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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

Self-focusing of cosh-Gaussian laser beam and its effect on the excitation of ion-acoustic wave and stimulated Brillouin backscattering in collisionless plasma

An analytical and numerical study has been carried out for self-focusing of an intense cosh-Gaussian laser beam in collisionless plasma and its impact on the excitation of ion-acoustic wave and stimulated Brillouin backscattering process. The analytical model has been developed under Wentzel–Kramers–Brillouin and paraxial ray approximations. The nonlinearities of ponderomotive force on electron and the relativistic oscillation of the electron mass have been used in this study. The nonlinear differential equations have been set up for the beam width parameters of the main beam, ion-acoustic wave, backscattered wave and back reflectivity of stimulated Brillouin scattering (SBS). These equations have been solved numerically for different values of decentred parameter (b), relative plasma density (ω{sub p0}/ω{sub 0}) and incident laser intensity (a). The results have been compared with only relativistic nonlinearity and Gaussian profile of laser beam. The focusing of laser beam, ion-acoustic wave and scattered wave are found to be strong under relativistic-ponderomotive regime compared to only relativistic regime. Further, it is observed that focusing/intensity of main laser beam, ion acoustic wave and SBS back reflectivity increases with increasing the values of b and ω{sub p0}/ω{sub 0}. Itis also found that back reflectivity of SBS process gets suppressed with the increase in the value of a. This study may be useful in laser induced fusion scheme where back scattering of SBS plays very important role.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Mesoscale Numerical Characterization of Kevlar and Carbon–Kevlar Hybrid Plain-Woven Fabric Compression Behavior

A mesoscale finite element model (FEM) of the plain-woven fabric representative elementary volume (REV/unit cell) is developed. The developed FEM is used to predict the nonlinear compaction behavior of monolithic and intraply hybrid fabric made of high-strength carbon and Kevlar fibers. For geometrical modeling of the fabric REV, TexGen, an open-source geometrical modeling software (developed at Nottingham University), is utilized, and for mechanical characterization, FE simulation tool Abaqus{sup ®} is used. Geometrical nonlinearity of the fabric, including periodic boundary conditions and yarn interactions, is incorporated in the REV FE model. Material nonlinearity caused by transversely isotropic behavior of fibrous yarns is implemented through the user material subroutine form in FE simulation along with local orientation assigned to each yarn in the REV. Material properties of fibers are extracted from the literature and supplier data. The compression behavior of monolithic Kevlar and hybrid carbon–Kevlar (carbon warp and Kevlar weft yarns, C–K) fabric is predicted using the proposed FE model. FEM-predicted results were found to have good agreement with the experimentally obtained ones. Results depict that C–K hybrid fabrics have improved compression strength. Hybridization effect is governed by yarns mutual interaction, yarn area at crossovers, and transverse in-plane properties of the interyarn hybridized fabric. The proposed FE model can be used to predict the mechanical behavior of woven fabrics with different weaving patterns, unit cell geometry, material properties, and loading conditions.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Neural Network-Based Variational Methods for Solving Quadratic Porous Medium Equations in High Dimensions

Here, in this paper, we propose and study neural network-based methods for solutions of high-dimensional quadratic porous medium equation (QPME). Three variational formulations of this nonlinear PDE are presented: a strong formulation and two weak formulations. For the strong formulation, the solution is directly parameterized with a neural network and optimized by minimizing the PDE residual. It can be proved that the convergence of the optimization problem guarantees the convergence of the approximate solution in the $L^1$ sense. The weak formulations are derived following (Brenier in Examples of hidden convexity in nonlinear PDEs, 2020) which characterizes the very weak solutions of QPME. Specifically speaking, the solutions are represented with intermediate functions who are parameterized with neural networks and are trained to optimize the weak formulations. Extensive numerical tests are further carried out to investigate the pros and cons of each formulation in low and high dimensions. This is an initial exploration made along the line of solving high-dimensional nonlinear PDEs with neural network-based methods, which we hope can provide some useful experience for future investigations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Validation of a Tapered Impact Damper for Traffic Signal Structure Vibrations Using the Method of Harmonic Balance

Significant vibration amplitudes and cycles can be produced when traffic signal structures with low inherent damping are excited near one of their natural frequencies. For the mitigation of wind-induced vibrations, dynamic vibration absorbers coupled to the structure are often used. Here, this research investigates the performance of a tapered impact damper, consisting of a hanging spring-mass oscillator inside a housing capable of reducing vibration amplitude over a broader frequency range than the conventional tuned mass damper. A nonlinear, two degree-of-freedom model is developed with coordinates representing the traffic structure and the tapered impact damper. This research focuses on the application of the harmonic balance method to approximate the periodic solutions of the nonlinear equations to compute the nonlinear dynamics of the damped traffic signal structure. After designing and manufacturing a tapered impact damper, the traffic signal structure is tested with and without the damper using free vibration snapback tests. The experimental frequency and damping backbone curves are used to validate the analytical model, and the effectiveness of the damper is discussed.

42 ENGINEERING↗
DOE OSTI2019

Solving scattering problems in the half-line using methods developed for scattering in the full line

We reduce the solution of the scattering problem defined on the half-line [0,∞) by a real or complex potential v(x) and a general homogeneous boundary condition at x=0 to that of the extension of v(x) to the full line that vanishes for x<0. We find an explicit expression for the reflection amplitude of the former problem in terms of the reflection and transmission amplitudes of the latter. We obtain a set of conditions on these amplitudes under which the potential in the half-line develops bound states, spectral singularities, and time-reversed spectral singularities where the potential acts as a perfect absorber. We examine the application of these results in the study of the scattering properties of a δ-function potential and a finite barrier potential defined in [0,∞), discuss optical systems modeled by these potentials, and explore the configurations in which these systems act as a laser or perfect absorber. In particular, we derive an explicit formula for the laser threshold condition for a slab laser with a single mirror and establish the surprising fact that a nearly perfect mirror gives rise to a lower threshold gain than a perfect mirror. We also offer a nonlinear extension of our approach which allows for utilizing a recently developed nonlinear transfer matrix method in the full line to deal with finite-range nonlinear scattering interactions defined in the half-line.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Multiscale simulations for multi-continuum Richards equations

In this paper, we study a multiscale method for simulating a dual-continuum unsaturated flow problem within complex heterogeneous fractured porous media. Mathematically, each of the dual continua is modeled by a multiscale Richards equation (for pressure head), and these equations are coupled to one another by transfer terms. On its own, Richards equation is already a nonlinear partial differential equation, and it is exceedingly difficult to solve numerically due to the extra nonlinear dependencies involving the soil water. To deal with multiple scales, our strategy is that starting from a microscopic scale, we upscale the coupled system of dual-continuum Richards equations via homogenization by the two-scale asymptotic expansion, to obtain a homogenized system, at an intermediate scale (level). Based on a hierarchical approach, the homogenization’s effective coefficients are computed through solving the arising cell problems. Furthermore, to tackle the nonlinearity, after time discretization, we use Picard iteration procedure for linearization of the homogenized Richards equations. At each Picard iteration, some degree of multiscale still remains from the intermediate level, so we utilize the generalized multiscale finite element method (GMsFEM) combining with a multi-continuum approach, to upscale the homogenized system to a macroscopic (coarse-grid) level. This scheme involves building uncoupled and coupled multiscale basis functions, which are used not only to construct coarse-grid solution approximation with high accuracy but also (with the coupled multiscale basis) to capture the interactions among continua. These prospects and convergence are demonstrated by several numerical results for the proposed method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Machine learning modeling and model predictive control of a closed-circuit reverse osmosis system

Closed-circuit reverse osmosis (CCRO) offers a flexible and energy-efficient alternative to conventional reverse osmosis by operating in a semi-batch mode that recycles brine, enabling higher recovery rates and reduced specific energy consumption (SEC). However, developing accurate, system-level dynamic models for CCRO remains challenging due to its nonlinear, multi-phase operation and sensitivity to variable feed water conditions. Traditional modeling approaches, such as NARMAX (nonlinear autoregressive moving average with exogenous inputs), often struggle to generalize across varying inlet feed concentrations, necessitating frequent parameter re-estimation and limiting their utility for real-time control applications. To address these limitations, we developed a long short-term memory (LSTM) neural network model trained on an extensive experimental data set from a CCRO pilot plant. The model accepts three inputs, feed flow rate, recirculation flow rate, and initial feed conductivity, and predicts three key outputs: reject conductivity, feed pump power draw, and recirculation pump power draw. We validated the LSTM model against experimental data, demonstrating its ability to distinguish between different feed conductivities and adapt to variable flow rates. Subsequently, we incorporated the LSTM model within a nonlinear model predictive control (MPC) scheme and conducted closed-loop simulations to optimize the integrated SEC (iSEC). In conclusion, the results project up to a 6% reduction in iSEC by using MPC to optimize performance over the entire experiment duration, without requiring any random excitation for data collection or parameter re-estimation.

Desalination↗
DOE OSTI2021

Non-intrusive data-driven model reduction for differential–algebraic equations derived from lifting transformations

In this paper we present a non-intrusive data-driven approach for model reduction of nonlinear systems. The approach considers the particular case of nonlinear partial differential equations (PDEs) that form systems of partial differential–algebraic equations (PDAEs) when lifted to polynomial form. Such systems arise, for example, when the governing equations include Arrhenius reaction terms (e.g., in reacting flow models) and thermodynamic terms (e.g., the Helmholtz free energy terms in a phase-field solidification model). Using the known structured form of the lifted algebraic equations, the approach computes the reduced operators for the algebraic equations explicitly, using straightforward linear algebra operations on the basis matrices. The reduced operators for the differential equations are inferred from lifted snapshot data using operator inference, which solves a linear least squares regression problem. The approach is illustrated for the nonlinear model of solidification of a pure material. The lifting transformations reformulate the solidification PDEs as a system of PDAEs that have cubic structure. The operators of the lifted system for this solidification example have affine dependence on key process parameters, permitting us to learn a parametric reduced model with operator inference. Numerical experiments show the effectiveness of the resulting reduced models in capturing key aspects of the solidification dynamics.

42 ENGINEERING↗
DOE OSTI2023

Constraint energy minimizing generalized multiscale finite element method for multi-continuum Richards equations

In fluid flow simulation, the multi-continuum model is a useful strategy. When the heterogeneity and contrast of coefficients are high, the system becomes multiscale, and some kinds of reduced order methods are demanded. Combining these techniques with nonlinearity, we will consider in this paper a dual-continuum model which is generalized as a multi-continuum model for a coupled system of nonlinear Richards equations as unsaturated flows, in complex heterogeneous fractured porous media; and we will solve it by a novel multiscale approach utilizing the constraint energy minimizing generalized multiscale finite element method (CEM-GMsFEM). In particular, such a nonlinear system will be discretized in time and then linearized by Picard iteration (whose global convergence is proved theoretically). Subsequently, we tackle the resulting linearized equations by the CEM-GMsFEM and obtain proper offline multiscale basis functions to span the multiscale space (which contains the pressure solution). More specifically, we first introduce two new sources of samples, and the GMsFEM is used over each coarse block to build local auxiliary multiscale basis functions via solving local spectral problems, that are crucial for detecting high-contrast channels. Second, per oversampled coarse region, local multiscale basis functions are created through the CEM as constrainedly minimizing an energy functional. Various numerical tests for our approach reveal that the error converges with the coarse-grid size and that only few oversampling layers as well as basis functions are needed.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Experimental and numerical investigations of a two-body floating-point absorber wave energy converter in regular waves

This paper presents experimental and numerical studies on the hydrodynamics of a two-body floating-point absorber (FPA) wave energy converter (WEC) under both extreme and operational wave conditions. In this study, the responses of the WEC in heave, surge, and pitch were evaluated for various regular wave conditions. For extreme condition analysis, we assume the FPA system has a survival mode that locks the power-take-off (PTO) mechanism in extreme waves, and the WEC moves as a single body in this scenario. A series of Reynolds-averaged Navier-Stokes (RANS) simulations was performed for the survival condition analysis, and the results were validated with the measurements from experimental wave tank tests. For the FPA system in operational conditions, both a boundary element method (BEM) and the RANS simulations were used to analyze the motion response and power absorption performance. Additional viscous damping, primarily induced by flow separation and vortex shedding, is included in the BEM simulation as a quadratic drag force proportional to the square of body velocity. The inclusion of viscous drag improves the accuracy of BEM's prediction of the heave response and the power absorption performance of the FPA system, which agrees well with experimental data and the RANS simulation results over a broad range of incident wave periods, except near resonance in large wave height scenarios. Overall, the experimental and numerical results suggest that nonlinear effects, caused by viscous damping and interaction between waves and the FPA, significantly influence the system response and power absorption performance. Nonlinear effects were found to be particularly significant when the wave height was large and the period was near or shorter than the resonant period of the FPA system. The study is expected to be helpful for understanding the nonlinear interaction between waves and the FPA system so that the structure of the FPA can be adequately designed.

16 TIDAL AND WAVE POWER↗
DOE OSTI2022

Reduced order models for thermal radiative transfer problems based on moment equations and data-driven approximations of the Eddington tensor

Here a new group of structure and asymptotic preserving reduced-order models (ROMs) for multidimensional nonlinear thermal radiative transfer (TRT) problems is presented. They are formulated by means of the nonlinear projective approach and data compression techniques. The nonlinear projection is applied to the Boltzmann transport equation (BTE) to derive a hierarchy of low-order moment equations. Approximation of the Eddington tensor that provides exact closure for the system of moment equations is found with projection-based data-driven methodologies. These include the (i) proper orthogonal decomposition (POD), (ii) dynamic mode decomposition (DMD) and (iii) a variant of the DMD. A parameterization is derived for this ROM for the temperature of radiation incoming to the problem domain (the radiation drive temperature). This parameterization is informed from results of a dimensionless study of the TRT problem. Analysis of the ROMs is performed on the classical Fleck-Cummings TRT multigroup test problem in 2D geometry with a radiation-driven Marshak wave. Numerical results are presented to demonstrate the performance of these ROMs for the simulation of evolving radiation and heat waves. Results show these models to be sufficiently accurate for practical computations with rather low-rank representations of the Eddington tensor. As the rank of the approximation is increased, the errors of solutions generated by the ROMs gradually decreases.

42 ENGINEERING↗
DOE OSTI2022

Low-Frequency Oscillations in Optical Measurements of Metal-Nanoparticle Vibrations

Time-resolved optical measurements of vibrating metal nanoparticles have been used extensively to probe the ultrafast mechanical properties of the nanoparticles and of the surrounding liquid, but nearly all investigations so far have been limited to the linear regime. Herein, we report the observation of a low-frequency oscillating signal in transient-absorption measurements of nanoparticles with octahedral gold cores and cubic silver shells; the signal appears at the difference of two mechanical vibrational frequencies in the particles, suggesting a nonlinear mixing process. We tentatively attribute this proposed mixing to a nonlinear coupling between a vibrational mode of the nanoparticle and its optical-frequency plasmon resonance. The optimization of this nonlinear transduction may enable high-efficiency opto-mechanical frequency mixing in the GHz-THz frequency regime.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2022

Strong-Field Control of Plasmonic Properties in Core–Shell Nanoparticles

Utilization of the plasmonic response in nanosystems is a key component of nanophotonics that is typically altered by varying the incident optical frequency or the material configuration. However, in this work we demonstrate that employing intense, femtosecond laser fields unlock nonlinear light–matter interactions such that precise control of the optical response is achieved solely by adjusting the incident intensity. The plasmonic properties of Au/SiO 2 nanoshells are manipulated by exploiting the nonlinear index of refraction of gold and experimentally observed by employing photoelectrons emitted during the interaction as a sensitive, sub-wavelength probe. A striking transition seen in the photoelectron energy spectrum between the weak and strong-field regime is verified by a modified Mie theory simulation that incorporates the nonlinear dielectric nanoshell response. The exhibited intensity-dependent optical control of the plasmonic response in prototypical core–shell nanoparticles paves the way toward ultrafast switching and opto-electronic signal modulation with more complex nanostructures.

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

Probing the Damage Zone at Parkfield

Rocks are heterogeneous materials that exhibit nonlinear elastic (anelastic) behavior at scales ranging from the laboratory to Earth. In the laboratory, typical, complex relationships exist between stress and strain that include hysteresis, finite relaxation times, strain rate, and history dependence. These behaviors are linked to important characteristics such as stress, porosity, permeability, material integrity, and material failure. In this work, we adopted a “pump-probe” type experiment common in laboratory studies, using solid earth tides as the low-frequency pump and empirical Green's function as the high-frequency probe. By probing the velocity at different points in the pump cycle, we constrained important information about the strain-modulus relationship. Near the San Andreas Fault, we observed strongly nonlinear elastic behavior that characterizes the damage zone. We also constrained important aspects of hysteretic behavior that are related to damage properties and possibly pore pressure. Away from the fault, the nonlinear behavior is diminished.

58 GEOSCIENCES↗
DOE OSTI2021

Does Regional Hydroclimate Change Scale Linearly With Global Warming?

Many aspects of climate change scale linearly with global warming. However, nonlinear changes are possible, especially in the context of hydroclimate, and under emissions scenarios with stabilized global temperature, as aspired to by current climate targets. In CMIP5 and 6, a progressively larger land area shows nonlinear changes as a function of global warming when considering precipitation, evaporation, and soil moisture, with the latter showing nonlinearity over ~50% of global land. Here, using ensemble simulations with the Community Earth System Model 1, in which individual forcing factors are held constant, we illustrate how nonadditive responses to anthropogenic greenhouse gases and industrial and fire-related aerosols can yield complex soil moisture changes in certain regions. This complexity contributes to uncertainty in regional soil moisture projections and suggests that the timing of, as well as model response uncertainty to, future aerosol reductions will have significant impacts on regional hydroclimate change as global temperatures stabilize.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Analytical and numerical modeling of optical second harmonic generation in anisotropic crystals using #SHAARP package

Electric-dipole optical second harmonic generation (SHG) is a second-order nonlinear process that is widely used as a sensitive probe to detect broken inversion symmetry and local polar order. Analytical modeling of the SHG polarimetry of a nonlinear optical material is essential to extract its point group symmetry and the absolute nonlinear susceptibilities. Current literature on SHG analysis involves numerous approximations and a wide range of (in)accuracies. We have developed an open-source package called the Second Harmonic Analysis of Anisotropic Rotational Polarimetry (#SHAARP.si) which derives analytical and numerical solutions of reflection SHG polarimetry from a single interface (.si) for bulk homogeneous crystals with arbitrary symmetry group, arbitrary crystal orientation, complex and anisotropic linear dielectric tensor with frequency dispersion, a general SHG tensor and arbitrary light polarization. #SHAARP.si enables accurate modeling of polarimetry measurements in reflection geometry from highly absorbing crystals or wedge-shaped transparent crystals. The package is extendable to multiple interfaces.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Towards Floquet Chern insulators of light

Topological photonics explores photonic systems that exhibit robustness against defects and disorder, enabled by protection from underlying topological phases. These phases are typically realized in linear optical systems and characterized by their intrinsic photonic band structures. Here we experimentally study Floquet Chern insulators in periodically driven nonlinear photonic crystals, where the topological phase is controlled by the polarization and the frequency of the driving field. Our transient sum-frequency generation measurements reveal strong hybridization of the Floquet photonic bands. The measured spectrum remains gapless under a linearly polarized drive but becomes gapped under a circularly polarized drive. Theoretical analysis confirms that the Floquet gap is topological, characterized by a non-zero Chern number—a consequence of time-reversal symmetry breaking induced by the circularly polarized driving field. Furthermore, this work offers opportunities to explore the role of classical optical nonlinearity in topological phases and their applications in nonlinear optoelectronics.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Second-harmonic generation tensors from high-throughput density-functional perturbation theory

Optical materials play a key role in enabling modern optoelectronic technologies in a wide variety of domains such as the medical or the energy sector. Among them, nonlinear optical crystals are of primary importance to achieve a broader range of electromagnetic waves in the devices. However, numerous and contradicting requirements significantly limit the discovery of new potential candidates, which, in turn, hinders the technological development. In the present work, the static nonlinear susceptibility and dielectric tensor are computed via density-functional perturbation theory for a set of 579 inorganic semiconductors. The computational methodology is discussed and the provided database is described with respect to both its data distribution and its format. Several comparisons with both experimental and ab initio results from literature allow to confirm the reliability of our data. The aim of this work is to provide a relevant dataset to foster the identification of promising nonlinear optical crystals in order to motivate their subsequent experimental investigation.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗