Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “linearization”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Multirate linearly-implicit GARK schemes

Many complex applications require the solution of initial-value problems where some components change fast, while others vary slowly. Multirate schemes apply different step sizes to resolve different components of the system, according to their dynamics, in order to achieve increased computational efficiency. The stiff components of the system, fast or slow, are best discretized with implicit base methods in order to ensure numerical stability. To this end, linearly implicit methods are particularly attractive as they solve only linear systems of equations at each step. This paper develops the Multirate GARK-ROS/ROW (MR-GARK-ROS/ROW) framework for linearly-implicit multirate time integration. The order conditions theory considers both exact and approximative Jacobians. The effectiveness of implicit multirate methods depends on the coupling between the slow and fast computations; an array of efficient coupling strategies and the resulting numerical schemes are analyzed. Multirate infinitesimal step linearly-implicit methods, that allow arbitrarily small micro-steps and offer extreme computational flexibility, are constructed. The new unifying framework includes existing multirate Rosenbrock(-W) methods as particular cases, and opens the possibility to develop new classes of highly effective linearly implicit multirate integrators.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Linear model decision trees as surrogates in optimization of engineering applications

Machine learning models are promising as surrogates in optimization when replacing difficult to solve equations or black-box type models. This work demonstrates the viability of linear model decision trees as piecewise-linear surrogates in decision-making problems. Linear model decision trees can be represented exactly in mixed-integer linear programming (MILP) and mixed-integer quadratic constrained programming (MIQCP) formulations. Furthermore, they can represent discontinuous functions, bringing advantages over neural networks in some cases. We present several formulations using transformations from Generalized Disjunctive Programming (GDP) formulations and modifications of MILP formulations for gradient boosted decision trees (GBDT). We then compare the computational performance of these different MILP and MIQCP representations in an optimization problem and illustrate their use on engineering applications. Importantly, we observe faster solution times for optimization problems with linear model decision tree surrogates when compared with GBDT surrogates using the Optimization and Machine Learning Toolkit (OMLT).

42 ENGINEERING↗
DOE OSTI2025

Hyperplane decision trees as piecewise linear surrogate models for chemical process design

Recent trends in chemical engineering research point towards an increasing reliance on data-driven modeling approaches. Neural networks, for instance, have proven to be accurate when data is plentiful and high-dimensional, but in many cases, they require computationally-intensive training procedures. Here, in this work, we describe hyperplane decision trees (HT) as a highly expressive and low-compute machine learning model architecture. These models are locally linear and have linear decision boundaries, resulting in a piecewise linear model of the data. This property allows them to be converted into mixed-integer linear constraints which can be globally optimized. Our open-source PyTorch implementation of this method is a fast, flexible, and accessible way to build accurate piecewise linear models of data.

Decision trees↗
DOE OSTI2016

Impact of ADC non-linearities on the sensitivity to sterile keV neutrinos with a KATRIN-like experiment

Here, ADC non-linearities are a major systematic effect in the search for keV-scale sterile neutrinos with tritium β-decay experiments like KATRIN. They can significantly distort the spectral shape and thereby obscure the tiny kink-like signature of a sterile neutrino. In this work we demonstrate various mitigation techniques to reduce the impact of ADC non-linearities on the tritium β-decay spectrum to a level of < ppm. The best results are achieved with a multi-pixel (≥ 10 4 pixels) detector using full waveform digitization. In this case, active-to-sterile mixing angles of the order of sin 2 θ = 10 –7 would be accessible from the viewpoint of ADC non-linearities. With purely peak-sensing ADCs a comparable sensitivity could be reached with highly linear ADCs, sufficient non-linearity corrections or by increasing the number of pixels to ≥ 10 5 .

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2022

A high accuracy/resolution spectral element/Fourier–Galerkin method for the simulation of shoaling non-linear internal waves and turbulence in long domains with variable bathymetry

A high-order hybrid continuous-Galerkin numerical method, designed for the simulation of non-linear, non -hydrostatic internal waves and turbulence in long computational domains with complex bathymetry, is presented. The spatial discretization in the non-periodic wave-propagating directions, utilizes the nodal spectral element method. Such a high-order element-based discretization allows the highly accurate representation of complex domain geometry along with the flexibility of concentrating resolution in areas of interest. Under the assumption of the normal-to-isobath propagation of non-linear internal waves, a third periodic direction is incorporated via a Fourier-Galerkin discretization. The distinct non-hydrostatic nature of non-linear internal waves and, any instabilities and turbulence therein, necessitates the numerically challenging solution of the pressure Poisson problem. A defining feature of this work is the application of a domain decomposition approach, combined with block-Jacobi/deflation-based preconditioning to the pressure Poisson problem. Such a combined approach is particularly suitable for the long high aspect-ratio complex domains of interest and enables the efficient high-accuracy reproduction of the non-hydrostatic dynamics of non-linear internal waves. Implementation details are also described in the context of the stability of the solver and its parallelization strategy. A series of benchmarks of increasing complexity demonstrate the robustness of the flow solver. The benchmarks culminate with the three-dimensional simulation of a convectively breaking mode-one non-linear internal wave over a realistic South-China-Sea bathymetric transect and background current/stratification profiles.

Deflation↗
DOE OSTI2016

Production of Linear Octenes from Oligomerization of 1-Butene over Carbon-Supported Cobalt Catalysts

Here, linear octenes were produced in high (70–85%) selectivity from oligomerization of liquid 1-butene using carbon-supported cobalt oxide catalysts in a continuous flow reactor. The liquid products were characterized by two-dimensional gas chromatography–mass spectrometry. Above 95% of the oligomers were C8 olefins, with the other products primarily being branched C12 olefins. The linear octene products at a conversion of 9.77% decreased in selectivity according to 3-octene > trans-2-octene > cis-2-octene > 4-octene. Methyl-heptenes including trans/cis-5-methyl-2-heptene > trans/cis-5-methyl-3-heptene > trans-3-methyl-2-heptene (at the lowest conversion) were the other major products summing to 15.6%. The selectivity of linear octenes decreased from 84 to 78% as the conversion increased from 10% to 29%. The product distribution suggests the reaction pathway involves a head-to-head coupling of two 1-butene molecules to form internal linear octenes. Head-to-tail coupling of two 1-butene molecules or a coupling between 1-butene and 2-butene forms the observed methyl-heptenes. The rate of head-to-head coupling is higher than the rate of head-to-tail or the rate of 1-butene to 2-butene coupling as indicated by the higher selectivity of linear octenes. The activated catalyst contained both Co 3 O 4 and CoO as confirmed by X-ray diffraction (XRD), in situ Raman spectroscopy, and X-ray absorption spectroscopy. The cobalt oxide particle size was estimated to be between 5 and 10 nm by high-resolution transmission electron microscopy and XRD. The Co 3 O 4 /CoO ratio decreased with increasing pretreatment temperature. Metallic cobalt, which has a low catalytic activity, formed at 550 °C.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Linear instabilities in the hot-ion regime in a high-field spherical tokamak

Abstract The present operating high-field compact spherical tokamak ST40 is an important step toward an ST-based fusion reactor (Gryaznevich and Asunta 2017 Fusion Eng. Des. 123 177; McNamara 2023 Nucl. Fusion 63 054002). Temperature and density profiles and their uncertainties in recent hot ion ST40 plasmas with central ion temperatures exceeding 8.6 keV, have been inferred using an integrated analysis of several diagnostics including line-of-sight integration and volume average measurements, as well as limited profile information from a charge-exchange-recombination spectrometer. A linear gyrokinetic stability analysis has been carried out to identify the most unstable micro-instabilities in these hot ion plasmas. In one of these plasmas, it is found that linear growth rates of both ion- and electron-scale ( k θ ρ s ⩾ 0.2 where k θ is the poloidal wavenumber and ρ s is the ion gyro-radius with sound speed) modes decrease from the edge toward the core of the plasma (i.e. from ρ = 0.8 to 0.3 where ρ is the square root of the normalized magnetic flux), while the change of linear growth rates at k θ ρ s < 0.2 is non-monotonic. In particular, at ρ = 0.3 no unstable mode was found at k θ ρ s > 5 , and about an order of magnitude reduction in the maximum linear growth rate in the ion-scale wavenumber range of 0.2 ⩽ k θ ρ s < 1 is seen at ρ = 0.3 compared with the ρ = 0.8 location. It is found through parametric scans that while the ion temperature gradient (ITG) mode/trapped electron mode (TEM) and kinetic ballooning mode (KBM)/kinetic shear Alfvén (KSA) mode are more important in the plasma core, ubiquitous mode (UM) is found to be the important ion-scale instability at ρ ⩾ 0.6 . At ρ = 0.8, two instabilities are found at the electron scale, with one being the typical electrostatic electron temperature gradient (ETG) mode at ρ e scale and beyond and the other being an unidentified low-real-frequency instability (at the intermediate scale between electron and ion gyroradii) which can propagate in the ion direction and is driven by ETG. The existence of UM at the ion scale and the low-real-frequency instability and ETG mode at the electron scale at ρ = 0.8 is supported by an extensive linear gyrokinetic stability analysis of another ST40 hot ion plasma in a wider parametric range, taking into account the uncertainties in the experimental profiles.

ubiquitous mode↗
DOE OSTI2025

Randomized Adiabatic Quantum Linear Solver Algorithm with Optimal Complexity Scaling and Detailed Running Costs

Solving linear systems of equations is a fundamental problem with a wide variety of applications across many fields of science, and there is increasing effort to develop quantum linear solver algorithms. Subaşı et al. [Phys. Rev. Lett. 122, 060504 (2019)] proposed a randomized algorithm inspired by adiabatic quantum computing, based on a sequence of random Hamiltonian simulation steps, with suboptimal scaling in the condition number 𝜅 of the linear system and the target error 𝜖. Here we go beyond these results in several ways. Firstly, using filtering [Lin and Tong, Quantum 4, 361 (2020)] and Poissonization techniques [Cunningham and Roland, ArXiv:2406.03972 (2024)], the algorithm complexity is improved to the optimal scaling 𝑂⁡(𝜅⁢log (1/𝜖))—an exponential improvement in 𝜖, and a shaving of a log 𝜅 scaling factor in 𝜅. Secondly, the algorithm is further modified to achieve constant factor improvements, which are vital as we progress towards hardware implementations on fault-tolerant devices. We introduce a cheaper randomized walk operator method replacing Hamiltonian simulation—which also removes the need for potentially challenging classical precomputations; randomized routines are sampled over optimized random variables; circuit constructions are improved. We obtain a closed formula rigorously upper bounding the expected number of times one needs to apply a block-encoding of the linear system matrix to output a quantum state encoding the solution to the linear system. The upper bound is 837⁢𝜅 at 𝜖 = 10 −10 for Hermitian matrices.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

NREL's Improved Linearity Testing of Photovoltaic Reference Cells

Photovoltaic devices are characterized under standard testing conditions that include a defined reference spectrum and total irradiance. International standards for reference cell calibrations require that reported reference cell response (typically Isc) vs. total irradiance must be linear. How can linearity be efficiently determined? In 2006 NREL developed a test bed, based on the "two-lamp method" that provided a low cost, but low accuracy method for determining whether cell response was linear with irradiance. This paper describes very simple changes to NREL's historical method [1] for determining linearity that yield greatly improved results. It also describes a method that can be used to quantify and correct for non-linearity.

41 EE - Solar Energy Technologies Office (EE-4S)↗
DOE OSTI2019

Linear Distribution System State Estimation Using Synchrophasor Data and Pseudo-Measurement

State estimation is often a challenging task in distribution systems due to deploying a limited number of measurement devices. Moreover, the integration of precise distributionlevel phasor measurement unites, a.k.a micro-PMUs, along with inaccurate pseudo-measurements in state estimation introduces another challenge. These issues might decrease the efficiency of traditional standard weighted least squares (WLS) for distribution system state estimation. This paper proposes a novel linear distribution system state estimation with taken different types of measurements, including micro-PMU measurements and line current measurements, into account. To involve pseudomeasurements into the linear state estimation, a linearization method based on the Taylor’s approximation is adopted to reformulate pseudo-measurement functions in a linear form. The results obtained via numerical simulations show that the proposed linear state estimation method performs similarly to the standard nonlinear WLS estimator. In addition, the sensitivity analyses results show that our method has a better performance compared to WLS once a limited number of highly precise micro-PMUs are accompanied with inaccurate pseudo-measurements in state estimation.

State estimation Distribution system Micro-PMU Lin↗
DOE OSTI2016

TU-H-BRA-01: The Physics of High Power Radiofrequency Isolation in a Novel Compact Linear Accelerator Based MRI Guided Radiation Therapy System

Purpose: To develop a method for isolating the radiofrequency waves emanating from linear accelerator components from the magnetic resonance imaging (MRI) system of an integrated MRI-linac. Methods: An MRI-guided radiation therapy system has been designed that integrates a linear accelerator with simultaneous MR imaging. The radiofrequency waves created by the accelerating process would degrade MR image quality, so a method for containing the radiofrequency waves and isolating the MR imager from them was developed. The linear accelerator radiofrequency modulator was placed outside the room, so a filter was designed to eliminate the radiofrequency corresponding to the proton Larmour frequency of 14.7 MHz. Placing the radiofrequency emitting components in a typical Faraday cage would have reduced the radiofrequency emissions, but the design would be susceptible to small gaps in the shield due to the efficiency of the Faraday cage reflecting internal radiofrequency emissions. To reduce internal radiofrequency reflections, the Faraday cage was lined with carbon fiber sheets. Carbon fiber has the property of attenuating the radiofrequency energy so that the overall radiofrequency field inside the Faraday cage is reduced, decreasing any radiofrequency energy emitted from small gaps in the cage walls. Results: Within a 1.2 MHz band centered on the Larmor frequency, the radiofrequency (RF) leakage from the Faraday cage was measured to be −90 dB with no RF on, −40 dB with the RF on and no shield, returning to −90 dB with the RF on and shields in place. The radiofrequency filter attenuated the linear accelerator modulator emissions in the 14.7 MHz band by 70 dB. Conclusions: One of the major challenges in designing a compact linear accelerator based MRI-guided radiation therapy system, that of isolating the high power RF system from the MRI, has been solved. The measured radiofrequency emissions are sufficiently small to enable system integration. This research was funded by ViewRay, Inc., Oakwood, OH.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

TU-H-BRA-02: The Physics of Magnetic Field Isolation in a Novel Compact Linear Accelerator Based MRI-Guided Radiation Therapy System

Purpose: To develop a method for isolating the MRI magnetic field from field-sensitive linear accelerator components at distances close to isocenter. Methods: A MRI-guided radiation therapy system has been designed that integrates a linear accelerator with simultaneous MR imaging. In order to accomplish this, the magnetron, port circulator, radiofrequency waveguide, gun driver, and linear accelerator needed to be placed in locations with low magnetic fields. The system was also required to be compact, so moving these components far from the main magnetic field and isocenter was not an option. The magnetic field sensitive components (exclusive of the waveguide) were placed in coaxial steel sleeves that were electrically and mechanically isolated and whose thickness and placement were optimized using E&M modeling software. Six sets of sleeves were placed 60° apart, 85 cm from isocenter. The Faraday effect occurs when the direction of propagation is parallel to the magnetic RF field component, rotating the RF polarization, subsequently diminishing RF power. The Faraday effect was avoided by orienting the waveguides such that the magnetic field RF component was parallel to the magnetic field. Results: The magnetic field within the shields was measured to be less than 40 Gauss, significantly below the amount needed for the magnetron and port circulator. Additional mu-metal was employed to reduce the magnetic field at the linear accelerator to less than 1 Gauss. The orientation of the RF waveguides allowed the RT transport with minimal loss and reflection. Conclusion: One of the major challenges in designing a compact linear accelerator based MRI-guided radiation therapy system, that of creating low magnetic field environments for the magnetic-field sensitive components, has been solved. The measured magnetic fields are sufficiently small to enable system integration. This work supported by ViewRay, Inc.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2018

Energy flow polynomials: a complete linear basis for jet substructure

We introduce the energy flow polynomials: a complete set of jet substructure observables which form a discrete linear basis for all infrared- and collinear-safe observables. Energy flow polynomials are multiparticle energy correlators with specific angular structures that are a direct consequence of infrared and collinear safety. We establish a powerful graph-theoretic representation of the energy flow polynomials which allows us to design efficient algorithms for their computation. Many common jet observables are exact linear combinations of energy flow polynomials, and we demonstrate the linear spanning nature of the energy flow basis by performing regression for several common jet observables. Using linear classification with energy flow polynomials, we achieve excellent performance on three representative jet tagging problems: quark/gluon discrimination, boosted W tagging, and boosted top tagging. Lastly, the energy flow basis provides a systematic framework for complete investigations of jet substructure using linear methods.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Non-linear flow modes of identified particles in Pb-Pb collisions at $ \sqrt{s_{\mathrm{NN}}} $ = 5.02 TeV

The pT-differential non-linear flow modes, v 4,22 , v 5,32 , v 6,33 and v 6,222 for π ± , K ± , K$^0_S$ , $p + \bar{p}, Λ + \bar{Λ}$ and &straightphi;-meson have been measured for the first time at $\sqrt{s_{NN}}$ = 5.02 TeV in Pb-Pb collisions with the ALICE detector at the Large Hadron Collider. The results were obtained with a multi-particle technique, correlating the identified hadrons with reference charged particles from a different pseudorapidity region. These non-linear observables probe the contribution from the second and third order initial spatial anisotropy coefficients to higher flow harmonics. All the characteristic features observed in previous p T -differential anisotropic flow measurements for various particle species are also present in the non-linear flow modes, i.e. increase of magnitude with increasing centrality percentile, mass ordering at low p T and particle type grouping in the intermediate p T range. Hydrodynamical calculations (iEBE-VISHNU) that use different initial conditions and values of shear and bulk viscosity to entropy density ratios are confronted with the data at low transverse momenta. These calculations exhibit a better agreement with the anisotropic flow coefficients than the non-linear flow modes. These observations indicate that non-linear flow modes can provide additional discriminatory power in the study of initial conditions as well as new stringent constraints to hydrodynamical calculations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2017

Implicit and Implicit–Explicit Strong Stability Preserving Runge–Kutta Methods with High Linear Order

Strong stability preserving (SSP) time discretizations preserve the monotonicity properties satisfied by the spatial discretization when coupled with the first order forward Euler, under a certain time-step restriction. The search for high order strong stability preserving time-stepping methods with high order and large allowable time-step has been an active area of research. It is known that implicit SSP Runge–Kutta methods exist only up to sixth order; however, if we restrict ourselves to solving only linear autonomous problems, the order conditions simplify and we can find implicit SSP Runge–Kutta methods of any linear order. In the current work we find implicit SSP Runge–Kutta methods with high linear order p lin ≤ 9 and nonlinear orders p = 2,3,4, that are optimal in terms of allowable SSP time-step. Next, we formulate a novel optimization problem for implicit–explicit (IMEX) SSP Runge–Kutta methods and find optimized IMEX SSP Runge–Kutta pairs that have high linear order p lin ≤ 7 and nonlinear orders up to p = 4. Here, we also find implicit methods with large linear stability regions that pair with known explicit SSP Runge–Kutta methods. These methods are then tested on sample problems to demonstrate the sharpness of the SSP coefficient and the typical behavior of these methods on test problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Optimal Linear Responses for Markov Chains and Stochastically Perturbed Dynamical Systems

The linear response of a dynamical system refers to changes to properties of the system when small external perturbations are applied. We consider the little-studied question of selecting an optimal perturbation so as to (i) maximise the linear response of the equilibrium distribution of the system, (ii) maximise the linear response of the expectation of a specified observable, and (iii) maximise the linear response of the rate of convergence of the system to the equilibrium distribution. We also consider the inhomogeneous, sequential, or time-dependent situation where the governing dynamics is not stationary and one wishes to select a sequence of small perturbations so as to maximise the overall linear response at some terminal time. We develop the theory for finite-state Markov chains, provide explicit solutions for some illustrative examples, and numerically apply our theory to stochastically perturbed dynamical systems, where the Markov chain is replaced by a matrix representation of an approximate annealed transfer operator for the random dynamical system.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Hyperentanglement concentration of nonlocal two-photon six-qubit systems with linear optics

Hyperentanglement, the entangled states in the multiple degrees of freedom (DOFs) of a photon system simultaneously, has attracted much attention recently as it can increase the capacity of quantum communication largely. Here we present the first scheme for concentrating the nonlocal two-photon six-qubit systems entangled in polarization, spatial-mode, and time-bin DOFs with linear optics. We construct the parity-check gates for the quantum states of nonlocal photon systems in all the three DOFs with linear-optical elements. Fortunately, our parity-check gate for one DOF does not affect the quantum states in the other two DOFs, which makes our hyperentanglement concentration protocol (hyper-ECP) can be implemented conveniently for polarization–spatial–time-bin partially hyperentangled states. This hyper-ECP is practical as it requires only linear-optical elements, and it can be directly generalized to improve the entanglement of nonlocal multi-photon systems entangled in three DOFs in the long-distance high-capacity quantum communication. - Highlights: • A linear hyperentanglement concentration protocol is proposed for photon systems. • Parity-check gates on one degree of freedom (DOF) will not affect the other two DOFs. • Polarization, spatial-mode, and time-bin DOFs are manipulated with linear optics. • Nonlocal maximally hyperentangled two-photon six-qubit systems are obtained. • Entanglement of multiphoton systems in three DOFs can be improved with this method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Gradient-based constrained optimization using a database of linear reduced-order models

A methodology grounded in model reduction is presented for accelerating the gradient-based solution of a family of linear or nonlinear constrained optimization problems where the constraints include at least one linear Partial Differential Equation (PDE). A key component of this methodology is the construction, during an offline phase, of a database of pointwise, linear, Projection-based Reduced-Order Models (PROM)s associated with a design parameter space and the linear PDE(s). A parameter sampling procedure based on an appropriate saturation assumption is proposed to maximize the efficiency of such a database of PROMs. A real-time method is also presented for interpolating at any queried but unsampled parameter vector in the design parameter space the relevant sensitivities of a PROM. The practical feasibility, computational advantages, and performance of the proposed methodology are demonstrated for several realistic, nonlinear, aerodynamic shape optimization problems governed by linear aeroelastic constraints.

97 MATHEMATICS AND COMPUTING↗