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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 1,567 records · Page 87
All sourcesNASA NTRSDOE OSTI
NASA NTRS1987

Nonlinear susceptibilities of finite conjugated organic polymers

Tight-binding calculations of the length dependence of the third-order molecular hyperpolarizability for polyenes and polyynes are reported. The pi-electron wave functions were determined by exploiting the limited translational symmetry of the molecules. Perturbation theory was used to calculate the longitudinal component of the electronic nonresonant hyperpolarizability. This is the first two-'band' calculation of third-order hyperpolarizabilities on finite pi-electron systems of varying length. In contrast to the results of the one-'band' models, the hyperpolarizability densities increase rapidly and then, after about 10-15 repeating units, approach an asymptotic value.

Beratan, David N.↗
DOE OSTI2025

Phase-field model of alloy solidification far from chemical equilibrium at the solid-liquid interface

We further develop a recently introduced phase-field model of far-from-equilibrium alloy solidification under additive manufacturing conditions [K. Ji et al., Phys. Rev. Lett. 130, 026203 (2023)]. This model utilizes enhanced solute diffusivity within the spatially diffuse interface region to quantitatively capture solute trapping with a larger interface width, thereby making simulations on experimentally relevant length and timescales computationally feasible. The main developments presented here include testing the robustness of different variational formulations, extending the model to concentrated alloys by incorporating solid and liquid free energies from thermodynamic databases, as illustrated for hypoeutectic Al-Ag alloys with CALPHAD, extending convergence tests as a function of interface width to 3D, and carrying out simulations in both 2D and 3D to examine existing theories of microstructure development. Our results indicate that the simplest variational formulation that interpolates the bulk free-energy density between its solid and liquid forms is the most robust. Remarkably, for hypoeutectic Al-Ag alloys, this formulation yields a high-velocity nonequilibrium phase diagram that is independent of interface width, thereby demonstrating that the framework of enhanced solute diffusivity can be nontrivially extended to concentrated alloys. Other variational formulations have restricted ranges of materials or processing parameters that can be reliably modeled. We use 2D simulations to construct high-velocity microstructure selection maps for dilute Al-Cu alloys. The results validate the important role of latent heat rejection at the interface and extend the limited predictions of linear stability analysis [A. Karma and A. Sarkissian, Phys. Rev. E 47, 513 (1993)] and sharp-interface 1D simulations to fully nonlinear regimes. Furthermore, 3D simulations, carried out using a computationally tractable axisymmetric cellular/dendritic interface shape, demonstrate a good convergence similar to that observed in 2D as a function of interface width. Full 3D simulations, in turn, reveal that the standard theory of absolute stability is a good predictor of the upper critical velocity beyond which steady-state growth becomes unstable, despite the different morphological manifestations of this instability in 2D and 3D.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Joint velocity and density reconstruction of the Universe with nonlinear differentiable forward modeling

Reconstructing the initial conditions of the Universe from late-time observations has the potential to optimally extract cosmological information. Due to the high dimensionality of the parameter space, a differentiable forward model is needed for convergence, and recent advances have made it possible to perform reconstruction with nonlinear models based on galaxy (or halo) positions. In addition to positions, future surveys will provide measurements of galaxies' peculiar velocities through the kinematic Sunyaev-Zel'dovich effect (kSZ), type Ia supernovae, the fundamental plane relation, and the Tully-Fisher relation. Here we develop the formalism for including halo velocities, in addition to halo positions, to enhance the reconstruction of the initial conditions. We show that using velocity information can significantly improve the reconstruction accuracy compared to using only the halo density field. Here we study this improvement as a function of shot noise, velocity measurement noise, and angle to the line of sight. We also show how halo velocity data can be used to improve the reconstruction of the final nonlinear matter overdensity and velocity fields. We have built our pipeline into the differentiable Particle-Mesh FlowPM package, paving the way to perform field-level cosmological inference with joint velocity and density reconstruction. This is especially useful given the increased ability to measure peculiar velocities in the near future.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1986

Joint nonlinearity effects in the design of a flexible truss structure control system

Nonlinear effects are introduced in the dynamics of large space truss structures by the connecting joints which are designed with rather important tolerances to facilitate the assembly of the structures in space. The purpose was to develop means to investigate the nonlinear dynamics of the structures, particularly the limit cycles that might occur when active control is applied to the structures. An analytical method was sought and derived to predict the occurrence of limit cycles and to determine their stability. This method is mainly based on the quasi-linearization of every joint using describing functions. This approach was proven successful when simple dynamical systems were tested. Its applicability to larger systems depends on the amount of computations it requires, and estimates of the computational task tend to indicate that the number of individual sources of nonlinearity should be limited. Alternate analytical approaches, which do not account for every single nonlinearity, or the simulation of a simplified model of the dynamical system should, therefore, be investigated to determine a more effective way to predict limit cycles in large dynamical systems with an important number of distributed nonlinearities.

Mercadal, Mathieu↗
NASA NTRS2003

Modeling, Simulation and Control of a Propellant Mixer

This paper addresses some modeling and control issues for a mixing chamber used in rocket engine testing at NASA Stennis Space Center. The mixer must combine high pressure liquid hydrogen (LH2) and gaseous hydrogen (GH2) to produce and output flow that meets certain thermodynamic properties before it is fed into a test article. More precisely, this paper considers that the quantities to be tracked and/or regulated are mixer internal pressure, exit mass flow, and exit temperature. The available control inputs are given by three value positions, namely those of the GH2, LH2 and exit valves. The mixer is modelled by a system of two nonlinear ordinary differential equations having density and internal energy as states. The model must be simple enough to lend itself to subsequent feedback controller design, yet its accuracy must be tested against real data. For this reason, the model includes function calls to thermodynamic property data. Some structural properties of the resulting model that pertain to controller design, such as controllability and uniqueness of the equilibrium point are shown to hold. Validation of the model against real data is also provided. As a first control approach, a small-signal (linear) model is developed based on the nonlinear model and simulated as well. Pulse disturbances are introduced to the valve positions and the quality of the linear model is ascertained by comparing its behavior against the nonlinear model simulations. Valve control strategies that simulate an operator-in-the-loop scenario are then explored demonstrating the need for automatic feedback control. Classical optimal single-output and multi-output Proportional/Integral controllers are designed based on the linear model and applied to the nonlinear model with excellent results to track simultaneous, constant setpoint changes in desired exit flow, exit temperature, and mixer pressure, as well as to reject unmeasurable but bounded additive step perturbations in the valve positions. A feedback linearization controller is designed and used to achieve tracking and regulation of the outputs over an extended range of the variables of interest.

Richter, Hanz↗
NASA NTRS1982

Optimization of the performance of a tandem microchannel plate detector as a function of interplate spacing and voltage

The effect of varying the size of the gap voltage and spacing on the performance of a tandem pair of microchannel plates (MCP) is investigated. Results show that increasing the voltage in the gap increases the gain of the pair and also produces a narrower Gaussian pulse-height distribution, although beyond a critical voltage the gain of the channel plate pair is found to plateau. A model is developed which explains the nonlinear gain behavior of individual microchannels and the behavior of the electron cloud emitted from the first MCP as it spreads out between the two MCPs and hits the surface of the second. The model calculates the plateau voltage as a function of the gap size, the gain of each MCP, and the diameter of the channels, and is found to show good agreement with the observed results. It is concluded that interplate gaps of up to several millimeters can be accommodated without a significant degradation in pulse-height distribution.

Rogers, D.↗
NASA NTRS1992

Comments on the present state and future directions of PDF methods

The one point probability density function (PDF) method is examined in light of its use in actual engineering problems. The PDF method, although relatively complicated, appears to be the only format available to handle the nonlinear stochastic difficulties caused by typical reaction kinetics. Turbulence modeling, if it is to play a central role in combustion modeling, has to be integrated with the chemistry in a way which produces accurate numerical solutions to combustion problems. It is questionable whether the development of turbulent models in isolation from the peculiar statistics of reactant concentrations is a fruitful line of development as far as propulsion is concerned. There are three issues for which additional viewgraphs are prepared: the one point pdf method; the amplitude mapping closure; and a hybrid strategy for replacing a full two point pdf treatment of reacting flows by a single point pdf and correlation functions. An appeal is made for the establishment of an adequate data base for compressible flow with reactions for Mach numbers of unity or higher.

Obrien, E. E.↗
NASA NTRS1995

Triggering of longitudinal combustion instabilities in solid rocket motors: Nonlinear combustion response

Pulsed oscillations in solid rocket motors are investigated with emphasis on nonlinear combustion response. The study employs a wave equation governing the unsteady motions in a two-phase flow, and a solution technique based on spatial- and time-averaging. A wide class of combustion response functions is studied to second-order in fluctuation amplitude to determine if, when, and how triggered instabilities arise. Conditions for triggering are derived from analysis of limit cycles, and regions of triggering are found in parametric space. Based on the behavior of model dynamical systems, introduction of linear cross-coupling and quadratic self-coupling among the acoustic modes appears to be the manner in which the nonlinear combustion response produces triggering to a stable limit cycle. Regions of initial conditions corresponding to stable pulses were found, suggesting that stability depends on initial phase angle and harmonic content, as well as the composite amplitude, of the pulse.

Wicker, J. M.↗
DOE OSTI2021

Multi-fidelity Bayesian neural networks: Algorithms and applications

Here we propose a new class of Bayesian neural networks (BNNs) that can be trained using noisy data of variable fidelity, and we apply them to learn function approximations as well as to solve inverse problems based on partial differential equations (PDEs). These multi-fidelity BNNs consist of three neural networks: The first is a fully connected neural network, which is trained following the maximum a posteriori probability (MAP) method to fit the low-fidelity data; the second is a Bayesian neural network employed to capture the cross-correlation with uncertainty quantification between the low- and high-fidelity data; and the last one is the physics-informed neural network, which encodes the physical laws described by PDEs. For the training of the last two neural networks, we first employ the mean-field variational inference (VI) to maximize the evidence lower bound (ELBO) to obtain informative prior distributions for the hyperparameters in the BNNs, and subsequently we use the Hamiltonian Monte Carlo (HMC) method to estimate accurately the posterior distributions for the corresponding hyperparameters. We demonstrate the accuracy of the present method using synthetic data as well as real measurements. Specifically, we first approximate a one- and four-dimensional function, and then infer the reaction rates in one- and two-dimensional diffusion-reaction systems. Moreover, we infer the sea surface temperature (SST) in the Massachusetts and Cape Cod Bays using satellite images and in-situ measurements. Taken together, our results demonstrate that the present method can capture both linear and nonlinear correlation between the low- and high-fidelity data adaptively, identify unknown parameters in PDEs, and quantify uncertainties in predictions, given a few scattered noisy high-fidelity data. Finally, we demonstrate that we can effectively and efficiently reduce the uncertainties and hence enhance the prediction accuracy with an active learning approach, using as examples a specific one-dimensional function approximation and an inverse PDE problem.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Operation of Natural Gas Pipeline Networks With Storage Under Transient Flow Conditions

Here, we formulate a nonlinear optimal control problem for intraday operation of a natural gas pipeline network that includes storage reservoirs. The dynamics of compressible gas flow through pipes, compressors, reservoirs, and wells are considered. In particular, a reservoir is modeled as a rigid, hollow container that stores gas under isothermal conditions and uniform density, and a well is modeled as a vertical pipe. For each pipe, flow dynamics are described by a coupled partial differential equation (PDE) system in density and mass flux variables, with momentum dissipation modeled using the Darcy–Wiesbach friction approximation. Compressors are modeled as scaling up the pressure of gas between the inlet and outlet. The governing equations for all network components are spatially discretized and assembled into a nonlinear differential-algebraic equation (DAE) system, which synthesizes above-ground pipeline and subsurface reservoir dynamics into a single reduced-order model. We seek to maximize an objective function that quantifies economic profit and network efficiency subject to the flow equations and inequalities that represent operating limitations. The problem is solved using a primal–dual interior point solver, and the solutions are validated in computational experiments and simulations on several pipeline test networks to demonstrate the effectiveness of the proposed methodology.

03 NATURAL GAS↗
NASA NTRS1991

Nonlinear magnetohydrodynamics by Galerkin-method computation

A fully spectral numerical code is used to explore the properties of voltage-driven dissipative magnetofluids inside a periodic cylinder with circular cross section. The trial functions are orthonormal eigenfunctions of the curl (Chandrasekhar-Kendall functions). Transitions are observed from axisymmetric resistive equilibria without flow to helically deformed laminar states with flow, and between pairs of helical laminar states with different pairs of poloidal and toroidal m and n numbers. States of minimum energy dissipation rate seem to be preferred. At high values of the pinch ratio, fully developed magnetohydrodynamic turbulence is observed.

Shan, Xiaowen↗
DOE OSTI2023

An Incremental Gradient Method for Optimization Problems With Variational Inequality Constraints

We consider minimizing a sum of agent-specific nondifferentiable merely convex functions over the solution set of a variational inequality (VI) problem in that each agent is associated with a local monotone mapping. This problem finds an application in computation of the best equilibrium in nonlinear complementarity problems arising in transportation networks. We develop an iteratively regularized incremental gradient method where at each iteration, agents communicate over a directed cycle graph to update their solution iterates using their local information about the objective and the mapping. The proposed method is single-timescale in the sense that it does not involve any excessive hard-to-project computation per iteration. We derive nonasymptotic agent-wise convergence rates for the suboptimality of the global objective function and infeasibility of the VI constraints measured by a suitably defined dual gap function. Finally, the proposed method appears to be the first fully iterative scheme equipped with iteration complexity that can address distributed optimization problems with VI constraints over cycle graphs.

convergence↗
DOE OSTI2026

Multiresolution Quantum Chemistry: Nonlinear Response Properties at the Basis Set Limit

We benchmark the accuracy of Dunning correlation-consistent Gaussian basis sets for computing frequencydependent second-order hyperpolarizabilities relevant to second-harmonic generation (SHG), using multiresolution analysis (MRA) as a reference. Basis set errors are analyzed using a unit-sphere representation of the effective hyperpolarizability vector, enabling direct assessment of directional error structure. We introduce a relative RMS total error metric that integrates directional deviations over the unit sphere and complement it with signed projection errors that distinguish over- and underestimation. Unsupervised clustering based on these signed directional metrics reveals four distinct convergence behaviors across a set of 68 molecules. Unitsphere visualizations of representative systems show that basis set errors are often highly anisotropic and localized along specific bond directions, even when global error measures appear small. Doubly augmented basis sets consistently outperform singly augmented ones, and core-polarization functions are required for uniform convergence in second-row systems. Overall, this work demonstrates that directional analysis combined with clustering provides a robust framework for understanding basis set convergence in nonlinear optical response properties.

Basis sets↗
DOE OSTI2022

Physics constrained learning for data-driven inverse modeling from sparse observations

Deep neural networks (DNN) have been used to model nonlinear relations between physical quantities. Those DNNs are embedded in physical systems described by partial differential equations (PDE) and trained by minimizing a loss function that measures the discrepancy between predictions and observations in some chosen norm. This loss function often includes the PDE constraints as a penalty term when only sparse observations are available. As a result, the PDE is only satisfied approximately by the solution. However, the penalty term typically slows down the convergence of the optimizer for stiff problems. We present a new approach that trains the embedded DNNs while numerically satisfying the PDE constraints. We develop an algorithm that enables differentiating both explicit and implicit numerical solvers in reverse-mode automatic differentiation. This allows the gradients of the DNNs and the PDE solvers to be computed in a unified framework. We demonstrate that our approach enjoys faster convergence and better stability in relatively stiff problems compared to the penalty method. Furthermore, our approach allows for the potential to solve and accelerate a wide range of data-driven inverse modeling, where the physical constraints are described by PDEs and need to be satisfied accurately.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Response of Sulfonated Polystyrene Melts to Nonlinear Elongation Flows

Ionizable polymers form dynamic networks with domains controlled by two distinct energy scales, ionic interactions and van der Waals forces; both evolve under elongational flows during their processing into viable materials. A molecular level insight of their nonlinear response, paramount to controlling their structure, is attained by fully atomistic molecular dynamics simulations of a model ionizable polymer, polystyrene sulfonate. As a function of increasing elongational flow rate, the systems display an initial elastic response, followed by an ionic fraction-dependent strain hardening, stress overshoot, and eventually strain-thinning. As the sulfonation fraction increases, the chain elongation becomes more heterogeneous. Finally, flow-driven ionic assembly dynamics that continuously break and reform control the response of the system.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Efficient generation and extreme compression of multidimensional solitary states in molecular gas-filled hollow-core fibers driven by picosecond Yb lasers

We present an in-depth study on the impact of spatiotemporal Raman enhancement in molecular gas-filled hollow-core fibers (HCFs), demonstrating the efficient generation and post-compression of multidimensional solitary states (MDSS). Through different experimental scenarios—employing large-core HCFs filled with molecular gases (N 2 and N 2 O) and driven by high energy, sub-picosecond and picosecond Fourier transform-limited ytterbium laser pulses—this work leverages multimode propagation and enhanced spatiotemporal interactions to achieve significant spectral broadening and asymmetric redshift, contrasting sharply with self-phase modulation. Our findings reveal that, beyond the regime of maximum nonadiabatic molecular alignment, spatiotemporal nonlinear enhancement primarily governs spectral broadening for input pulse durations up to 1 ps. The process shows limited sensitivity to input pulse duration and the two investigated molecular gases (N 2 and N 2 O), with only subtle differences in broadening arising from their distinct Raman spectroscopic properties. Furthermore, post-compression of MDSS was achieved in various cases. Notably, using 7 mJ, 1 ps laser pulses, we generated 22 fs pulses with a 47% energy conversion efficiency of the input pulse energy. These results position MDSS as a powerful platform for generating high-energy, ultrashort pulses with tunable wavelengths, offering a robust solution for applications such as high harmonic generation.

47 OTHER INSTRUMENTATION↗
NASA NTRS1972

A computer-aided regulator design.

A unified computer-aided method for the design of linear and nonlinear regulators is discussed. The general mathematical programming approach considered involves the determination of a vector that solves the problem of minimizing the objective function subject to constraints. Classical design problems stated are related to stability design, dominant mode design, and comprehensive design. A computer algorithm is also developed.

Karmarkar, J. S.↗
NASA NTRS1975

Track/train dynamics test procedure transfer function test

A transfer function vibration test was made on an 80 ton open hopper freight car in an effort to obtain validation data on the car's nonlinear elastic model. Test configuration, handling, test facilities, test operations, and data acquisition/reduction activities necessary to meet the conditions of test requirements are given.

Vigil, R. A.↗