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Results for “Nonlinear processes”

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.

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At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Origin of the multiphoton-regime harmonic-generation plateau structure

A physical interpretation is provided for the formation of the multiphoton-regime plateau feature in the spectra of nonlinear and correlated process of high-order harmonic generation (HHG) of two-active-electron atoms interacting with an intense linearly polarized laser field. While in the strong-field tunneling regime the plateau feature is well known to be due to rescattering effects of the freed electron, its counterpart in the multiphoton regime is due to atomic resonance effects involving both singly excited states and doubly excited states. Here, we propose a strategy to uncover which kind of these states are responsible for this phenomenon. By studying the sensitivity of HHG to the initial state in helium, in this work we show that this multiphoton-regime plateau structure mostly originates from singly excited states.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2024

GP-BayesOpInf

SAND2025-01851O GP-BayesOpInf is a software tool that uses algorithms to combine Gaussian process regression, principal component analysis, and linear Bayesian inference to produce a probabilistic reduced-order model for time-dependent systems. Numerical examples include the compressible Euler equations for an ideal gas, a heat diffusion process with a nonlinear reaction term, and a set of ordinary differential equations describing a compartmental model in epidemiology. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

SciDAC↗
DOE OSTI2024

Measuring signatures in photon angular spectra to distinguish nonlinear Compton scattering models

The collision of a high-energy electron beam with a laser pulse may be used to study radiation reaction and nonlinear Compton scattering among many other processes in strong-field quantum electrodynamics. Predictions from simulation and theory for these interactions rely on a number of approximations and assumptions that have not been experimentally tested. Here, experimentally measurable signatures are identified that might be able to distinguish between radiation reaction models, i.e., classical or quantum, or between the local constant field and local monochromatic approximations used to calculate the properties of the nonlinear Compton process. These signatures are considered through Monte Carlo simulations of various experimental conditions that are relevant to today's laser facilities. Potential detection schemes for measuring the signatures are proposed. We find that single-photon counting of keV photons to resolve harmonics and scintillator-based detection of MeV photons may allow us to validate nonlinear Compton scattering models and radiation reaction models respectively. This will require electron beams with divergence angles less than 2 mrad and less than 20% energy spread.

Russell, Brandon K↗
DOE OSTI2022

Automated identification of dominant physical processes

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

42 ENGINEERING↗
DOE OSTI2020

A Causal Inference Model Based on Random Forests to Identify the Effect of Soil Moisture on Precipitation

Soil moisture influences precipitation mainly through its impact on land–atmosphere interactions. Understanding and correctly modeling soil moisture–precipitation (SM–P) coupling is crucial for improving weather forecasting and subseasonal to seasonal climate predictions, especially when predicting the persistence and magnitude of drought. However, the sign and spatial structure of SM–P feedback are still being debated in the climate research community, mainly due to the difficulty in establishing causal relationships and the high degree of nonlinearity in land–atmosphere processes. To this end, we developed a causal inference model based on the Granger causality analysis and a nonlinear machine learning model. This model includes three steps: nonlinear anomaly decomposition, nonlinear Granger causality analysis, and evaluation of the quality of SM–P feedback, which eliminates the nonlinear response of interannual and seasonal variability and the memory effects of climatic factors and isolates the causal relationship of local SM–P feedback. We applied this model by using National Climate Assessment–Land Data Assimilation System (NCA-LDAS) datasets over the United States. Here, the results highlight the importance of nonlinear atmosphere responses in land–atmosphere interactions. In addition, the strong feedback over the southwestern United States and the Great Plains both highlight the impacts of topographic factors rather than only the sensitivity of evapotranspiration to soil moisture. Furthermore, the SM–P index defined by our framework is used to benchmark Earth system models (ESMs), which provides a new metric for efficiently identifying potential model biases in modeling local land–atmosphere interactions and may help the development of ESMs in improving simulations of water cycle variability and extremes.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Nonlinear dynamics of topological Dirac fermions in 2D spin-orbit coupled materials

Abstract The graphene family materials are two-dimensional staggered monolayers with a gapped energy band structure due to intrinsic spin-orbit coupling. The mass gaps in these materials can be manipulated on-demand via biasing with a static electric field, an off-resonance circularly polarized laser, or an exchange interaction field, allowing the monolayer to be driven through a multitude of topological phase transitions. We investigate the dynamics of spin-orbit coupled graphene family materials to unveil topological phase transition fingerprints embedded in the nonlinear regime and show how these signatures manifest in the nonlinear Kerr effect and in third-harmonic generation processes. We show that the resonant nonlinear spectral response of topological fermions can be traced to specific Dirac cones in these materials, enabling characterization of topological invariants in any phase by detecting the cross-polarized component of the electromagnetic field. By shedding light on the unique processes involved in harmonic generation via topological phenomena our findings open an encouraging path towards the development of novel nonlinear systems based on two-dimensional semiconductors of the graphene family.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Extremized nonlinear and linearized responses in soft metamaterials enabled by gradient-based design and grayscale digital light processing

In this study, we develop a gradient-based design approach that exploits grayscale digital light processing (DLP) 3D printing for extremizing the nonlinear and linearized response of soft metamaterials — materials that harness engineered geometric instabilities to undergo large and programmable changes in configuration. Grayscale DLP approaches modulate local mechanical properties at the pixel scale by tuning the light intensity within a single grayscale image, unlocking an exceptionally large design space. To effectively navigate this space, we develop smooth mappings between local light intensity values and global quantities of interest that characterize the behavior of soft metamaterials. Enabling these smooth mappings are robust and differentiable nonlinear finite element simulations powered by a trust region solver. A PDE-constrained optimization problem is then solved to invert these mappings and produce light intensity distributions that endow the printed part with varying stiffness and flexibility in distinctive regions. It is shown that optimizing the distribution of soft and stiff phases throughout a metamaterial structure results in markedly different buckling and self-contact configurations to drive extremized nonlinear compression and linearized vibration responses. Optimized light intensity distributions are translated to grayscale images and directly used to print soft metamaterial samples, showing remarkable agreement between the buckling and self-contact response in simulated and measured deformed configurations.

Additive manufacturing↗
DOE OSTI2025

Photon–photon chemical thermodynamics of frequency conversion processes in highly multimode systems

Abstract Frequency generation in highly multimode nonlinear optical systems is inherently a complex process, giving rise to an exceedingly convoluted landscape of evolution dynamics. While predicting and controlling the global conversion efficiencies in such nonlinear environments has long been considered impossible, here, we formally address this challenge even in scenarios involving a very large number of spatial modes. By utilizing fundamental notions from optical statistical mechanics, we develop a universal theoretical framework that effectively treats all frequency components as chemical reactants/products, capable of undergoing optical thermodynamic reactions facilitated by a variety of multi-wave mixing effects. These photon–photon reactions are governed by conservation laws that directly determine the optical temperatures and chemical potentials of the ensued chemical equilibria for each frequency species. In this context, we develop a comprehensive stoichiometric model and formally derive an expression that relates the chemical potentials to the optical stoichiometric coefficients, in a manner akin to atomic/molecular chemical reactions. This advancement unlocks new predictive capabilities that can facilitate the optimization of frequency generation in highly multimode photonic arrangements, surpassing the limitations of conventional schemes that rely exclusively on nonlinear optical dynamics. Notably, we identify a universal regime of Rayleigh–Jeans thermalization where an optical reaction at near-zero optical temperatures can promote the complete and entropically irreversible conversion of light to the fundamental mode at a target frequency. Our theoretical results are corroborated by numerical simulations in settings where second-harmonic generation, sum-frequency generation and four-wave mixing processes can manifest.

Optics↗
DOE OSTI2022

Evaluating the demand response potential of ammonia plants

Demand-side management/demand response (DSM/DR) are key strategies for mitigating the inherent variability in electricity generation rates by renewable sources. This article represents—to our knowledge—the first foray into assessing the DR potential of ammonia plants. Ammonia plants are interesting candidates for DR initiatives because of their significant electricity use (for operating compressors driving the synthesis loop) and the ability to store the ammonia product relatively easily and safely. Our approach is based on formulating and solving an optimal DR scheduling problem for an ammonia plant while accounting for the process dynamics. To this end, we introduce a new Hammerstein–Wiener-inspired modeling framework based on injecting linear dynamics in a first-principles static nonlinear model of the process. The results are encouraging; for the cases considered, peak-time power consumption decreases between 3.57% and 7.40%, coupled with 1.39% to 3.70% reductions in operating cost.

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

A fast reduced model for a shell-and-tube based latent heat thermal energy storage heat exchanger and its application for cost optimal design by nonlinear programming

Numerical simulation of latent heat thermal energy storage (LHTES) systems plays a fundamental role in studying the physical process and guiding the engineering design. Discretization of the PDEs describing the nonlinear solidification/melting process of phase change materials (PCMs) leads to a large-scale complex dynamics system, where the system behavior depends on a set of parameters. In a design setting, repeated model evaluations are required over the set of parameters results in significant computational burden. In this paper, an explicit analytic solution was built for the propagation of the solidification front in a cylindrical coordinate. The analytic solution approach is further employed to develop a low computational reduced model (RM) as a module for a shell-and-tube based LHTES heat exchanger. The levelized Cost of Energy (LCOE) is used as a design metric and the RM model is used to apply system-level constraints in the nonlinear programming formulation that facilitates efficient global optimal design of the PCM properties, flow conditions and tube geometries. The use of LCOE as the design metric prevents over design of the heat transfer rate and also establishes a fair ground for evaluation of different thermal storage technologies and their integrated applications with other systems. Optimal results showed that a higher effectiveness results in a higher LCOE; the velocity of the HTF and the length of the channel are highly correlated with each other; both larger PCM latent energy and conductivity result in lower LCOE.

25 ENERGY STORAGE↗
DOE OSTI2022

Phenomenological Model of Nonlinear Dynamics and Deterministic Chaotic Gas Migration in Bentonite: Experimental Evidence and Diagnostic Parameters

Understanding gas migration in compacted clay materials, e.g., bentonite and claystone, is important for the design and performance assessment of an engineered barrier system of a radioactive waste repository system, as well as many practical applications. Existing field and laboratory data on gas migration processes in low-permeability clay materials demonstrate the complexity of flow and transport processes, including various types of instabilities, caused by nonlinear dynamics of coupled processes of liquid–gas exchange, dilation, fracturing, fracture healing, etc., which cannot be described by classical models of fluid dynamics in porous media. We here show that the complexity of gas migration processes can be explained using a phenomenological concept of nonlinear dynamics and deterministic chaos theory. To do so, we analyzed gas pressure and gas influx (i.e., input) and outflux (i.e., output), recorded during the gas injection experiment in the compact Mx80-D bentonite sample, and calculated a set of the diagnostic parameters of nonlinear dynamics and chaos, such a global embedding dimension, a correlation dimension, an information dimension, and a spectrum of Lyapunov exponents, as well as plotted 2D and 3D pseudo-phase-space strange attractors, based on the univariate influx and outflux time series data. These results indicate the presence of phenomena of low-dimensional deterministic chaotic behavior of gas migration in bentonite. In particular, during the onset of gas influx in the bentonite core, before the breakthrough, the development of gas flow pathways is characterized by the process of chaotic gas diffusion. After the breakthrough, with inlet-to-outlet movement of gas, the prevailing process is chaotic advection. During the final phase of the experiment, with no influx to the sample, the relaxation pattern of gas outflux is resumed back to a process of chaotic diffusion. The types of data analysis and a proposed phenomenological model can be used to establish the basic principles of experimental data-gathering, modeling predictions, and a research design.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Prediction of residual stresses in additively manufactured parts using lumped capacitance and classical lamination theory

Several industries are interested in Laser Powder Bed Fusion (L-PBF) Additively Manufactured (AM) metal parts because their designs can be made arbitrarily complex while retaining bulk-type material properties. However, the residual stresses (RS) and distortions caused by the heat gradients inherent to L-PBF processes are detrimental to the structural integrity of the parts and must be taken into consideration during the part design cycle. Predicting the state of stresses in as-built 3D printed parts is a difficult problem that is typically approached with the use of transient thermomechanical Finite Element Models (FEMs). However, the nonlinearities associated with AM processes are difficult to capture in these FEMs without increasing the computational cost of the simulation, limiting their ability to be incorporated into practical design cycles. This work presents a novel analytical framework that combines lumped capacitance nonlinear heat transfer with time dependent classical lamination theory to efficiently and accurately predict RS in as-built L-PBF parts without the need of FEMs. The simulation was compared to Neutron Diffraction (ND) residual strain measurements taken at Oak Ridge National Laboratories (ORNL) as well as Synchrotron X-ray Diffraction (XRD) strain data published by the National Institute of Standards and Technology (NIST). The simulation predictions and the experimental data showed excellent agreement for the in-plane strain directions, and general agreement for the out of plane strain component, highlighting an area where further development can be implemented.

42 ENGINEERING↗
DOE OSTI2023

O’Hare Airport Short-Term Ground Transportation Modal Demand Forecast Using Gaussian Processes

Here, the principal objective of this study is to analyze the spatial and temporal variation of ground transportation airport demand and provide demand forecast to inform planning capability and explore alternatives for investments to accommodate airport growth. Because of its good adaptability and strong generalization ability for dealing with high-dimensional input, small-sample, and nonlinear spatial data, Gaussian process (GP) regression is used to provide forecast estimates using data from transportation network company (TNC) trips and urban rail passengers at Chicago's O'Hare International Airport. TNC airport trips differ significantly, with three times more distance, more than twice the travel time, and half of the share requests compared with nonairport trips. This highlights the need for separate demand models. Hourly analysis of the rail service indicates that this is likely heavily used by airport workers, whereas TNC services focus on travelers because of variations in the peak demand hours. Heteroscedastic GP regression is implemented because of differences in trip variance between night and day hours. Estimates are given for weekdays and weekend trips, and the 95% confidence intervals are calculated. The introduction of flight schedule information into the models shows marginal improvements in their performance. However, fitting a GP regression becomes computationally expensive with increased sample size and the introduction of spatial components. Transportation planners and policymakers can use the results and methods implemented in this study to optimize transportation assets and provide long-range simulations of the current and future conditions in the area.

42 ENGINEERING↗
DOE OSTI2022

Harmonic Generation and Inverse Cascade in the z-Pinch Driven, Preseeded Multimode, Magneto-Rayleigh-Taylor Instability

We report the magneto-Rayleigh-Taylor instability (MRTI) plays an essential role in astrophysical systems and in magneto-inertial fusion, where it is known to be an important degradation mechanism of confinement and target performance. In this Letter, we show for the first time experimental evidence of mode mixing and the onset of an inverse-cascade process resulting from the nonlinear coupling of two discrete preseeded axial modes (400- and 550 - μm wavelengths) on an Al liner that is magnetically imploded using the 20-MA, 100-ns rise-time Z Machine at Sandia National Laboratories. Four radiographs captured the temporal evolution of the MRTI. We introduce a novel unfold technique to analyze the experimental radiographs and compare the results to simulations and to a weakly nonlinear model. We find good quantitative agreement with simulations using the radiation magnetohydrodynamics code hydra. Spectral analysis of the MRTI time evolution obtained from the simulations shows evidence of harmonic generation, mode coupling, and the onset of an inverse-cascade process. The experiments provide a benchmark for future work on the MRTI and motivate the development of new analytical theories to better understand this instability.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Flexible cryogenic air separation unit—An application for low-carbon fossil-fuel plants

In this study, the rapid integration of intermittent renewable sources into the electricity grid is driving the need for a flexible cryogenic air separation unit (ASU) coupled with a low-carbon fossil-fuel plant. However, the state-of-the-art ASU process is highly integrated and nonlinear, which can significantly restrict its ramping rate. In this work, we study the fundamental dynamics of a state-of-the-art double-column ASU, focusing on the dynamic characteristics of the highly integrated and nonlinear heat and mass transfers, and we propose basic control methods for achieving high process ramping rates. We found that the vapor–liquid countercurrent flows in the low-pressure column are critical to the cryogenic rectification of air, which governs the ramp rate of the ASU. This countercurrent flow structure is created through a complex heat integration process in the ASU. Here, this process is simplified as a countercurrent heat transfer to reduce the complexity of studying the ASU dynamics. To preserve this flow structure, the heat integration is maintained so that its heat duty follows the ASU load, using several basic controllers on the critical stream flowrates. A flow-driven dynamic ASU model is built in Aspen Plus Dynamics to capture the basic ramping dynamics. This model revealed a fundamental mismatch in the dynamics in the ASU column that causes a significant loss of O 2 product purity when ramping down the ASU and slightly increases the purity when ramping up. Based on these findings, we propose a basic control method for rapidly ramping down/up the ASU while maintaining O 2 product purity. Simulation results show the ASU basic dynamic process successfully ramps at a rate up to 10 %/min (40–100 % load) while maintaining the O 2 product purity at 95.2–95.6 mol%.

42 ENGINEERING↗
DOE OSTI2022

Quantifying transport and electrocatalytic reaction processes in a gastight rotating cylinder electrode reactor via integration of Computational Fluid Dynamics modeling and experiments

Understanding the complexity of the multiple processes of mass, momentum, charge, and heat transport, and how these affect reaction kinetics at the electrode/electrolyte interface is one of the major challenges in the field of energy and catalysis. The rapid and rational scale-up of electrocatalytic systems to industrial scales require a detailed understanding of nonlinear transport-reaction processes, accessible only through the building of multi-physics models that capture with high fidelity the complexity of real-world devices. The gastight rotating cylinder electrode (RCE) reactor is a promising lab-scale tool that can decouple transport from intrinsic kinetics to generate data for first-principle models useful in the design of industrial, electrochemical reactors. Computational Fluid Dynamics (CFD) studies have previously been used to investigate the bulk flow in RCE reactors for simple corrosion and electroplating processes. However, the quantification of changes in local concentration within the viscous layer where catalysis takes place requires capturing the correct flow conditions inside the hydrodynamic boundary layer near the surface of the electrode. Further, this requires simulations with spatial resolution in the nm and μm scale and temporal resolutions between ms and s scales that are similar to the timescales for reactions on the electrode surface. In this study, experimental electrocatalysis is combined with CFD modeling to elucidate and parameterize the hydrodynamics in a gastight RCE reactor. CFD simulations of the electrochemical ferricyanide reduction reaction under mass transport limited conditions are used to evaluate the validity of the CFD model parameters by comparing calculated dimensionless mass transport descriptors to dimensionless correlations obtained experimentally. Justifications for assumptions and details of the simulation methods used in this study are presented to provide a detailed understanding of the effect that each model parameter has on the ability to accurately simulate electrocatalysis in RCE systems. The simulation methodology reported here is a first step towards the development of multi-scale models for the study of transport dependent electrocatalytic processes, such as the electrochemical transformation of CO 2 to fuels and chemicals.

42 ENGINEERING↗
DOE OSTI2021

Current profile and normalized beta control via feedback linearization and Lyapunov techniques

Abstract Simultaneous control of the current profile and normalized plasma beta is an essential control problem in the development of advanced tokamak scenarios. However, this control problem is especially challenging due to the nonlinear nature of the current, heat, and particle transport dynamics, as well as the difficulty to understand and accurately model such processes. In this work, a nonlinear, robust, model-based controller for the simultaneous regulation of the current profile and normalized beta has been designed using feedback linearization and Lyapunov redesign techniques. Feedback linearization avoids approximate linearization of the plasma dynamics, retaining the original physics content of the model. Moreover, the use of Lyapunov redesign techniques makes the controller robust against the uncertainties arising during the modeling process. The controller’s performance in the presence of unknown dynamics is tested in nonlinear, one-dimensional simulations using the Control Oriented Transport SIMulator (COTSIM) code, which employs plasma models that are significantly more complex than those employed for control synthesis.

Physics↗