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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 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

On the numerical treatment of nonlinear source terms in reaction-convection equations

The objectives of this paper are to investigate how various numerical treatments of the nonlinear source term in a model reaction-convection equation can affect the stability of steady-state numerical solutions and to show under what conditions the conventional linearized analysis breaks down. The underlying goal is to provide part of the basic building blocks toward the ultimate goal of constructing suitable numerical schemes for hypersonic reacting flows, combustions and certain turbulence models in compressible Navier-Stokes computations. It can be shown that nonlinear analysis uncovers much of the nonlinear phenomena which linearized analysis is not capable of predicting in a model reaction-convection equation.

Lafon, A.↗
NASA NTRS1995

A deterministic particle method for one-dimensional reaction-diffusion equations

We derive a deterministic particle method for the solution of nonlinear reaction-diffusion equations in one spatial dimension. This deterministic method is an analog of a Monte Carlo method for the solution of these problems that has been previously investigated by the author. The deterministic method leads to the consideration of a system of ordinary differential equations for the positions of suitably defined particles. We then consider the time explicit and implicit methods for this system of ordinary differential equations and we study a Picard and Newton iteration for the solution of the implicit system. Next we solve numerically this system and study the discretization error both analytically and numerically. Numerical computation shows that this deterministic method is automatically adaptive to large gradients in the solution.

Mascagni, Michael↗
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 OSTI2020

Rapid data-driven model reduction of nonlinear dynamical systems including chemical reaction networks using ℓ 1 -regularization

We develop a new data-driven paradigm for efficient model reduction of a broad class of nonlinear dynamical systems. Our model reduction method directly enables the interpretation of key components of the dynamical system, unlike traditional projection-based model reduction methods that focus on reducing computational complexity more than interpretability. Our method is not application specific and is simple to implement on nonlinear dynamical systems arising from a variety of different fields. It requires minimal parameterization using a single parameter to trade-off between model complexity and estimation error. We use a data-driven paradigm to formulate model reduction as an efficient convex optimization problem that scales polynomially in the original size of the complex system, enabling systems with as many as thousands of components to be reduced in a matter of minutes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Bayesian learning with Gaussian processes for low-dimensional representations of time-dependent nonlinear systems

This work presents a data-driven method for learning low-dimensional time-dependent physics-based surrogate models whose predictions are endowed with uncertainty estimates. We use the operator inference approach to model reduction that poses the problem of learning low-dimensional model terms as a regression of state space data and corresponding time derivatives by minimizing the residual of reduced system equations. Standard operator inference models perform well with accurate training data that are dense in time, but producing stable and accurate models when the state data are noisy and/or sparse in time remains a challenge. Another challenge is the lack of uncertainty estimation for the predictions from the operator inference models. Our approach addresses these challenges by incorporating Gaussian process surrogates into the operator inference framework to (1) probabilistically describe uncertainties in the state predictions and (2) procure analytical time derivative estimates with quantified uncertainties. The formulation leads to a generalized least-squares regression and, ultimately, reduced-order models that are described probabilistically with a closed-form expression for the posterior distribution of the operators. The resulting probabilistic surrogate model propagates uncertainties from the observed state data to reduced-order predictions. Furthermore, we demonstrate the method is effective for constructing low-dimensional models of two nonlinear partial differential equations representing a compressible flow and a nonlinear diffusion–reaction process, as well as for estimating the parameters of a low-dimensional system of nonlinear ordinary differential equations representing compartmental models in epidemiology.

Data-driven model reduction↗
NASA NTRS1986

Model reference adaptive attitude control of spacecraft using reaction wheels

A nonlinear model reference adaptive control law for large angle rotational maneuvers of spacecraft using reaction wheels in the presence of uncertainty is presented. The derivation of control law does not require any information on the values of the system parameters and the disturbance torques acting on the spacecraft. The controller includes a dynamic system in the feedback path. The control law is a nonlinear function of the attitude error, the rate of the attitude error, and the compensator state. Simulation results are prsented to show that large angle rotational maneuvers can be performed in spite of the uncertainty in the system.

Singh, Sahjendra N.↗
DOE OSTI2025

Modeling kinetic effects of charged vacancies on electromechanical responses of ferroelectrics: Rayleighian approach

Understanding the time-dependent effects of charged vacancies on the electromechanical responses of materials is at the forefront of research for designing materials exhibiting metal-insulator transitions and memristive behavior. A Rayleighian approach is used to develop a model for studying the nonlinear kinetics of the reaction leading to generation of vacancies and electrons via the dissociation of vacancy-electron pairs. Also, diffusion and elastic effects of charged vacancies are considered to model polarization-electric potential and strain-electric potential hysteresis loops. The model captures multiphysics phenomena by introducing couplings among polarization, the electric potential, stress, strain, and concentrations of charged (multivalent) vacancies and electrons (treated as classical negatively charged particles), where the concentrations can vary due to association-dissociation reactions. A derivation of coupled time-dependent equations based on the Rayleighian approach is presented. Three limiting cases of the governing equations are considered, highlighting the effects of (1) nonlinear reaction kinetics on the generation of charged vacancies and electrons, (2) Vegard's law (i.e., the concentration-dependent local strain) on asymmetric strain-electric potential relations, and (3) coupling between a fast component and the slow component of the net polarization on the polarization-electric-field relations. The Rayleighian approach discussed in this work should pave the way for developing a multiscale modeling framework in a thermodynamically consistent manner while capturing multiphysics phenomena in ferroelectric materials. Published by the American Physical Society 2025

Kumar, Rajeev (ORCID:0000000194943488)↗
NASA NTRS1987

The thermal stability of coronal loops by nonlinear diffusion asymptotics

A nonlinear reaction-diffusion equation and some additional constraints are derived which describe the time-dependent behavior of the temperature structure of the plasma in coronal loops. The equation is analyzed using nonlinear diffusion asymptotics, in particular singular perturbation techniques, and the results are interpreted in the context of the physical problem of the thermal stability and temporal behavior of the plasma. The results are consistent with the possibility of cyclic thermal behavior of the plasma, as suggested by Kuin and Martens (1982).

Pakkert, J. W.↗
DOE OSTI2020

Pattern formation in a coupled membrane-bulk reaction-diffusion model for intracellular polarization and oscillations

Reaction-diffusion systems have been widely used to study spatio-temporal phenomena in cell biology, such as cell polarization. Coupled bulk-surface models naturally include compartmentalization of cytosolic and membrane-bound polarity molecules. Here we study the distribution of the polarity protein Cdc42 in a mass-conserved membrane-bulk model, and explore the effects of diffusion and spatial dimensionality on spatio-temporal pattern formation. We first analyze a one-dimensional (1-D) model for Cdc42 oscillations in fission yeast, consisting of two diffusion equations in the bulk domain coupled to nonlinear ODEs for binding kinetics at each end of the cell. In 1-D, our analysis reveals the existence of symmetric and asymmetric steady states, as well as anti-phase relaxation oscillations typical of slow-fast systems. We then extend our analysis to a two-dimensional (2-D) model with circular bulk geometry, for which species can either diffuse inside the cell or become bound to the membrane and undergo a nonlinear reaction-diffusion process. We also consider a nonlocal system of PDEs approximating the dynamics of the 2-D membrane-bulk model in the limit of fast bulk diffusion. In all three model variants we find that mass conservation selects perturbations of spatial modes that simply redistribute mass. In 1-D, only anti-phase oscillations between the two ends of the cell can occur, and in-phase oscillations are excluded. In higher dimensions, no radially symmetric oscillations are observed. Instead, the only instabilities are symmetry-breaking, either corresponding to stationary Turing instabilities, leading to the formation of stationary patterns, or to oscillatory Turing instabilities, leading to traveling and standing waves. Codimension-two Bogdanov—Takens bifurcations occur when the two distinct instabilities coincide, causing traveling waves to slow down and to eventually become stationary patterns. Our work clarifies the effect of geometry and dimensionality on behaviors observed in ma.ss-conserved cell polarity models.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1980

Meteorological and air pollution modeling for an urban airport

Results are presented of numerical experiments modeling meteorology, multiple pollutant sources, and nonlinear photochemical reactions for the case of an airport in a large urban area with complex terrain. A planetary boundary-layer model which predicts the mixing depth and generates wind, moisture, and temperature fields was used; it utilizes only surface and synoptic boundary conditions as input data. A version of the Hecht-Seinfeld-Dodge chemical kinetics model is integrated with a new, rapid numerical technique; both the San Francisco Bay Area Air Quality Management District source inventory and the San Jose Airport aircraft inventory are utilized. The air quality model results are presented in contour plots; the combined results illustrate that the highly nonlinear interactions which are present require that the chemistry and meteorology be considered simultaneously to make a valid assessment of the effects of individual sources on regional air quality.

Swan, P. R.↗
DOE OSTI2021

Evaluation of alkali–silica reaction damage in concrete using linear and nonlinear resonance techniques

Here in this study, the initiation and development of alkali–silica reaction (ASR) in concrete prisms containing reactive coarse (RCA) and reactive fine (RFA) aggregates were monitored over one year using linear and nonlinear resonance techniques. Although the linear resonance test could detect initiation and development of ASR damage in RCA specimens, it failed in the RFA specimens. Petrographic analysis confirmed the presence of early-stage ASR damage and the presence of different microcracking patterns in the RFA and RCA specimens, which may explain differences in the linear resonance data. For both RCA and RFA specimens, the nonlinear resonance test results were able to detect the initiation of ASR damage and showed a strong correlation with the ASR expansion for all specimens from different mix designs. The results demonstrate the high sensitivity of the nonlinear resonance test and its potential for quantitative evaluation of the ASR damage state of concrete specimens without a baseline measurement.

36 MATERIALS SCIENCE↗
DOE OSTI2020

PPINN: Parareal physics-informed neural network for time-dependent PDEs

Physics-informed neural networks (PINNs) encode physical conservation laws and prior physical knowledge into the neural networks, ensuring the correct physics is represented accurately while alleviating the need for supervised learning to a great degree. While effective for relatively short-term time integration, when long time integration of the time-dependent PDEs is sought, the time–space domain may become arbitrarily large and hence training of the neural network may become prohibitively expensive. To this end, we develop a parareal physics-informed neural network (PPINN), hence decomposing a long-time problem into many independent short-time problems supervised by an inexpensive/fast coarse-grained (CG) solver. In particular, the serial CG solver is designed to provide approximate predictions of the solution at discrete times, while initiate many fine PINNs simultaneously to correct the solution iteratively. There is a two-fold benefit from training PINNs with small-data sets rather than working on a large-data set directly, i.e., training of individual PINNs with small-data is much faster, while training the fine PINNs can be readily parallelized. Consequently, compared to the original PINN approach, the proposed PPINN approach may achieve a significant speed-up for long-time integration of PDEs, assuming that the CG solver is fast and can provide reasonable predictions of the solution, hence aiding the PPINN solution to converge in just a few iterations. To investigate the PPINN performance on solving time-dependent PDEs, we first apply the PPINN to solve the Burgers equation, and subsequently we apply the PPINN to solve a two-dimensional nonlinear diffusion–reaction equation. Furthermore, our results demonstrate that PPINNs converge in a few iterations with significant speed-ups proportional to the number of time-subdomains employed.

42 ENGINEERING↗
DOE OSTI2020

Multilevel Techniques for Compression and Reduction of Scientific Data---The Unstructured Case

Previous work on multilevel techniques for compression and reduction of scientific data is extended to the case of data given on unstructured meshes in two and three dimensions. The centerpiece of the work is a decomposition algorithm which is shown to be optimal, in terms of both storage and operational complexity, applicable to unstructured grids in both two and three dimensions, and which implicitly gives a Riesz basis that can be exploited to reduce the data while maintaining rigorous bounds on the loss incurred. The flexibility of the approach is illustrated by applications to potential flow around an airfoil and the effect of compression on quantities of interest relevant to airfoil design; compression of computational simulation of a nonlinear reaction-diffusion system with special attention given to the problem of time series reduction; and, data from a simulation of magnetically confined plasma in a fusion reactor reduced so as to preserve the electric field computed from the data.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1980

Post-buckling behavior of a beam-column on a nonlinear elastic foundation with a gap

The structural behavior of an elastic beam-column placed with a gap between two nonlinearity elastic layers each resting on a rigid foundation was examined. The beam-column was laterally supported at both ends and subjected to a uniform transverse load and axial compression. Its slenderness was such that the axial compressive force exceeds the amount that would be necessary to buckle it as a simple supported column. The elastic layers were represented by an elastic foundation with a strongly nonlinear specific reaction taken as a rapidly increasing function of the layer compression. The analytical model developed simulated the entire pattern of the deflection and stress state including layer and end support reactions, under gradually increasing axial force.

Kuznetsov, E. N.↗
NASA NTRS1984

Modeling of the aerodynamic response to arbitrary aircraft maneuvres - A numerical validation

The regime of validity of an aerodynamic mathematical model, applicable to describe the nonlinear aerodynamic reactions to a delta wing maneuvering at high angles of attack is investigated. An unsteady vortex-lattice method is used to compute the unsteady flowfields, and thus to evaluate the aerodynamic data required by the model, in terms of specified characteristic motions. Time-histories of the aerodynamic responses to complex motions are generated by means of the model and the evaluated aerodynamic data, and are compared with baseline aerodynamic responses obtained from direct vortex-lattice computations. The validity of the mathematical modeling approach for the maneuvering delta wing is demonstrated by the close agreement of the force and moment responses obtained from the two approaches.

Katz, J.↗
NASA NTRS1985

Selfsimilar time dependent shock structures

Diffusive shock acceleration as an astrophysical mechanism for accelerating charged particles has the advantage of being highly efficient. This means however that the theory is of necessity nonlinear; the reaction of the accelerated particles on the shock structure and the acceleration process must be self-consistently included in any attempt to develop a complete theory of diffusive shock acceleration. Considerable effort has been invested in attempting, at least partially, to do this and it has become clear that in general either the maximum particle energy must be restricted by introducing additional loss processes into the problem or the acceleration must be treated as a time dependent problem (Drury, 1984). It is concluded that stationary modified shock structures can only exist for strong shocks if additional loss processes limit the maximum energy a particle can attain. This is certainly possible and if it occurs the energy loss from the shock will lead to much greater shock compressions. It is however equally possible that no such processes exist and we must then ask what sort of nonstationary shock structure develops. The ame argument which excludes stationary structures also rules out periodic solutions and indeed any solution where the width of the shock remains bounded. It follows that the width of the shock must increase secularly with time and it is natural to examine the possibility of selfsimilar time dependent solutions.

Beck, R.↗