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At least 397 records · Page 22
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Data-driven Vulnerability Analysis of Networked Pipeline System

This paper introduces an attack generation framework for evaluating the vulnerability of nonlinear networked pipeline systems. The vulnerability analysis is formulated as determining the presence of feasible attack sets, defined by boundary functions representing the effectiveness and stealthiness of attack signals with respect to the objective and attack detection module. The framework utilizes three data-driven models, including two discriminative models that learn the boundary functions and a generative model that produces elements of the feasible attack set. A new loss function ensures successful attack generation with high probability.

03 NATURAL GAS↗
DOE OSTI2024

Semi-Lagrangian nodal discontinuous Galerkin method for the BGK model

In this work, we propose a semi-Lagrangian (SL) nodal discontinuous Galerkin (DG) solver for the BGK equation. The BGK model was introduced by Bhatnagar, Gross, and Krook [1] as a relaxation model for the fundamental Boltzmann equation [5], which describes the kinetic dynamic of rarefied gases with a probability distribution function. The challenges of designing efficient numerical schemes for the Boltzmann equation mainly come from its high dimensionality and complicated nonlinear collision operator. The BGK model gains interests since it has much lower computational cost, due to the relatively simple structure of the relaxation operator in replacement of the collision operator, while simultaneously preserving several important physical properties, such as macroscopic quantities and dissipation of entropy.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Prediction of nonlinear specific heat during single crystal HMX phase transition

Here, we develop a thermodynamically consistent chemo-thermo-mechanical model for the β → δ phase transition of energetic HMX crystals. In contrast to previous models, which either considered specific heat to be a constant or utilized a calibrated function, this model provides novel expressions for the specific heats at constant volume and constant elastic strains derived directly from continuum mechanics. In addition, the model provides a novel prediction for the critical temperature at which the chemical heating rate achieves its extremum for Arrhenius kinetics. The numerical solution predicts highly nonlinear specific heat behavior including order of magnitude changes.

42 ENGINEERING↗
DOE OSTI2022

Effect of triangularity on ion-temperature-gradient-driven turbulence

The linear and nonlinear properties of ion-temperature-gradient-driven turbulence with adiabatic electrons are modeled for axisymmetric configurations for a broad range of triangularities δ, both negative and positive. Peak linear growth rates decrease with negative δ but increase and shift toward a finite radial wavenumber kx with positive δ. The growth-rate spectrum broadens as a function of kx with negative δ and significantly narrows with positive δ. Here, the effect of triangularity on linear instability properties can be explained through its impact on magnetic polarization and curvature. Nonlinear heat flux is weakly dependent on triangularity for |δ|≤0.5, decreasing significantly with extreme δ, regardless of sign. Zonal modes play an important role in nonlinear saturation in the configurations studied, and artificially suppressing zonal modes increased nonlinear heat flux by a factor of about four for negative δ, increasing with positive δ by almost a factor of 20. Proxies for zonal-flow damping and drive suggest that zonal flows are enhanced with increasing positive δ.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Systems and methods for dynamically reconfigurable artificial synapses and neurons with tunable activation functions

An ionic redox transistor comprises a solid channel, a solid reservoir layer, and a solid electrolyte layer disposed between the channel and the reservoir layer. The channel exhibits a substantially linear current-voltage relationship in a first range of voltages, and a nonlinear current-voltage relationship in a second range of voltages that is greater than the first range of voltages. One or both of the substantially linear current-voltage relationship or the nonlinear current-voltage relationship of the channel is varied by changing the concentration of ions such as oxygen vacancies in the channel. Ion or vacancy transport between the channel and the reservoir layer across the electrolyte layer occurs in response to applying a voltage between the channel and the reservoir layer. Subject to the first range of voltages, the channel can function as a synapse device. Subject to the second range of voltages, the channel can function as a neuron device.

Talin, Albert Alec↗
DOE OSTI2024

Phase-space entropy cascade and irreversibility of stochastic heating in nearly collisionless plasma turbulence

We consider a nearly collisionless plasma consisting of a species of “test particles” in one spatial and one velocity dimension, stirred by an externally imposed stochastic electric field—a kinetic analog of the Kraichnan model of passive advection. The mean effect on the particle distribution function is turbulent diffusion in velocity space—known as stochastic heating. Accompanying this heating is the generation of fine-scale structure in the distribution function, which we characterize with the collisionless (Casimir) invariant C 2 ∝ ∫ ∫ d x d v 〈 f 2 〉 —a quantity that here plays the role of (negative) entropy of the distribution function. We find that C 2 is transferred from large scales to small scales in both position and velocity space via a phase-space cascade enabled by both particle streaming and nonlinear interactions between particles and the stochastic electric field. We compute the steady-state fluxes and spectrum of C 2 in Fourier space, with k and s denoting spatial and velocity wave numbers, respectively. In our model, the nonlinearity in the evolution equation for the spectrum turns into a fractional Laplacian operator in k space, leading to anomalous diffusion. Whereas even the linear phase mixing alone would lead to a constant flux of C 2 to high s (towards the collisional dissipation range) at every k , the nonlinearity accelerates this cascade by intertwining velocity and position space so that the flux of C 2 is to both high k and high s simultaneously. Integrating over velocity (spatial) wave numbers, the k -space ( s -space) flux of C 2 is constant down to a dissipation length (velocity) scale that tends to zero as the collision frequency does, even though the rate of collisional dissipation remains finite. The resulting spectrum in the inertial range is a self-similar function in the ( k , s ) plane, with power-law asymptotics at large k and s . Our model is fully analytically solvable, but the asymptotic scalings of the spectrum can also be found via a simple phenomenological theory whose key assumption is that the cascade is governed by a “critical balance” in phase space between the linear and nonlinear timescales. We argue that stochastic heating is made irreversible by this entropy cascade and that, while collisional dissipation accessed via phase mixing occurs only at small spatial scales rather than at every scale as it would in a linear system, the cascade makes phase mixing even more effective overall in the nonlinear regime than in the linear one. Published by the American Physical Society 2024

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

A Tensor Network-Based Quantum Algorithm for the Nonlinear 1D Burgers' Equation

In this work, we implement a tensor network-based quantum algorithm to solve unsteady, nonlinear partial differential equations (PDEs). The challenge lies in how to effectively represent, encode, process, and evolve the nonlinear system of PDEs on quantum computers. We will discuss the new techniques using the compressible 1-dimensional (1D) Burgers' equation as an example, because it represents the fundamental nonlinear feature and yet removes certain complexity in physics, allowing us to focus on the design of quantum algorithms. Previous attempts to solve nonlinear PDEs in quantum computation have often involved storing multiple copies of solutions or employing linearizations. Neither is practical due to exponential scaling with evolution time or insufficient solution accuracy. Our framework is based on matrix product states (MPSs) and matrix product operators (MPOs). For example, the velocity field is represented by MPS, whereas the linear and nonlinear spatial differential terms of the velocity field are processed by MPOs. Our primary focus herein is to verify and validate the various tensor network components of the algorithm using solutions obtained by the classical algorithms on high performance computing (HPC) architectures. We use a classical time marching method to demonstrate the functionality of the tensor network operations to model the PDE and their robustness with the time evolution of the system. Our classical simulation results demonstrate the utility of tensor network-based operations in modeling nonlinear PDEs and highlight the necessity as well as potential advantages of using quantum simulations for these techniques.

Gopalakrishnan Meena, Murali [ORNL] (ORCID:0000000↗
DOE OSTI2024

Nonlinear susceptibilities for weakly turbulent magnetized plasma: Electromagnetic formalism

This is a companion paper to the previous work [P. H. Yoon, Phys. Plasmas 31, 032309 (2024)] in which the nonlinear susceptibilities of weakly turbulent magnetized plasma are derived under a simplifying assumption of electrostatic interaction. The present paper extends the analysis to a general situation of electromagnetic interaction. The main novelty of the previous and present papers is that by employing the Bessel function addition theorem, the mathematical definitions for the susceptibilities are substantially simplified, a procedure that has not been discussed in the existing literature. In the present paper, a full set of Maxwell’s equations are considered in conjunction with the nonlinear Vlasov equation, which is solved by a perturbative method. The result is a fully general nonlinear susceptibility, given in tensorial form, which is applicable for weakly turbulent magnetized plasmas.

Materials Science↗
DOE OSTI2020

Self‐Assembled NiO Nanocrystal Arrays as Memristive Elements

Abstract Memristive switching, a nonlinear current–voltage ( I – V ) characteristic, has seen a tremendous surge in interest as an approach to achieve implementation of synaptic functions. The memristive switching behavior of self‐assembled NiO nanocrystals is investigated via scanning probe microscopy, based on first‐order reversal curve current–voltage spectroscopy. Synaptic switching is clearly observed as a direct consequence of filament growth (i.e., gradually increased conductance) in the nanocrystals. A spatial dependency of the conduction in the nanocrystals suggests that there is a localization of the switching filament. The current understanding of this localization ignores features related to local lateral variation current, which can generate an excessive local heat and temperature such as electrical dissipation. The observation of low electrical dissipation at the edge of the nanocrystals shows that less energy is wasted as heat such that the bias applied can be utilized more efficiently to assist the nucleation of the filament and thus reduces the power consumption. Electrical power dissipation is also found to scale with nanocrystal height and has spatial dependence within the nanocrystals. The combination of synaptic switching and high density of the nanocrystals demonstrate that it is feasible to exploit them to create a basic architecture for neuromorphic memory devices.

Kurnia, Fran↗
DOE OSTI2020

Spectral fluctuations in the Sachdev-Ye-Kitaev model

We present a detailed quantitative analysis of spectral correlations in the Sachdev-Ye-Kitaev (SYK) model. We find that the deviations from universal Random Matrix Theory (RMT) behavior are due to a small number of long-wavelength fluctuations (of the order of the number of Majorana fermions N ) from one realization of the ensemble to the next one. These modes can be parameterized effectively in terms of Q-Hermite orthogonal polynomials, the main contribution being due to scale fluctuations for which we give a simple analytical estimate. Our numerical results for N = 32 show that only the lowest eight polynomials are needed to eliminate the nonuniversal part of the spectral fluctuations. The covariance matrix of the coefficients of this expansion can be obtained analytically from low-order double-trace moments. We evaluate the covariance matrix of the first six moments and find that it agrees with the numerics. We also analyze the spectral correlations in terms of a nonlinear σ-model, which is derived through a Fierz transformation, and evaluate the one and two-point spectral correlation functions to two-loop order. The wide correlator is given by the sum of the universal RMT result and corrections whose lowest-order term corresponds to scale fluctuations. However, the loop expansion of the σ-model results in an ill-behaved expansion of the resolvent, and it gives universal RMT fluctuations not only for q= 4 or higher even q-body interactions, but also for the q= 2 SYK model albeit with a much smaller Thouless energy while the correct result in this case should have been Poisson statistics. In our numerical studies we analyze the number variance and spectral form factor for N = 32 and q = 4. We show that the quadratic deviation of the number variance for large energies appears as a peak for small times in the spectral form factor. After eliminating the long-wavelength fluctuations, we find quantitative agreement with RMT up to an exponentially large number of level spacings for the number variance or exponentially short times in the case of the spectral form factor.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Landau discriminants

Scattering amplitudes in quantum field theories have intricate analytic properties as functions of the energies and momenta of the scattered particles. In perturbation theory, their singularities are governed by a set of nonlinear polynomial equations, known as Landau equations, for each individual Feynman diagram. The singularity locus of the associated Feynman integral is made precise with the notion of the Landau discriminant, which characterizes when the Landau equations admit a solution. In order to compute this discriminant, we present approaches from classical elimination theory, as well as a numerical algorithm based on homotopy continuation. These methods allow us to compute Landau discriminants of various Feynman diagrams up to 3 loops, which were previously out of reach. For instance, the Landau discriminant of the envelope diagram is a reducible surface of degree 45 in the three-dimensional space of kinematic invariants. We investigate geometric properties of the Landau discriminant, such as irreducibility, dimension and degree. In particular, we find simple examples in which the Landau discriminant has codimension greater than one. Furthermore, we describe a numerical procedure for determining which parts of the Landau discriminant lie in the physical regions. In order to study degenerate limits of Landau equations and bounds on the degree of the Landau discriminant, we introduce Landau polytopes and study their facet structure. Finally, we provide an efficient numerical algorithm for the computation of the number of master integrals based on the connection to algebraic statistics.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Accelerated Sparse Recovery via Gradient Descent with Nonlinear Conjugate Gradient Momentum

This paper applies an idea of adaptive momentum for the nonlinear conjugate gradient to accelerate optimization problems in sparse recovery. Specifically, we consider two types of minimization problems: a (single) differentiable function and the sum of a non-smooth function and a differentiable function. In the first case, we adopt a fixed step size to avoid the traditional line search and establish the convergence analysis of the proposed algorithm for a quadratic problem. This acceleration is further incorporated with an operator splitting technique to deal with the non-smooth function in the second case. As a result, we use the convex ι 1 and the nonconvex ι 1 – ι 2 functionals as two case studies to demonstrate the efficiency of the proposed approaches over traditional methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Heteroanionic Control of Exemplary Second-Harmonic Generation and Phase Matchability in 1D LiAsS 2– x Se x

The isostructural heteroanionic compounds β-LiAsS 2–x Se x (x = 0, 0.25, 1, 1.75, 2) show a positive correlation between selenium content and second-harmonic response and greatly outperform the industry standard AgGaSe 2 . These materials crystallize in the noncentrosymmetric space group Cc as one-dimensional $\frac{1}{∞}$ [AsQ 2 ] - (Q = S, Se, S/Se) chains consisting of corner-sharing AsQ3 trigonal pyramids with charge-balancing Li + atoms interspersed between the chains. LiAsS 2–x Se x melts congruently for 0 ≤ x ≤ 1.75, but when the Se content exceeds x = 1.75, crystallization is complicated by a phase transition. This behavior is attributed to the β- to α-phase transition present in LiAsSe 2 , which is observed in the Se-rich compositions. The band gap decreases with increasing Se content, starting at 1.63 eV (LiAsS 2 ) and reaching 1.06 eV (β-LiAsSe 2 ). Second-harmonic generation measurements as a function of wavelength on powder samples of β-LiAsS 2–x Se x show that these materials exhibit significantly higher nonlinearity than AgGaSe 2 (d 36 = 33 pm/V), reaching a maximum of 61.2 pm/V for LiAsS 2 . In comparison, single-crystal measurements for LiAsSSe yielded a d eff = 410 pm/V. LiAsSSe, LiAsS 0.25 Se 1.75 , and β-LiAsSe 2 show phase-matching behavior for incident wavelengths exceeding 3 μm. The laser-induced damage thresholds from two-photon absorption processes are on the same order of magnitude as AgGaSe 2 , with S-rich materials slightly outperforming AgGaSe 2 and Se-rich materials slightly underperforming AgGaSe 2 .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Estimation of the orientation of stress in the Earth’s crust without earthquake or borehole data

Abstract Mechanical stress acting in the Earth’s crust is a fundamental property that is important for a wide range of scientific and engineering applications. The orientation of maximum horizontal compressive stress can be estimated by inverting earthquake source mechanisms and measured directly from borehole-based measurements, but large regions of the continents have few or no observations. Here we present an approach to determine the orientation of maximum horizontal compressive stress by measuring stress-induced anisotropy of nonlinear susceptibility, which is the derivative of elastic modulus with respect to strain. Laboratory and Earth experiments show that nonlinear susceptibility is azimuthally dependent in an anisotropic stress field and is maximum in the orientation of maximum horizontal compressive stress. We observe this behavior in the Earth—in Oklahoma and New Mexico, U.S.A, where maximum nonlinear susceptibility coincides with the orientation of maximum horizontal compressive stress measured using traditional methods. Our measurements use empirical Green’s functions and solid-earth tides and can be applied at different temporal and spatial scales.

58 GEOSCIENCES↗
DOE OSTI2022

Faster network disruption from layered oscillatory dynamics

Nonlinear complex network-coupled systems typically have multiple stable equilibrium states. Following perturbations or due to ambient noise, the system is pushed away from its initial equilibrium, and, depending on the direction and the amplitude of the excursion, it might undergo a transition to another equilibrium. It was recently demonstrated [M. Tyloo, J. Phys. Complex. 3 03LT01 (2022)] that layered complex networks may exhibit amplified fluctuations. Here, I investigate how noise with system-specific correlations impacts the first escape time of nonlinearly coupled oscillators. Interestingly, I show that, not only the strong amplification of the fluctuations is a threat to the good functioning of the network but also the spatial and temporal correlations of the noise along the lowest-lying eigenmodes of the Laplacian matrix. Finally, I analyze first escape times on synthetic networks and compare noise originating from layered dynamics to uncorrelated noise.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

A Data-Driven Approach for High-Impedance Fault Localization in Distribution Systems [SWR-24-13]

This software provides a data-driven approach for efficiently identifying high impedance faults (HIFs) in distribution systems. To tackle the nonlinearity of the voltage current trajectory of HIFs, we first formulate linear least squares problems to approximate the trajectory with piecewise functions. Then we collect the function features of all segments as inputs and use the support vector machine approach to efficiently identify HIFs at different locations.

Zhou, Yuqi↗
DOE OSTI2026

Using Machine Learning to Understand Electric and Hybrid Vehicles Ownership in Burdened and Nonburdened Communities

Transitioning to electric and hybrid vehicles (EHVs) for all communities is a pivotal step toward sustainable transportation and environmental conservation. This paper aims to understand the adoption of EHVs, focusing on burdened communities (BCs) in the United States. The EHV ownership-based analysis combines two datasets—behavioral data from the Puget Sound Regional Travel Survey integrated with BCs (Justice40) data covering transportation insecurity, environmental burden, social vulnerability, health vulnerability, and climate and disaster risk burden. After creating this unique database, descriptive analysis and modeling are used to analyze the data and predict EHV ownership in the future. Specifically, we use a new method that combines particle swarm optimization (PSO) with a stacking model named PSO-Stacking, which incorporates heterogeneous base learners of machine learning and deep learning. PSO applies a customized objective function to select the optimal hyperparameters for heterogeneous learners within the stacking model, effectively addressing challenges such as multicollinearity, data imbalance, nonlinearity, and overfitting. The proposed solution covers more accurate results than standard benchmark models for EHV ownership in BCs and non-BCs. In addition, the results of the PSO-Stacking method are explained using the local interpretable model-agnostic explanations technique. Results show a negative correlation between the BCs indicators, that is, higher transportation insecurity associated with lower EHV ownership. Furthermore, BCs have higher future climate risk scores, diesel particulate matter levels, and PM2.5 in the air than non-BCs because of higher conventional vehicle ownership. These communities are at higher risk and can benefit from electrification, EV infrastructure, and EV policies to address environmental challenges.

Aslam, Zeeshan [ORNL]↗
DOE OSTI2023

Learning Symbolic Expressions: Mixed-Integer Formulations, Cuts, and Heuristics

Here, in this paper, we consider the problem of learning a regression function without assuming its functional form. This problem is referred to as symbolic regression. An expression tree is typically used to represent a solution function, which is determined by assigning operators and operands to the nodes. Cozad and Sahinidis propose a nonconvex mixed-integer nonlinear program (MINLP), in which binary variables are used to assign operators and nonlinear expressions are used to propagate data values through nonlinear operators, such as square, square root, and exponential. We extend this formulation by adding new cuts that improve the solution of this challenging MINLP. We also propose a heuristic that iteratively builds an expression tree by solving a restricted MINLP. We perform computational experiments and compare our approach with a mixed-integer program–based method and a neural network–based method from the literature.

97 MATHEMATICS AND COMPUTING↗