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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
NASA NTRS1977

A mathematical study of a random process proposed as an atmospheric turbulence model

A random process is formed by the product of a local Gaussian process and a random amplitude process, and the sum of that product with an independent mean value process. The mathematical properties of the resulting process are developed, including the first and second order properties and the characteristic function of general order. An approximate method for the analysis of the response of linear dynamic systems to the process is developed. The transition properties of the process are also examined.

Sidwell, K.↗
DOE OSTI2026

Higher-order LaSDI: Reduced order modeling with multiple time derivatives

Solving complex partial differential equations (PDEs) is essential across scientific disciplines but often requires numerical models that can be prohibitively expensive in time-sensitive applications. Reduced-order models (ROMs) address this challenge by exploiting low-dimensional structure to create fast approximations. The Latent Space Dynamics Identification (LaSDI) framework has demonstrated success in learning ROMs for parameterized PDE families, but remains limited to first-order systems. Here, in this paper, we propose Higher-Order LaSDI (HLaSDI), which extends the LaSDI framework to PDEs with arbitrary order of time derivatives. This generalization significantly expands the applicability of LaSDI-based methods to systems previously outside their scope, including hyperbolic PDEs. We demonstrate HLaSDI’s accuracy and efficiency on several linear and nonlinear benchmark problems.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2021

Detection and Tracking of Aircraft in the Far-Field from Small Unmanned Aerial Systems

Onboard far-field aircraft detection is needed for safe non-cooperative traffic mitigation in autonomous small Unmanned Aerial System (sUAS) operations. Machine vision systems, based on standard optics and visible light detectors, possess the ideal size, weight, and power (SWaP) requirements for sUAS. This work presents the design and analysis of a novel aircraft detection and tracking pipeline based on optical sensing alone. Key contributions of the work include a refined range inequality model based on sensing and detection with FAA well-clear separation assurance distances between aircraft in mind, a detector fusion method to maximize the benefit of two image detectors, and a comparative analysis of Linear Kalman-filtering and Extended Kalman-filtering to seek optimal tracking performance. The pipeline is evaluated offline against multiple intruder platforms, using two types of flight encounters: multirotor sUAS vs. fixed-wing sUAS and multirotor sUAS vs. general aviation(GA)plane. Analysis is restricted to the rate-limiting head-on and departing collision volume cases vertically separated for safety. Results indicate that it is feasible to use the proposed optical spatial-temporal tracking algorithm to provide adequate alerting time to prevent penetration of well-clear separation volumes for both sUAS and GA aircraft.

Unmanned Aerial System↗
DOE OSTI2022

Building Load Control Using Distributionally Robust Chance-Constrained Programs with Right-Hand Side Uncertainty and the Risk-Adjustable Variants

Aggregation of heating, ventilation, and air conditioning (HVAC) loads can provide reserves to absorb volatile renewable energy, especially solar photo-voltaic (PV) generation. In this paper, we decide HVAC control schedules under uncertain PV generation, using a distributionally robust chance-constrained (DRCC) building load control model under two typical ambiguity sets: the moment-based and Wasserstein ambiguity sets. We derive mixed integer linear programming (MILP) reformulations for DRCC problems under both sets. Especially, for the Wasserstein ambiguity set, we use the right-hand side (RHS) uncertainty to derive a more compact MILP reformulation than the commonly known MILP reformulations with big-M constants. All the results also apply to general individual chance constraints with RHS uncertainty. Furthermore, we propose an adjustable chance-constrained variant to achieve tradeoff between the operational risk and costs. We derive MILP reformulations under the Wasserstein ambiguity set and second-order conic programming (SOCP) reformulations under the moment-based set. Using real-world data, we conduct computational studies to demonstrate the efficiency of the solution approaches and the effectiveness of the solutions. Summary of Contribution: The problem studied in this paper is motivated by a building load control problem that uses the aggregation of heating, ventilation, and air conditioning (HVAC) loads as flexible reserves to absorb uncertain solar photovoltaic (PV) generation. The problem is formulated as distributionally robust chance-constrained (DRCC) programs with right-hand side (RHS) uncertainty. In addition, we propose a risk-adjustable variant of the DRCC programs, where the risk level, instead of being predetermined, is treated as a decision variable. The paper aims to provide tractable reformulations and solution algorithms for both the (general) DRCC and the (general) adjustable DRCC models with RHS uncertainty.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

A reactive molecular dynamics model for uranium/hydrogen containing systems

Uranium-based materials are valuable assets in the energy, medical, and military industries. However, understanding their sensitivity to hydrogen embrittlement is particularly challenging due to the toxicity of uranium and the computationally expensive nature of quantum-based methods generally required to study such processes. In this regard, we have developed a Chebyshev Interaction Model for Efficient Simulation (ChIMES) that can be employed to compute energies and forces of U and UH3 bulk structures with vacancies and hydrogen interstitials with accuracy similar to that of Density Functional Theory (DFT) while yielding linear scaling and orders of magnitude improvement in computational efficiency. Here, we show that the bulk structural parameters, uranium and hydrogen vacancy formation energies, and diffusion barriers predicted by the ChIMES potential are in strong agreement with the reference DFT data. We then use ChIMES to conduct molecular dynamics simulations of the temperature-dependent diffusion of a hydrogen interstitial and determine the corresponding diffusion activation energy. Our model has particular significance in studies of actinides and other high-Z materials, where there is a strong need for computationally efficient methods to bridge length and time scales between experiments and quantum theory.

36 MATERIALS SCIENCE↗
NASA NTRS1973

Amplitude variations of whistler-mode signals caused by their interaction with energetic electrons of the magnetosphere

Whistler mode waves that propagate through the magnetosphere exchange energy with energetic electrons by wave-particle interaction mechanisms. Using linear theory, a detailed investigation is presented of the resulting amplitude variations of the wave as it propagates. Arbitrary wave frequency and direction of propagation are considered. A general class of electron distributions that are nonseparable in particle energy and pitch-angle is proposed. It is found that the proposed distribution model is consistent with available whistler and particle observations. This model yields insignificant amplitude variation over a large frequency band, a feature commonly observed in whistler data. This feature implies a certain equilibrium between waves and particles in the magnetosphere over a wide spread of particle energy, and is relevant to plasma injection experiments and to monitoring the distribution of energetic electrons in the magnetosphere.

Bernard, L. C.↗
NASA NTRS1975

Upwind second-order difference schemes and applications in unsteady aerodynamic flows

Explicit second-order upwind difference schemes in combination with spatially symmetric schemes can produce larger stability bounds and better numerical resolution than symmetric schemes alone. However, if conservation form is essential, a special operator is required for transition between schemes. An operational approach has been devised for deriving transition operators so that strict conservation and local consistency are maintained. Various aspects of hybrid schemes are studied numerically for model linear and nonlinear equations. To demonstrate the utility of combining two different algorithms, MacCormack's explicit, noncentered, second-order method is combined with a completely upwind version, and numerical solutions of the Euler equations are obtained for two-dimensional, transonic flows with embedded supersonic regions and shock waves. The general utility of the operational approach for combining schemes is emphasized by deriving a second-order conservative scheme for the steady transonic small-disturbance potential equation.

Warming, R. F.↗
NASA NTRS1990

Inverse methods for assessing ship-of-opportunity networks and estimating circulation and winds from tropical expendable bathythermograph data

Inverse methods for estimating the surface ciculation of the equatorial Pacific by combining a linear reduced-gravity shallow-water model with the Tropical Ocean-Global Atmosphere ship-of-opportunity expendable bathythermograph (TOGA SOP XBT) observing program are examined. It is demonstrated that a simple linear model of the upper circulation of the equatorial Pacific can be successfully used as a weak constraint when smoothing the TOGA SOP XBT data. A circulation is sought as the weighted least squares fit to the dynamics and the data. The solution method is an expansion in representer functions, and the generalized inverse problem is thereby reduced from a functional problem to an algebraic problem for the coefficients of the representer. A specific inverse calculation using synthetic forcing and data is presented.

Bennett, Andrew F.↗
NASA NTRS1990

Parameterization of eddy sensible heat transports in a zonally averaged dynamic model of the atmosphere

A Charney-Branscome based parameterization has been tested as a way of representing the eddy sensible heat transports missing in a zonally averaged dynamic model (ZADM) of the atmosphere. The ZADM used is a zonally averaged version of a general circulation model (GCM). The parameterized transports in the ZADM are gaged against the corresponding fluxes explicitly simulated in the GCM, using the same zonally averaged boundary conditions in both models. The Charney-Branscome approach neglects stationary eddies and transient barotropic disturbances and relies on a set of simplifying assumptions, including the linear appoximation, to describe growing transient baroclinic eddies. Nevertheless, fairly satisfactory results are obtained when the parameterization is performed interactively with the model. Compared with noninteractive tests, a very efficient restoring feedback effect between the modeled zonal-mean climate and the parameterized meridional eddy transport is identified.

Genthon, Christophe↗
NASA NTRS2002

Nonlinear Viscoelastic Mechanics of Cross-linked Rubbers

The paper develops a general theory for finite rubber viscoelasticity, and specifies it in the form, convenient for solving problems important for rubber, tire and space industries. Based on the quasi-linear approach of non-equilibrium thermodynamics, a general nonlinear theory has been developed for arbitrary nonisothermal deformations of viscoelastic solids. In this theory, the constitutive equations are presented as the sum of known equilibrium (rubber elastic) and non-equilibrium (liquid polymer viscoelastic) terms. These equations are then simplified using several modeling arguments. Stability constraints for the proposed constitutive equations are also discussed. It is shown that only strong ellipticity criteria are applicable for assessing stability of the equations governing viscoelastic solids.

Freed, Alan D.↗
NASA NTRS2008

The Impact of Soil Reflectance on the Quantification of the Green Vegetation Fraction from NDVI

The green vegetation fraction (Fg) is an important climate and hydrologic model parameter. A common method to calculate Fg is to create a simple linear mixing rnodeP between two NDVI endmembers: bare soil NDVI (NDVI(sub o)) and full vegetation NDVI (NDVI(sub infinity)). Usually it is assumed that NDVI(sub o), is close to zero (NDVI(sub o) approx.-0.05) and is generally chosen from the lowest observed NDVI values. However, the mean soil NDVI computed from 2906 samples is much larger (NDVI=0.2) and is highly variable (standard deviation=O. 1). We show that the underestimation of NDVI(sub o) yields overestimations of Fg. The largest errors occur in grassland and shrubland areas. Using parameters for NDVI(sub o) and NDVI(sub infinity) derived from global scenes yields overestimations of Fg ((Delta) Fg*) that are larger than 0.2 for the majority of U.S. land cover types when pixel NDVI values are 0.2<NDVI(sub pixel)<0.4. Figure 1 shows how the Fg overestimation varies for the most common land cover types in the conterminous U.S. for typical seasonal NDVI values. When using conterminous U.S. scenes to derive NDV(sub o) and NDVI(sub infinity), the overestimation is less (0.10-0.17 for 0.2<NDVI(sub pixel)<0.4). As a result, parts of the conterminous U.S. are affected at different times of the year depending on the local seasonal NDVI cycle. We propose using global databases of NDVI(sub o) along with information on historical NDVI(sub pixel) values to compute a statistically most-likely estimate of Fg (Fg*). Using in situ measurements made at the Sevilleta LTER, we show that this approach yields better estimates of Fg than using global invariant NDVI(sub o) values estimated from whole scenes (Figure 2). At the two studied sites, the Fg estimate was adjusted by 52% at the grassland and 86% at the shrubland. More significant advances will require information on spatial distribution of soil reflectance.

Montandon, L. M.↗
NASA NTRS2019

The Southern Ocean Sea Surface Temperature Response to Ozone Depletion: A Multi-Model Comparison

The effect of the Antarctic ozone hole extends downwards from the stratosphere, with clear signatures in surface weather patterns including a positive trend in the Southern Annular Mode (SAM). Several recent studies have used coupled climate models to investigate the impact of these changes on Southern Ocean sea surface temperature (SST), notably motivated by the observed cooling from the late 1970s. Here we examine the robustness of these model results through comparison of both previously published and new simulations. We focus on the calculation of ‘climate response functions' (CRFs), transient responses to an instantaneous step-change in ozone concentrations. The CRF for most models consists of a rapid cooling of SST, followed by a slower warming trend. However, inter-model comparison reveals large uncertainties, such that even the sign of the impact of ozone depletion on historical SST, when reconstructed from the CRF, remains unconstrained. Comparison of these CRFs with SST responses to a hypothetical step-change in the SAM, inferred through lagged linear regression, shows broadly similar results. Causes of uncertainty are explored by examining relationships between model climatologies and their CRFs. The inter-model spread in CRFs can be reproduced by varying a single subgrid-scale mixing parameter within a single model. Antarctic sea-ice CRFs are also calculated: these do not generally exhibit the two-time-scale behavior of SST, suggesting a complex relationship between the two. Finally, by constraining model climatology-response relationships with observational values, we conclude that ozone depletion in unlikely to have been the primary driver of the observed SST cooling trend.

Climate response functions (CRF)↗
DOE OSTI2022

A survey of unsupervised learning methods for high-dimensional uncertainty quantification in black-box-type problems

Constructing surrogate models for uncertainty quantification (UQ) on complex partial differential equations (PDEs) having inherently high-dimensional O(10 n ), n ≥ 2, stochastic inputs (e.g., forcing terms, boundary conditions, initial conditions) poses tremendous challenges. The “curse of dimensionality” can be addressed with suitable unsupervised learning techniques used as a pre-processing tool to encode inputs onto lower-dimensional subspaces while retaining its structural information and meaningful properties. In this work, we review and investigate thirteen dimension reduction methods including linear and nonlinear, spectral, blind source separation, convex and non-convex methods and utilize the resulting embeddings to construct a mapping to quantities of interest via polynomial chaos expansions (PCE). Here, we refer to the general proposed approach as manifold PCE (m-PCE), where manifold corresponds to the latent space resulting from any of the studied dimension reduction methods. To investigate the capabilities and limitations of these methods we conduct numerical tests for three physics-based systems (treated as black-boxes) having high-dimensional stochastic inputs of varying complexity modeled as both Gaussian and non-Gaussian random fields to investigate the effect of the intrinsic dimensionality of input data. We demonstrate both the advantages and limitations of the unsupervised learning methods and we conclude that a suitable m-PCE model provides a cost-effective approach compared to alternative algorithms proposed in the literature, including recently proposed expensive deep neural network-based surrogates and can be readily applied for high-dimensional UQ in stochastic PDEs.

42 ENGINEERING↗
DOE OSTI2021

Electric and magnetic black holes in a new nonlinear electrodynamics model

Highlights: • We introduce a new NED model which is comparable with the BI model in the weak-field limit. • We find an electric black hole solution in the context of Einstein’s gravity minimally coupled with the new NED model. • We study the thermal stability of the electric black hole solution. • Modified Smarr’s formula consistent with the first law of black hole thermodynamics is obtained. A new nonlinear electrodynamics (NED) model is introduced in the form of a nonpolynomial Lagrangian which admits static spherical and also plane wave solutions in a flat space. Upon coupling with gravity the electric field is finite and comparable with the Born–Infeld counterpart. The electric and magnetic black hole solutions in the Einstein’s gravity coupled with this NED model are presented. The solutions give both asymptotically and in the weak field limit Reissner–Nordström (RN) black hole and unlike the other known models our electric solution is expressed in terms of elementary functions in a closed form. We study the first law and derive the modified Smarr’s formula for the electric type extension of our model. Considerable rich structure, especially thermodynamic ones, ranging from first to the second order phase transitions are added to the RN black hole of linear electrodynamics with this NED model. Having the exact solution for the metric function at our disposal we investigate the stability of the electric black hole from both the thermodynamical and causal points of view.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Renormalized classical theory of quantum magnets

Here, we derive a renormalized classical spin (RCS) theory for 𝑆 >1/2 quantum magnets by constraining a generalized classical theory that includes all multipolar fluctuations to a reduced CP 1 phase space of dipolar SU(2) coherent states. When the spin Hamiltonian $\hat{ℋ}$(𝑆) is linear in the spin operators $\hat{𝑺}$ 𝑗 for each lattice site 𝑗, the RCS Hamiltonian $\tilde{ℋ}$ cl coincides with the usual classical model ℋ cl = lim 𝑆→∞⁡ $\hat{ℋ}$(𝑆). In the presence of nonlinear terms, however, the RCS theory is more accurate than ℋ cl . For the many materials modeled by spin Hamiltonians with (nonlinear) single-ion anisotropy terms, the use of the RCS theory is essential to accurately model phase diagrams and to extract the correct Hamiltonian parameters from neutron-scattering data.

magnetic anisotropy↗
NASA NTRS1975

Importance of helicopter dynamics to the mathematical model of the helicopter

A mathematical model of the helicopter requires appropriate representation of the constituent elements of rotor dynamics. General-purpose programs that model a variety of configurations for a broad range of operating conditions result in varying and incompatible levels of sophistication. Analysis of specific dynamic problems facilitates the identification of configuration parameters which determine system behavior. For the present analysis, the nonlinear equations of a torsionally rigid hingeless rotor are linearized about an equilibrium condition to determine flap-lag stability characteristics in hover. A collocation method was used to obtain the coupled natural frequencies and modes. These modes allow exact treatment of the effect of elastic coupling which more than compensates for the destabilizing inertial coupling. The sensitivity of damping to the number of modes was found to be small, and reasonable accuracy was obtained the first flapwise and edgewise coupled modes. The range of destabilizing precone was found to be small.

White, W. F., Jr.↗
NASA NTRS1977

Finite state modeling of aeroelastic systems

A general theory of finite state modeling of aerodynamic loads on thin airfoils and lifting surfaces performing completely arbitrary, small, time-dependent motions in an airstream is developed and presented. The nature of the behavior of the unsteady airloads in the frequency domain is explained, using as raw materials any of the unsteady linearized theories that have been mechanized for simple harmonic oscillations. Each desired aerodynamic transfer function is approximated by means of an appropriate Pade approximant, that is, a rational function of finite degree polynomials in the Laplace transform variable. The modeling technique is applied to several two dimensional and three dimensional airfoils. Circular, elliptic, rectangular and tapered planforms are considered as examples. Identical functions are also obtained for control surfaces for two and three dimensional airfoils.

Vepa, R.↗