching theory for molten brushes on the surfaces of arbitrary curvature and identify four distinct regimes of interest for which brushes are predicted to possess end-exclusion zones, notably including regimes of positive mean curvature but negative Gaussian curvature. Through numerical solutions of the strong-stretching brush equations, we report predicted scaling of the size of the end-exclusion zone, the chain end distribution, the chain polarization, and the free energy of stretching with mean and Gaussian surface curvatures. Through these results, we present a comprehensive picture of how the brush geometry influences the end-exclusion zones and exact strong-stretching free energies, which can be applied, for example, to model the full spectrum of brush geometries encountered in block copolymer melt assembly.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Automated identification of dominant physical processes

The identification of processes that locally and approximately dominate dynamical system behavior has enabled significant advances in understanding and modeling nonlinear differential dynamical systems. Conventional methods of dominant process identification involve piecemeal and ad hoc (non-rigorous, informal) scaling analyses to identify dominant balances of governing equation terms and to delineate the spatiotemporal boundaries (boundaries in space and/or time) of each dominant balance. For the first time, we present an objective global measure of the fit of dominant balances to observations, which is desirable for automation, and was previously undefined. Furthermore, we propose a formal definition of the dominant balance identification problem in the form of an optimization problem. Here, we show that the optimization can be performed by various machine learning algorithms, enabling the automatic identification of dominant balances. Our method is algorithm agnostic and it eliminates reliance upon expert knowledge to identify dominant balances which are not known beforehand.

42 ENGINEERING↗
DOE OSTI2026

Stoichiometrically-informed symbolic regression for extracting chemical reaction mechanisms from data

A data-driven computational method is introduced to extract chemical reaction mechanisms from time series chemical concentration data. It is realized through the use of dynamic symbolic regression in which a sparse analytical form for a dynamical system is discoverable from the underlying data. We specifically develop the stoichiometrically-informed symbolic regression (SISR) method to address a standing challenge in complex chemical reaction networks: given a time-series dataset of concentrations of several components, what is the mechanism and the associated rate constants? SISR finds the optimal mechanism, kinetic equations and rate constants by combining differential optimization with a genetic optimization approach that searches a symbolic space of possible reaction mechanisms. Use of SISR in several paradigmatic examples spanning linear and nonlinear reaction schemes results in excellent agreement between true and predicted mechanisms, including when the method is applied to noisy data. The advantages of a stoichiometrically-informed approach such as SISR to address reaction discovery is illustrated through comparison with the use of generic state-of-the-art data-driven approaches.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Acausality-driven instabilities in relativistic viscous hydrodynamics

We investigate non-linear instabilities stemming from superluminal propagation of information in Israel-Stewart-like models of relativistic viscous fluid dynamics. In relativity, the characteristic speed of propagation of information, $w$, and the speed of the fluid, $v$, allow us to differentiate between regimes of the hydrodynamic equations that are acausal but stable ($w>1$), unstable ($v^{2} w^{2} \geq 1$), and covariantly ill-posed ($w^{2} \leq 0$). As an analytical benchmark, we present a new solution that illustrates these distinct regimes. We compare this analytical solution to the result of a numerical relativistic viscous fluid dynamics solver, and confirm that the analytical result can be recovered numerically in the stable regime, whether causal or acausal. The onset of numerical instabilities is further found to occur in the regime predicted by the analytical solution.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2019

Chapter Six - Derivation, cross-validation, and comparison of analytic formulas for electrostatic deflector aberrations

Here, we derived first and second order analytic aberration formulas in the horizontal transverse plane for an electrostatic deflector specified by the reference orbit radius, the central angle spanning the deflector, and its inhomogeneity coefficients. The derivation was performed using an iterative order-by-order perturbation method in a Frenet–Serret beamline coordinate system. We produced a C program edabrt for calculation of the first and second order aberrations using the formulas that we derived. The electrostatic deflector aberration formulas from Wollnik (1965) disagree with COSY INFINITY and the aberration formulas that we derived here, and they also deviate from the first and second order symplecticity conditions. The reason for this discrepancy is that the aberration formulas from Wollnik (1965) consider only motion in the main field of the deflector and do not properly account for fringe field effects, in particular the necessarily occurring change of kinetic energy due to the change in potential. The code GIOS uses electrostatic aberration formulas from Wollnik (1965) and exhibits the same discrepancy. We performed a comparison of first and second order electrostatic deflector aberrations for (1) the analytic formulas derived in this work, (2) differential-algebraic (DA) numerical integration of the equations of motion using the code COSY INFINITY, (3) the aberration formulas from Wollnik (1965), (4) aberrations computed using the code GIOS, and (5) the aberration formulas from Wollnik (1965) adjusted to account for the occurring change in potential. An electrostatic spherical deflector and an electrostatic cylindrical deflector were used as test cases for this comparison. There is excellent agreement between methods (1), (2), and (5), and these three methods satisfy the first and second order symplecticity conditions.

43 PARTICLE ACCELERATORS↗
DOE OSTI2021

Bringing discrete-time Langevin splitting methods into agreement with thermodynamics

In light of the recently published complete set of statistically correct Grønbech–Jensen (GJ) methods for discrete-time thermodynamics, we revise a differential operator splitting method for the Langevin equation in order to comply with the basic GJ thermodynamic sampling features, namely, the Boltzmann distribution and Einstein diffusion, in linear systems. This revision, which is based on the introduction of time scaling along with flexibility of a discrete-time velocity attenuation parameter, provides a direct link between the ABO splitting formalism and the GJ methods. This link brings about the conclusion that any GJ method has at least weak second order accuracy in the applied time step. It further helps identify a novel half-step velocity, which simultaneously produces both correct kinetic statistics and correct transport measures for any of the statistically sound GJ methods. Explicit algorithmic expressions are given for the integration of the new half-step velocity into the GJ set of methods. Finally, numerical simulations, including quantum-based molecular dynamics (QMD) using the QMD suite Los Alamos Transferable Tight-Binding for Energetics, highlight the discussed properties of the algorithms as well as exhibit the direct application of robust, time-step-independent stochastic integrators to QMD.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Self-similar Reynolds-averaged mechanical–scalar turbulence models for reshocked Richtmyer–Meshkov instability-induced mixing in the small Atwood number limit

Analytical self-similar solutions to two-, three-, and four-equation Reynolds-averaged mechanical–scalar turbulence models describing incompressible turbulent Richtmyer–Meshkov instability-induced mixing in planar geometry derived in the small Atwood number limit are extended to construct models for reshocked Richtmyer–Meshkov mixing. In this study, the models are based on the turbulent kinetic energy K and its dissipation rate ε, together with the scalar variance S and its dissipation rate χ modeled either differentially or algebraically. The three- and four-equation models allow for a simultaneous description of mechanical and scalar mixing, i.e., mixing layer growth and molecular mixing. Mixing layer growth parameters and other physical observables were obtained explicitly as functions of the model coefficients and were used to calibrate the model coefficients. Here, the solutions for the singly shocked Richtmyer–Meshkov case for the mixing layer width and the turbulent fields are used to construct piecewise-continuous generalizations of these quantities for times after reshock. For generality, the post-reshock mixing layer width is not assumed to grow with the same power-law as the pre-reshock width, and an impulsive approximation applied to Rayleigh–Taylor instability growth is used to establish the expression for the post-reshock width. A four-equation model is then used to illustrate the spatiotemporal behavior of the mean and turbulent fields and late-time turbulent equation budgets across the mixing layer. The reference solutions derived here can provide systematic calibrations and better understanding of mechanical–scalar turbulence models and their predictions for reshocked Richtmyer–Meshkov instability-induced turbulent mixing in the very large Reynolds number limit.

42 ENGINEERING↗
DOE OSTI2020

NSFnets (Navier-Stokes flow nets): Physics-informed neural networks for the incompressible Navier-Stokes equations

In the last 50 years there has been a tremendous progress in solving numerically the Navier-Stokes equations using finite differences, finite elements, spectral, and even meshless methods. Yet, in many real cases, we still cannot incorporate seamlessly (multi-fidelity) data into existing algorithms, and for industrial-complexity applications the mesh generation is time consuming and still an art. Moreover, solving ill-posed problems (e.g., lacking boundary conditions) or inverse problems is often prohibitively expensive and requires different formulations and new computer codes. Here, we employ physics-informed neural networks (PINNs), encoding the governing equations directly into the deep neural network via automatic differentiation, to overcome some of the aforementioned limitations for simulating incompressible laminar and turbulent flows. We develop the Navier-Stokes flow nets (NSFnets) by considering two different mathematical formulations of the Navier-Stokes equations: the velocity-pressure (VP) formulation and the vorticity-velocity (VV) formulation. Since this is a new approach, we first select some standard benchmark problems to assess the accuracy, convergence rate, computational cost and flexibility of NSFnets; analytical solutions and direct numerical simulation (DNS) databases provide proper initial and boundary conditions for the NSFnet simulations. The spatial and temporal coordinates are the inputs of the NSFnets, while the instantaneous velocity and pressure fields are the outputs for the VP-NSFnet, and the instantaneous velocity and vorticity fields are the outputs for the VV-NSFnet. This is unsupervised learning and, hence, no labeled data are required beyond boundary and initial conditions and the fluid properties. The residuals of the VP or VV governing equations, together with the initial and boundary conditions, are embedded into the loss function of the NSFnets. No data is provided for the pressure to the VP-NSFnet, which is a hidden state and is obtained via the incompressibility constraint without extra computational cost. Unlike the traditional numerical methods, NSFnets inherit the properties of neural networks (NNs), hence the total error is composed of the approximation, the optimization, and the generalization errors. Here, we empirically attempt to quantify these errors by varying the sampling (“residual”) points, the iterative solvers, and the size of the NN architecture. For the laminar flow solutions, we show that both the VP and the VV formulations are comparable in accuracy but their best performance corresponds to different NN architectures. The initial convergence rate is fast but the error eventually saturates to a plateau due to the dominance of the optimization error. For the turbulent channel flow, we show that NSFnets can sustain turbulence at , but due to expensive training we only consider part of the channel domain and enforce velocity boundary conditions on the subdomain boundaries provided by the DNS data base. We also perform a systematic study on the weights used in the loss function for balancing the data and physics components, and investigate a new way of computing the weights dynamically to accelerate training and enhance accuracy. In the last part, we demonstrate how NSFnets should be used in practice, namely for ill-posed problems with incomplete or noisy boundary conditions as well as for inverse problems. We obtain reasonably accurate solutions for such cases as well without the need to change the NSFnets and at the same computational cost as in the forward well-posed problems. As a result, we also present a simple example of transfer learning that will aid in accelerating the training of NSFnets for different parameter settings.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

A high-order WENO-limited finite-volume algorithm for atmospheric flow using the ADER-differential transform time discretization

A high-order-accurate weighted essentially non-oscillatory (WENO) limited upwind finite-volume scheme is detailed for the compressible, nonhydrostatic, inviscid Euler equations using an arbitrary derivatives (ADER) time-stepping scheme based on differential transforms (DTs). A second-order-accurate alternating Strang dimensional splitting is compared against multidimensional simulation with 2D transport using solid body rotation of various data. The two were found to give nearly identical accuracy in orthogonal, Cartesian coordinates. Orders of convergence are demonstrated at up to ninth-order accuracy with 2D transport. 1D transport is used to confirm that error decreases monotonically with increasing order of accuracy with WENO limiting even for discontinuous data. Further, WENO limiting always decreased the error compared with simulation without limiting in the L 1 norm. A series of standard 2D compressible nonhydrostatic Euler equation test cases were validated against previous results from literature. Finally, it was demonstrated that increasing the order of accuracy led to better resolved features and increased power for kinetic energy at small wavelengths.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Bootstrapping closed string field theory

The determination of the string vertices of closed string field theory is shown to be a conformal field theory problem solvable by combining insights from Liouville theory, hyperbolic geometry, and conformal bootstrap. We first demonstrate how Strebel differentials arise from hyperbolic string vertices by performing a WKB approximation to the associated Fuchsian equation, which we subsequently use it to derive a Polyakov-like conjecture for Strebel differentials. This result implies that the string vertices are generated by the interactions of n zero momentum tachyons, or equivalently, a certain limit of suitably regularized on-shell Liouville action. We argue that the latter can be related to the interaction of three zero momentum tachyons on a generalized cubic vertex through classical conformal blocks. We test this claim for the quartic vertex and discuss its generalization to higher-string interactions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

A Unified Workflow for Sensitivity-Based Kinetic Analysis in Microkinetic Models

Degrees of rate control (DRC), apparent activation energies, and apparent reaction orders are established local sensitivity diagnostics for interpreting microkinetic models, but applying them routinely to large mechanisms often requires substantial reaction-specific bookkeeping, perturbation design, and postprocessing. Here, in this study, we present a unified derivative-based workflow that evaluates these quantities from a single compiled reaction-network model and target-rate definition. For any user-provided microkinetic model, the workflow compiles the mechanism into stoichiometrically consistent mass-action rate equations, solves the surface dynamics, and uses automatic differentiation to compute sensitivities with respect to rate constants, temperature, and gas partial pressures. By combining their calculations in the same framework, the workflow clearly demonstrates the relationships between different DRCs and the apparent activation energy. Using existing examples of propylene partial oxidation and methane oxidation on Pd(100), we verify expected transient redistribution of rate control, distinguish net Campbell DRCs from one-sided directional sensitivities, and show how apparent activation energy can be reconstructed either from one-sided DRCs or from state-based DRCs while critical mechanistic insights are obtained consistently. In the methane oxidation case, a pathway-subset test further illustrates how a simplified mechanism preserves key kinetic signatures of a full model, showing the potential of our user-friendly tool for model construction beyond kinetic analysis.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Learning Constitutive Relations From Soil Moisture Data via Physically Constrained Neural Networks

Abstract The constitutive relations of the Richardson‐Richards equation encode the macroscopic properties of soil water retention and conductivity. These soil hydraulic functions are commonly represented by models with a handful of parameters. The limited degrees of freedom of such soil hydraulic models constrain our ability to extract soil hydraulic properties from soil moisture data via inverse modeling. We present a new free‐form approach to learning the constitutive relations using physically constrained neural networks. We implemented the inverse modeling framework in a differentiable modeling framework, JAX, to ensure scalability and extensibility. For efficient gradient computations, we implemented implicit differentiation through a nonlinear solver for the Richardson‐Richards equation. We tested the framework against synthetic noisy data and demonstrated its robustness against varying magnitudes of noise and degrees of freedom of the neural networks. We applied the framework to soil moisture data from an upward infiltration experiment and demonstrated that the neural network‐based approach was better fitted to the experimental data than a parametric model and that the framework can learn the constitutive relations.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Sensitivity of Au + Au collisions to the symmetric nuclear matter equation of state at 2–5 nuclear saturation densities

We demonstrate that proton and pion flow measurements in heavy-ion collisions at incident energies ranging from 1 to 20 GeV per nucleon in the fixed target frame can be used for an accurate determination of the symmetric nuclear matter equation of state at baryon densities equal 2–4 times nuclear saturation density n 0 . We simulate Au + Au collisions at these energies using a hadronic transport model with an adjustable vector mean-field potential dependent on baryon density n B . Here, we show that the mean field can be parametrized to reproduce a given density dependence of the speed of sound at zero temperature $c$$^{2}_{s}$ (n B , T = 0), which we vary independently in multiple density intervals to probe the differential sensitivity of heavy-ion observables to the equation of state at these specific densities. Recent flow data from the STAR experiment at the center-of-mass energies √ s NN = {3.0, 4.5} GeV can be described by our model, and a Bayesian analysis of these data indicates a hard equation of state at n B ϵ (2, 3)n 0 and a possible phase transition at n B ϵ (3, 4)n 0 . More data at √ s NN = 2–5 GeV, as well as a more thorough analysis of the model systematic uncertainties will be necessary for a more precise conclusion.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗