Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “nonlinear analysis”

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 667 records · Page 37

Quantum Fluctuations and Multifractally enhanced Superconductivity in Disordered Thin Films

The interplay between electron–electron interactions and weak localization (or anti-localization) phenomena in two-dimensional systems can significantly enhance the superconducting transition temperature. For this work, we develop the theory of quantum fluctuations within such multifractally enhanced superconducting states in thin films. In conditions of weak disorder, we employ the Finkel’stein nonlinear sigma model to derive an effective action for the superconducting order parameter and the quasiclassical Green’s function, meticulously accounting for the influence of quantum fluctuations. This effective action, applicable for interactions of any strength, reveals the critical role of well-known collective modes in a dirty superconductor, and its saddle-point analysis leads to modified Usadel and gap equations. These equations comprehensively incorporate the renormalizations stemming from the interplay between interactions and disorder, resulting in the non-trivial energy dependence of the gap function. Notably, our analysis establishes a direct relation between the self-consistent gap equation at the superconducting transition temperature and the known renormalization group equations for interaction parameters in the normal state.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

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↗

Floquet stability analyses of stratified oscillating boundary layers on adiabatic slopes

The presence of a no-slip, impermeable, adiabatic, sloped boundary in an otherwise quiescent, stably stratified, Boussinesq flow generates baroclinic vorticity within a diffusive boundary layer. Such conditions are typical of the oscillating boundary layers on adiabatic abyssal slopes, sloped lake bathymetry and sloped coastal bathymetry in the absence of high-wavenumber internal waves, mean flows, far-field turbulence on larger scales, and resonant tidal–bathymetric interaction. We investigate the linear stability of the oscillating flow within non-dimensional parameter space typical of the $M_2$ tide and hydraulically smooth, middle-latitude abyssal slopes through Floquet linear stability analysis. The flow dynamics depends on three non-dimensional variables: the Reynolds number for Stokes’ second problem, the Prandtl number, and a frequency ratio that accounts for the resonance conditions ($C$, criticality) of the buoyant restoring force and the tidal forcing. The Floquet analysis results suggest that oscillating laminar boundary layers on adiabatic abyssal slopes are increasingly unstable as Reynolds number, criticality parameter and/or spanwise disturbance wavenumber are increased. We also show that the two-dimensional Floquet linear instability necessarily generates three-dimensional baroclinic vorticity, which suggests that the evolution of the gravitational instabilities may be nonlinear as $t→∞$.

42 ENGINEERING↗

Integration of machine learning with neutron scattering for the Hamiltonian tuning of spin ice under pressure

Quantum materials research requires co-design of theory with experiments and involves demanding simulations and the analysis of vast quantities of data, usually including pattern recognition and clustering. Artificial intelligence is a natural route to optimise these processes and bring theory and experiments together. Here, we propose a scheme that integrates machine learning with high-performance simulations and scattering measurements, covering the pipeline of typical neutron experiments. Our approach uses nonlinear autoencoders trained on realistic simulations along with a fast surrogate for the calculation of scattering in the form of a generative model. We demonstrate this approach in a highly frustrated magnet, Dy 2 Ti 2 O 7 , using machine learning predictions to guide the neutron scattering experiment under hydrostatic pressure, extract material parameters and construct a phase diagram. Our scheme provides a comprehensive set of capabilities that allows direct integration of theory along with automated data processing and provides on a rapid timescale direct insight into a challenging condensed matter system.

36 MATERIALS SCIENCE↗

Waveform retrieval for ultrafast applications based on convolutional neural networks

Electric field waveforms of light carry rich information about dynamical events on a broad range of timescales. The insight that can be reached from their analysis, however, depends on the accuracy of retrieval from noisy data. In this article, we present a novel approach for waveform retrieval based on supervised deep learning. We demonstrate the performance of our model by comparison with conventional denoising approaches, including wavelet transform and Wiener filtering. The model leverages the enhanced precision obtained from the nonlinearity of deep learning. The results open a path toward an improved understanding of physical and chemical phenomena in field-resolved spectroscopy.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Electrochemical CO2 Reduction over Metal-/Nitrogen-Doped Graphene Single-Atom Catalysts Modeled Using the Grand-Canonical Density Functional Theory

Renewably driven, electrochemical conversion of carbon dioxide into value-added products is expected to be a critical tool in global decarbonization. However, theoretical studies based on the computational hydrogen electrode largely ignore the nonlinear effects of the applied potential on the calculated results, leading to inaccurate predictions of catalytic behavior or mechanistic pathways. Here, we use grand canonical density functional theory (GC-DFT) to model electrochemical CO2 reduction (CO2R) over metal- and nitrogen-doped graphene catalysts (MNCs) and explicitly include the effects of the applied potential. We used GC-DFT to compute the CO2 to CO reaction intermediate energies at -0.3, -0.7, and -1.2 VSHE catalyzed by MNCs each doped with 1 of the 10 3d block metals coordinated by four pyridinic nitrogen atoms. Our results predict that Sc-, Ti-, Co-, Cu-, and Zn-N4Cs effectively catalyze CO2R at moderate to large reducing potentials (-0.7 to -1.2 VSHE). ZnN4C is a particularly promising electrocatalyst for CO2R to CO both at low and moderate applied potentials based on our thermodynamic analysis. Our findings also explain the observed pH independence of CO production over FeN4C and predict that the rate-determining step of CO2R over FeN4C is not *CO2- formation but rather *CO desorption. Additionally, the GC-DFT-computed density of states analysis illustrates how the electronic states of MNCs and adsorbates change non-uniformly with applied potential, resulting in a significantly increased *CO2- stability relative to other intermediates and demonstrating that the formation of the adsorbed *CO2- anion is critical to CO2R activation. This work demonstrates how GC-DFT paves the way for physically realistic and accurate theoretical simulations of reacting electrochemical systems.

CO2 reduction↗

Prediction of the energetic particle redistribution by an improved critical gradient model and analysis of the transport threshold

Based on the theory of critical gradient model (CGM) and following the simulation method proposed by Waltz et al., a combination of TGLFEP and EPtran code is employed to predict the energetic particle (EP) transport induced by Alfvén eigenmodes (AEs). To be consistent with the experiment, recent improvements to the simulation method include consideration of threshold evolution and orbit loss due to finite orbit width. The revised CGM is applied to simulate two DIII-D experimental discharges (#142111 and #153071). It well reproduces the experimental profiles with multiple unstable AEs and large-scale EP transport. Discharge #142111 had previously been simulated using a nonlinear MHD-kinetic code MEGA with a transport mechanism based on stochasticity induced by overlapping AE. By comparing the simulated EP profiles, we find that the AE transport threshold is approximated by both the MEGA nonlinear stability threshold and the proposed CGM threshold (error <5% for single n and <17% for multiple n simulation). Both of them are larger than the linear stability threshold of the most unstable AE mode by a quantity of the order of the flux needed to sustain EP transport by the background turbulence. Additionally, we have also applied the improved CGM to simulate the α particle redistribution for a China Fusion Engineering Test Reactor steady state scenario. Because of the clear separation between the AE unstable region and the loss cone, only a moderate α particle loss of ~9.6% is predicted.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Remote quantification of Cm(III) and HNO 3 by fluorescence spectroscopy and chemometrics

A unique approach to remotely quantify Cm(III) (0–100 µg mL −1 ) in HNO 3 (1–12 M) using steady-state laser fluorescence spectroscopy and multivariate regression models was developed. Photoluminescence is amenable to remote measurements using fiber-optic cables and is sensitive to numerous lanthanide and actinide species. In-line measurements can provide feedback to support complex processing in harsh environments (e.g., hot cells) to help guide and optimize radiochemical separations. In this work, Cm(III) spectra were acquired remotely in a glove box as a function of HNO 3 concentration to better understand spectral characteristics and evaluate the utility of multivariate regression models in this system. Furthermore, the Cm(III) fluorescence peak shape, width, position, and intensity changed significantly as a function of HNO 3 concentration, likely because of the displacement of emission quenching inner-sphere water molecules and complexation with nitrate ions. Despite significant covariance and nonlinearity in the data, a D-optimal design strategy successfully minimized training set sample size and was used to build effective partial least squares regression models for Cm(III) and HNO 3 concentrations without a priori knowledge of solution conditions. Chemometrics for modeling complex fluorescence spectra are promising and may find widespread applicability for online analysis in numerous chemical systems found in the nuclear field.

Actinide↗

Laser-plasma instabilities in long scale-length plasmas relevant to shock-ignition

We present 2D particle-in-cell simulations of laser-plasma instabilities (LPI) performed using conditions relevant to experiments on the OMEGA and NIF laser facilities. The laser intensity used is 2×10 15 W cm -2 , which allows comparison with previous experiments and simulations investigating shock ignition, though this is a relatively low intensity for the scheme. We find that the large convective gain of the instabilities leads to dynamics that are largely controlled by pump depletion and to scattering or absorption by LPIs predominantly occurring away from the quarter-critical density. The two-plasmon decay (TPD) instability is dominant for OMEGA-type conditions and remains important at the NIF-scale. In both cases, most absorption from TPD occurs near its Landau cutoff density, and we examine its nonlinear dynamics in this region, focusing on the ion-acoustic waves responsible for saturation. For NIF-type conditions, stimulated Raman scattering (SRS) and stimulated Brillouin scattering divert significant fractions of laser energy, and we find that SRS backscatter can occur with high gain at low densities due to kinetic effects. An in-depth analysis of hot-electron production is performed to identify the main sources and their characteristic electron temperature. For both simulations presented, the overall hot-electron temperature lies between 30 and 35 keV. This is relatively low and will likely increase shock pressure; however, the distributions also contain a significant number of high-energy (E k >100 keV) electrons that would likely cause unacceptable preheat. We, therefore, suggest some strategies that may be utilized to minimize this high-energy component. I. INTROD

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Analytical benchmark solution for 1-D neutron transport coupled with thermal conduction and material expansion

In this work we present fully analytical solutions for a class of finite, homogeneous, 1-D slab benchmark problems with nonlinear temperature feedback effects. The proposed class of benchmarks include multiplicative 1-D neutron transport (limited to quasistatic S{sub 2} with μ = ±1) coupled with thermal conduction, convection, Doppler broadening, and expansion effects along the length of the slab. This class of benchmark models, along with the corresponding analytical solutions, are valuable for validating multiphysics analysis frameworks that support coupled neutronics/thermal/structural calculations. Analytical solutions for the benchmarks are obtained by introducing an ansatz that the equilibrium flux and temperature distributions in the slab have the same shape. Specific values for the total microscopic cross section, σ{sub t,0}, and conductive heat transfer coefficient, h, that satisfy the assumed ansatz are then determined. A discussion of the procedure for generating benchmark models and analytical solutions is provided, along with numerical results for an example set of model parameters and thoughts on practical applications of the benchmarks for multiphysics code validation. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Modeling hydraulic fracture opening and closure with proppant transport and settlement

Hydraulic fracturing is a widely used reservoir stimulation technique for improving fluid circulation in rock formations with extremely low permeability, particularly in enhanced geothermal systems (EGS). To better understand the complex processes involved and improve hydraulic stimulation performance, we have developed ELK (ELectrical fracKing), a MOOSE-based 3D finite element application designed to model the behavior of proppant-fluid mixtures in propagating fractures. ELK integrates both the fluid and proppant components, incorporating particle-driven processes such as gravity settling, particle-particle interactions, and strong density and viscosity contracts, in addition to conventional fluid-driven fracture propagation. In this contribution, we extend ELK to model propped fracture closure, which occurs after the injection phase due to a dramatic drop in the effective stress on the fracture plane. During the shut-in, flowback, and production periods, the fracture width decreases, with the closure behavior depending on proppant concentration.. At low concentrations, closure follows a nonlinear joint law linked to the stiffness of asperities in the fracture walls. While at high concentrations, it is controlled by the properties of packed proppant bed. The extended ELK application is validated against several benchmark examples, including the propagation of an inclined frictional crack, fracture opening and sliding in response to fluid injection, and flowback analysis. We believe that ELK’s enhanced capabilities can serve as a valuable tool for the design and optimization of EGS deployment.

15 - GEOTHERMAL ENERGY↗

Local Multimodal Electro-Chemical-Structural Characterization of Solid-Electrolyte Grain Boundaries

Typical models of polycrystalline ionic materials treat the grain boundary properties as single valued, without consideration of the full range of values that define the macroscopically measured average. Here a unique experimental platform suitable for local multimodal characterization of individual grain boundaries in bicrystal fibers is reported. A variation of three orders of magnitude in the grain boundary conductivity of ceria is observed, as measured across six individual bicrystals by both alternating current impedance spectroscopy and direct current (D.C.) linear sweep voltammetry. Nonlinear behavior of the D.C. measurements is consistent with resistance due to a space charge effect. Time-of-flight secondary ion beam spectroscopy reveals a correlation between grain boundary resistance and the concentration of impurities Si, Al, and Ca segregated at the grain boundaries, although the bulk concentrations of these impurities are negligible. Electron backscatter diffraction analysis of the crystal orientations suggests a correlation between the misorientation across the grain boundaries and grain boundary resistance. These correlations point towards a grain boundary resistance that arises from impurity-generated space charge effects and variations in impurity concentration and hence resistivity driven by the energetics of impurity segregation to grain boundaries of differing surface energies.

36 MATERIALS SCIENCE↗

Disentangling multiple scattering with deep learning: application to strain mapping from electron diffraction patterns

Abstract A fast, robust pipeline for strain mapping of crystalline materials is important for many technological applications. Scanning electron nanodiffraction allows us to calculate strain maps with high accuracy and spatial resolutions, but this technique is limited when the electron beam undergoes multiple scattering. Deep-learning methods have the potential to invert these complex signals, but require a large number of training examples. We implement a Fourier space, complex-valued deep-neural network, FCU-Net, to invert highly nonlinear electron diffraction patterns into the corresponding quantitative structure factor images. FCU-Net was trained using over 200,000 unique simulated dynamical diffraction patterns from different combinations of crystal structures, orientations, thicknesses, and microscope parameters, which are augmented with experimental artifacts. We evaluated FCU-Net against simulated and experimental datasets, where it substantially outperforms conventional analysis methods. Our code, models, and training library are open-source and may be adapted to different diffraction measurement problems.

36 MATERIALS SCIENCE↗

Finite-size effects in lead scandium tantalate relaxor thin films

Large electromechanical effects in relaxor ferroelectrics are generally attributed to the collective response of an ensemble of correlated, nanometer-sized polar structures induced by chemical and charge disorder. Here, we study finite-size effects on such polar order (i.e., how it evolves when sample dimensions approach the polarization correlation length) in 7–70-nm-thick films of the relaxor ferroelectric PbSc 0.5 Ta 0.5 O 3 . Temperature-dependent polarization studies reveal a linear suppression of the polarization and nonlinearity associated with relaxor order as the film thickness decreases to ≈ 30 nm. Below this thickness, however, the suppression rapidly accelerates, and polarization is completely absent by film thicknesses of ≈ 7 nm, despite the continued observation of a broad peak in dielectric permittivity and frequency dispersion. Diffuse-scattering measurements reveal the diffuse-scattering symmetry, and analysis suggests the films have a polarization correlation length of ≈ 23 nm. Finally, taken together, it is apparent that reduction of sample size and the resulting distribution of polar structures drive suppression and eventual quenching of the electrical response of relaxors, which may be attributed to increasing dipole-dipole and dipole-interface interactions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

A Probabilistic Scheme for Semilinear Nonlocal Diffusion Equations with Volume Constraints

This work presents a probabilistic scheme for solving semilinear nonlocal diffusion equations with volume constraints and integrable kernels. The nonlocal model of interest is defined by a time-dependent semilinear partial integro-differential equation (PIDE), in which the integro-differential operator consists of both local convection-diffusion and nonlocal diffusion operators. Here, our numerical scheme is based on the direct approximation of the nonlinear Feynman–Kac formula that establishes a link between nonlinear PIDEs and stochastic differential equations. The exploitation of the Feynman–Kac representation avoids solving dense linear systems arising from nonlocal operators. Compared with existing stochastic approaches, our method can achieve first-order convergence after balancing the temporal and spatial discretization errors, which is a significant improvement of existing probabilistic/stochastic methods for nonlocal diffusion problems. Error analysis of our numerical scheme is established. The effectiveness of our approach is shown in two numerical examples. The first example considers a three-dimensional nonlocal diffusion equation to numerically verify the error analysis results. The second example presents a physics problem motivated by the study of heat transport in magnetically confined fusion plasmas.

97 MATHEMATICS AND COMPUTING↗

Midfidelity model verification for a point-absorbing wave energy converter with linear power take-off

In the preliminary design stage of a wave energy converter (WEC), researchers need fast and reliable simulation tools. High-fidelity numerical models are usually employed to study the wave-structure interaction, but the computational cost is demanding. As an alternative, midfidelity models can provide simulations in the order of real time. In this study, we operate Uppsala University’s WEC in a relatively mild sea state and model it using WEC-Sim. The model is verified based on OpenFOAM simulations. To analyze the ability of the midfidelity model to capture WEC dynamics, we investigate the system separately with 1, 2, and 3 degrees of freedom. We examine the contribution of viscous phenomena, and study both linear and weakly nonlinear solutions provided by WEC-Sim. Our results indicate that the viscous effects can be neglected in heave and surge motion, but not for pitch. We also find that the weakly nonlinear WEC-Sim solution successfully agrees with the computational fluid dynamics, whereas the linear solution could suggest misleading results.

16 TIDAL AND WAVE POWER↗

Goal-oriented a-posteriori estimation of model error as an aid to parameter estimation

In this work, a Bayesian model calibration framework is presented that utilizes goal-oriented a-posterior error estimates in quantities of interest (QoIs) for classes of high-fidelity models characterized by PDEs. It is shown that for a large class of computational models, it is possible to develop a computationally inexpensive procedure for calibrating parameters of high-fidelity models of physical events when the parameters of low-fidelity (surrogate) models are known with acceptable accuracy. The main ingredients in the proposed model calibration scheme are goal-oriented a-posteriori estimates of error in QoIs computed using a so-called lower fidelity model compared to those of an uncalibrated higher fidelity model. The estimates of error in QoIs are used to define likelihood functions in Bayesian inversion analysis. A standard Bayesian approach is employed to compute the posterior distribution of model parameters of high-fidelity models. As applications, parameters in a quasi-linear second-order elliptic boundary-value problem (BVP) are calibrated using a second-order linear elliptic BVP. In a second application, parameters of a tumor growth model involving nonlinear time-dependent PDEs are calibrated using a lower fidelity linear tumor growth model with known parameter values.

A-posterior estimates↗

Measurement bias in self-heating x-ray free electron laser experiments from diffraction studies of phase transformation in titanium

X-ray self-heating is a common by-product of X-ray Free Electron Laser (XFEL) techniques that can affect targets, optics, and other irradiated materials. Diagnosis of heating and induced changes in samples may be performed using the x-ray beam itself as a probe. However, the relationship between conditions created by and inferred from x-ray irradiation is unclear and may be highly dependent on the material system under consideration. Here, we report on a simple case study of a titanium foil irradiated, heated, and probed by a MHz XFEL pulse train at 18.1 keV delivered by the European XFEL using measured x-ray diffraction to determine temperature and finite element analysis to interpret the experimental data. We find a complex relationship between apparent temperatures and sample temperature distributions that must be accounted for to adequately interpret the data, including beam averaging effects, multivalued temperatures due to sample phase transitions, and jumps and gaps in the observable temperature near phase transformations. The results have implications for studies employing x-ray probing of systems with large temperature gradients, particularly where these gradients are produced by the beam itself. Finally, this study shows the potential complexity of studying nonlinear sample behavior, such as phase transformations, where biasing effects of temperature gradients can become paramount, precluding clear observation of true transformation conditions.

Crystallography↗