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All sources NASA NTRS DOE OSTI

DOE OSTI2020

A generalized Boltzmann kinetic theory for strongly magnetized plasmas with application to friction

Coulomb collisions in plasmas are typically modeled using the Boltzmann collision operator, or its variants, which apply to weakly magnetized plasmas in which the typical gyroradius of particles significantly exceeds the Debye length. Conversely, O’Neil has developed a kinetic theory to treat plasmas that are so strongly magnetized that the typical gyroradius of particles is much smaller than the distance of the closest approach in a binary collision. Here, we develop a generalized collision operator that applies across the full range of magnetization strength. Since there is no closed-form solution for the scattering cross section when plasma is strongly magnetized, the input to the collision operator is obtained by numerically calculating particle trajectories. To demonstrate novel physics associated with strong magnetization, it is used to compute the friction force on a massive test charge. In addition to the traditional stopping power component, this is found to exhibit a transverse component that is perpendicular to both the velocity and Lorentz force vectors in the strongly magnetized regime, as was predicted recently using linear response theory. As a result, good agreement is found between the collision theory and linear response theory in the regime in which both apply, but the new collision theory also applies to stronger magnetization strength regimes than the linear response theory is expected to apply in.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS2011

Discretely Conservative Finite-Difference Formulations for Nonlinear Conservation Laws in Split Form: Theory and Boundary Conditions

Simulations of nonlinear conservation laws that admit discontinuous solutions are typically restricted to discretizations of equations that are explicitly written in divergence form. This restriction is, however, unnecessary. Herein, linear combinations of divergence and product rule forms that have been discretized using diagonal-norm skew-symmetric summation-by-parts (SBP) operators, are shown to satisfy the sufficient conditions of the Lax-Wendroff theorem and thus are appropriate for simulations of discontinuous physical phenomena. Furthermore, special treatments are not required at the points that are near physical boundaries (i.e., discrete conservation is achieved throughout the entire computational domain, including the boundaries). Examples are presented of a fourth-order, SBP finite-difference operator with second-order boundary closures. Sixth- and eighth-order constructions are derived, and included in E. Narrow-stencil difference operators for linear viscous terms are also derived; these guarantee the conservative form of the combined operator.

Fisher, Travis C.↗

DOE OSTI2023

Online real-time learning of dynamical systems from noisy streaming data

Abstract Recent advancements in sensing and communication facilitate obtaining high-frequency real-time data from various physical systems like power networks, climate systems, biological networks, etc. However, since the data are recorded by physical sensors, it is natural that the obtained data is corrupted by measurement noise. In this paper, we present a novel algorithm for online real-time learning of dynamical systems from noisy time-series data, which employs the Robust Koopman operator framework to mitigate the effect of measurement noise. The proposed algorithm has three main advantages: (a) it allows for online real-time monitoring of a dynamical system; (b) it obtains a linear representation of the underlying dynamical system, thus enabling the user to use linear systems theory for analysis and control of the system; (c) it is computationally fast and less intensive than the popular extended dynamic mode decomposition (EDMD) algorithm. We illustrate the efficiency of the proposed algorithm by applying it to identify the Van der Pol oscillator, the chaotic attractor of the Henon map, the IEEE 68 bus system, and a ring network of Van der Pol oscillators.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Primitive quantum gates for dihedral gauge theories

We describe the simulation of dihedral gauge theories on digital quantum computers. The nonabelian discrete gauge group $D_N$-- the dihedral group -- serves as an approximation to $U(1)\times\mathbb{Z}_2$ lattice gauge theory. In order to carry out such a lattice simulation, we detail the construction of efficient quantum circuits to realize basic primitives including the nonabelian Fourier transform over $D_N$, the trace operation, and the group multiplication and inversion operations. For each case the required quantum resources scale linearly or as low-degree polynomials in $n=\log N$. We experimentally benchmark our gates on the Rigetti Aspen-9 quantum processor for the case of $D_4$. The fidelity of all $D_4$ gates was found to exceed $80\%$.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

Predicting Metabolic Reaction Networks with Perturbation-Theory Machine Learning (PTML) Models

Background: Checking the connectivity (structure) of complex Metabolic Reaction Networks(MRNs) models proposed for new microorganisms with promising properties is an importantgoal for chemical biology. Objective: In principle, we can perform a hand-on checking (Manual Curation). However, this is achallenging task due to the high number of combinations of pairs of nodes (possible metabolic reactions). Results: The CPTML linear model obtained using the LDA algorithm is able to discriminate nodes(metabolites) with the correct assignation of reactions from incorrect nodes with values of accuracy,specificity, and sensitivity in the range of 85-100% in both training and external validation dataseries. Methods: In this work, we used Combinatorial Perturbation Theory and Machine Learning techniquesto seek a CPTML model for MRNs >40 organisms compiled by Barabasis’ group. First, wequantified the local structure of a very large set of nodes in each MRN using a new class of node indexcalled Markov linear indices fk. Next, we calculated CPT operators for 150000 combinationsof query and reference nodes of MRNs. Last, we used these CPT operators as inputs of differentML algorithms. Conclusion: Meanwhile, PTML models based on Bayesian network, J48-Decision Tree and RandomForest algorithms were identified as the three best non-linear models with accuracy greaterthan 97.5%. The present work opens the door to the study of MRNs of multiple organisms usingPTML models.

Pharmacology & Pharmacy↗

NASA NTRS1972

A computer program for the geometrically nonlinear static and dynamic analysis of arbitrarily loaded shells of revolution, theory and users manual

A digital computer program known as SATANS (static and transient analysis, nonlinear, shells) for the geometrically nonlinear static and dynamic response of arbitrarily loaded shells of revolution is presented. Instructions for the preparation of the input data cards and other information necessary for the operation of the program are described in detail and two sample problems are included. The governing partial differential equations are based upon Sanders' nonlinear thin shell theory for the conditions of small strains and moderately small rotations. The governing equations are reduced to uncoupled sets of four linear, second order, partial differential equations in the meridional and time coordinates by expanding the dependent variables in a Fourier sine or cosine series in the circumferential coordinate and treating the nonlinear modal coupling terms as pseudo loads. The derivatives with respect to the meridional coordinate are approximated by central finite differences, and the displacement accelerations are approximated by the implicit Houbolt backward difference scheme with a constant time interval. The boundaries of the shell may be closed, free, fixed, or elastically restrained. The program is coded in the FORTRAN 4 language and is dimensioned to allow a maximum of 10 arbitrary Fourier harmonics and a maximum product of the total number of meridional stations and the total number of Fourier harmonics of 200. The program requires 155,000 bytes of core storage.

Ball, R. E.↗

DOE OSTI2020

Eigenmode analysis of the sheared-flow Z-pinch

Experiments have demonstrated that a Z-pinch can persist for thousands of times longer than the growth time of global magnetohydrodynamic (MHD) instabilities such as the m=0 sausage and m=1 kink modes. These modes have growth times on the order of ta=a/vi, where vi is the ion thermal speed and a is the pinch radius. Axial flows with duz/dr ≲ vi/a have been measured during the stable period, and the commonly accepted theory is that this amount of shear is sufficient to stabilize these modes as predicted by numerical studies using the ideal MHD equations. However, these studies only consider specific equilibrium profiles that typically have a modest magnitude for the logarithmic pressure gradient, qP≡d ln P/d ln r, and may not represent experimental conditions. Linear stability of the sheared-flow Z-pinch is studied here via a direct eigen-decomposition of the matrix operator obtained from the linear ideal MHD equations. Several equilibrium profiles with a large variation of qP are examined. Considering a practical range of k, 1/3 ≲ ka ≲ 10, it is shown that the shear required to stabilize m=0 modes can be expressed as duz/dr≥Cγ0/(ka)α. Here, γ0=γ0(ka) is the profile-specific growth rate in the absence of shear, which scales approximately with |qP|. Both C and α are profile-specific constants, but C is order unity and α≈1. It is further demonstrated that even a large value of shear, duz/dr=3vi/a, is not sufficient to provide linear stabilization of the m=1 kink mode for all profiles considered. This result is in contrast to the currently accepted theory predicting stabilization at much lower shear, duz/dr=0.1vi/a, and suggests that the experimentally observed stability cannot be explained within the linear ideal-MHD model.

Angus, J. R. (ORCID:0000000314740002)↗

DOE OSTI2024

Dualities among massive, partially massless and shift symmetric fields on (A)dS

We catalog all the electromagnetic-like dualities that exist between free dynamical bosonic fields of arbitrary symmetry type and mass on (anti-) de Sitter space in all dimensions, including dualities among the partially massless and shift symmetric fields. This generalizes to all these field types the well known fact that a massless p-form is dual to a massless (D − p − 2)-form in D spacetime dimensions. In the process, we describe the structure of the Weyl modules (the spaces of local operators linear in the fields and their derivative relations) for all the massive, partially massless and shift symmetric fields.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2026

Perturbative second-order optical susceptibility of bulk materials: a symmetry-enforced return to non-orthogonal localized basis sets

The second-order optical susceptibility of semiconductors $\chi^{(2)}_{ijk}(-2\omega;\omega,\omega)$ finds application in metrology, spectroscopy, telecommunications, material characterization, and quantum information. Pioneering calculations of $\chi^{(2)}_{ijk}(-2\omega;\omega,\omega)$ utilized non-orthogonal Gaussian orbitals centered at atoms. That formulation transitioned into plane-wave-based algorithms as time went by. As of late, nevertheless, multiple tools for calculating optical susceptibilities have recast the problem using Wannier (i.e. localized) orbitals, making a comeback onto frameworks based on localized basis sets. Here, in this work, we present an approach for calculating $\chi^{(2)}_{ijk}(-2\omega;\omega,\omega)$ reliant on numerical pseudo-atomic orbitals (PAOs) within perturbation theory in the velocity gauge. Its salient feature is a calculation of ‘Slater–Koster-like’ two-center integrals of the momentum operator in between PAOs identified by symmetry. The approach was successfully tested on paradigmatic cubic silicon carbide (3C-SiC) and gallium arsenide, for which linear responses are contributed as well.

Huamán, Angiolo [Univ. of Arkansas, Fayetteville, ↗

DOE OSTI2024

Deep Koopman Neural Network for Analyzing High-Energy-Density Simulations of Electrical Wire Explosions

Megaampere-scale electrical wire experiments (EWEs) provide a platform for studying magnetohydrodynamic (MHD) instability growth in magneto-inertial fusion (MIF) devices. Even when nonlinear simulations of these experiments can digitally reproduce much of the experimentally observed instability growth, interpreting the results and understanding mode growth and evolution can be non-trivial. As a first step toward providing better interpretation of these simulation features, this work investigates the use of a deep neural network that uses Koopman operator theory to analyze the dynamics of pulsed-power-driven explosions of EWEs. This deep neural network is trained on 1-D resistive MHD simulations of EWEs. This neural network learns to transform the nonlinear data into a lower-dimensional representation where the time dynamics are linear. Layers of this neural network are shown to learn features of the simulations, including the locations of shock waves and different physical regimes of the simulation. Using the learned features, the network can compress a time state of the simulation consisting of 5120 data point into a 36-parameter lower-dimensional latent space embedding. Furthermore, these embeddings are shown to be clustered in the latent space by initial radius and time state.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

Mitigation-Aware Bidding Strategies in Electricity Markets

Market power exercise in the electricity markets distorts market prices and diminishes social welfare. Many markets have implemented market power mitigation processes to eliminate the impact of such behavior. The design of mitigation mechanisms has a direct influence on investors' profitability and thus mid-/long-term resource adequacy. In order to evaluate the effectiveness of the existing market power mitigation mechanisms, this paper proposes a mitigation-aware strategic bidding model and studies the bidding strategies of the market participants under current practice. The proposed bidding model has a bilevel structure with strategic participant's profit maximization problem in the upper level and the dispatch problem for market operators in the lower level. In particular, the consideration of potential offer mitigation is incorporated as upper-level constraints based on the conduct and impact tests. This bilevel problem is reduced to a single-level mixed-integer linear program using the KKT optimality conditions, duality theory, and linearization. Numerical results illustrate how a strategic player can exercise market power to achieve a higher profit even under the current market power mitigation process and we analyze the social impact that the market power exercise results.

Wu, Yiqian↗

NASA NTRS1985

Ultrasonic characterization of changes in viscoelastic properties of epoxy during cure

A technique for using the longitudinal velocity (LV) of an ultrasonic wave to monitor the extent of cross linking (CL) during the cure of thermosetting resins is described. The method was developed by monitoring the rate of change in LV during the cure of a bisphenol-A epoxy resin with an amine adduct. The experiment included variations in the temperature and stoichiometry in order to express the rate of change in terms of the reaction kinetics. The pulse-echo method was used with a single transducer operating at 20 MHz. Numerical models were defined to account for the acoustic response of a single layer, the attenuation and the reflection coefficient. A linear relationship was observed between the inverse of the temperature and the log of the rate of change in the velocity, supporting the theory that the velocity could be used to monitor the extent of the cross-linking reaction. An activation energy of 11.9 kcal/mole was calculated for the mixture being investigated.

Winfree, W. P.↗

NASA NTRS1988

Convergence of Galerkin approximations for operator Riccati equations: A nonlinear evolution equation approach

An approximation and convergence theory was developed for Galerkin approximations to infinite dimensional operator Riccati differential equations formulated in the space of Hilbert-Schmidt operators on a separable Hilbert space. The Riccati equation was treated as a nonlinear evolution equation with dynamics described by a nonlinear monotone perturbation of a strongly coercive linear operator. A generic approximation result was proven for quasi-autonomous nonlinear evolution system involving accretive operators which was then used to demonstrate the Hilbert-Schmidt norm convergence of Galerkin approximations to the solution of the Riccati equation. The application of the results was illustrated in the context of a linear quadratic optimal control problem for a one dimensional heat equation.

Rosen, I. G.↗

NASA NTRS1993

Optimal fixed-finite-dimensional compensator for Burgers' equation with unbounded input/output operators

The problem of using reduced order dynamic compensators to control a class of nonlinear parabolic distributed parameter systems was considered. Concentration was on a system with unbounded input and output operators governed by Burgers' equation. A linearized model was used to compute low-order-finite-dimensional control laws by minimizing certain energy functionals. Then these laws were applied to the nonlinear model. Standard approaches to this problem employ model/controller reduction techniques in conjunction with linear quadratic Gaussian (LQG) theory. The approach used is based on the finite dimensional Bernstein/Hyland optimal projection theory which yields a fixed-finite-order controller.

Burns, John A.↗

NASA NTRS1996

Dynamics of Permanent-Magnet Biased Active Magnetic Bearings

Active magnetic radial bearings are constructed with a combination of permanent magnets to provide bias forces and electromagnets to generate control forces for the reduction of cost and the operating energy consumption. Ring-shaped permanent magnets with axial magnetization are attached to a shaft and share their magnet stators with the electromagnets. The magnet cores are made of solid iron for simplicity. A simplified magnetic circuit of the combined magnet system is analyzed with linear circuit theory by approximating the characteristics of permanent magnets with a linear relation. A linearized dynamical model of the control force is presented with the first-order approximation of the effects of eddy currents. Frequency responses of the rotor motion to disturbance inputs and the motion for impulsive forces are tested in the non-rotating state. The frequency responses are compared with numerical results. The decay of rotor speed due to magnetic braking is examined. The experimental results and the presented linearized model are similar to those of the all-electromagnetic design.

Fukata, Satoru↗

NASA NTRS1979

Robust stability of linear systems: Some computational considerations

The cases of both additive and multiplicative perturbations were discussed and a number of relationships between the two cases were given. A number of computational aspects of the theory were also discussed, including a proposed new method for evaluating general transfer or frequency response matrices. The new method is numerically stable and efficient, requiring only operations to update for new values of the frequency parameter.

Laub, A. J.↗

NASA NTRS1973

A linear accelerator for simulated micrometeors.

Review of the theory, design parameters, and construction details of a linear accelerator designed to impart meteoric velocities to charged microparticles in the 1- to 10-micron diameter range. The described linac is of the Sloan Lawrence type and, in a significant departure from conventional accelerator practice, is adapted to single particle operation by employing a square wave driving voltage with the frequency automatically adjusted from 12.5 to 125 kHz according to the variable velocity of each injected particle. Any output velocity up to about 30 km/sec can easily be selected, with a repetition rate of approximately two particles per minute.

Slattery, J. C.↗

NASA NTRS1988

Properties of aircraft tire materials

A summary is presented of measured elastomeric composite response suitable for linear structural and thermoelastic analysis in aircraft tires. Both real and loss properties are presented for a variety of operating conditions including the effects of temperature and frequency. Suitable micro-mechanics models are used for predictions of these properties for other material combinations and the applicability of laminate theory is discussed relative to measured values.

Dodge, Richard N.↗