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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 811 records · Page 45

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NASA NTRS1974

Transient cooling of solid bodies of classical form by radiation

An approximate analytic method is presented for analysis of the unsteady process of radiative cooling of solid bodies of classical form. The nonlinear heat transfer problem is solved by the cascade linearization technique with use of the iteration method. Comparison of the results obtained even in the first approximation with the available numerical solutions indicates adequate engineering accuracy of the proposed technique.

Novikov, V. S.↗

NASA NTRS1981

Analysis of coherent satellite communication systems in the presence of interference and noise

The general analysis presented can be used to evaluate the performance of M-ary phase shift keying (MPSK) used over a nonlinear satellite channel in the presence of interference (CW tone and ISI) and channel noise. The numerical evaluation is based on the classical moment technique for approximating the probability distribution from moments of a random variable. The mathematical formulation of error probabilities of MPSK signals transmitted over nonlinear satellite repeaters is presented to include the effect of CW tone interference as well as the intersymbol interference. The approach is general and can be extended to include the effect of the synchronization.

Huang, T.-C.↗

NASA NTRS1985

The evolution of Ertel's potential vorticity during stratospheric sudden warmings

In the winter stratosphere of the Northern Hemisphere, the disruption of the westerly vortex and associated warming of polar latitudes is a well known phenomenon. It has become apparent that some important dynamical processes in the stratosphere are highly nonlinear and are best thought of locally rather than in terms of the interaction between the zonal-mean flow and harmonic waves around latitude circles. The importance of nonlinear processes was suggested by McIntyre and Palmer (1983, 1984) who used isentropic maps of Ertel's Potential Vorticity to show that during disturbed episodes material lines may become strongly and irreversibly deformed in certain places. They adopted the term planetary wave breaking to describe this process. Isentropic maps of Q are used to follow the evolution of a Canadian warming in November - December 1981 and a particularly strong warming in January 1982. The advection of Q over large distances on isentropic surfaces was a striking feature of the flow during each event. This could be identified because of our ability to follow the movement of material lines due to the approximate conservation of Q over several days. The advection of Q was a nonlinear process because its changing distribution affected the advecting wind field. The Canadian warming did not lead to a permanent change in the structure of the westerly vortex, as defined by the coarse-grain field of Q, whereas the January event was accompanied by a substantial loss of resolved Q which was never fully recovered.

Fairlie, T. D. A.↗

DOE OSTI2020

Fast Approximate Methods for Modified Gravity Cosmological Simulations

The accelerated expansion of the Universe poses a major theoretical puzzle. Although the assumption of a non-zero cosmological constant provides a minimal extension of general relativity that is consistent with observational data, many theories of modified gravity have been suggested as possible alternatives. Predictions of structure formation for these models in the fully nonlinear regime are very expensive and it is difficult, if not impossible, to explore such a huge space of models and parameters using high-resolution N-body simulations. Even in the mildly nonlinear regime, perturbative methods can become extremely complex. We explore whether simplified dynamical approximations, applicable for a certain set of cosmological probes, can be used to investigate models of modified gravity with acceptable accuracy in the latter instance. For the case of chameleon gravity, we find that these methods can indeed be used to explore the region around the baryon acoustic oscillation scale, k ~ 0:1 hMpc-1 but not much further.

cosmology↗

NASA NTRS1989

Pulse modulated control synthesis for a flexible spacecraft

The describing function method is employed for the nonlinear control analysis and design of a flexible spacecraft equipped with pulse modulated reaction jets. The method provides a means of characterizing the pulse modulator in terms of its gain and phase for structural mode limit cycle analysis. Although the describing function method is inherently inexact and is not widely used in practice, a new way of utilizing it for practical control design problems is presented. It is shown that the approximations inherent in the method can be accounted as a modeling uncertainty for the nonlinear control robustness analysis. The pulse modulated control system of the Intelsat 5 spacecraft is used as an example to illustrate the concept and methodology developed in the paper. The nonlinear stability margins predicted by the describing function analysis are verified from nonlinear simulations.

Anthony, Tobin C.↗

DOE OSTI2025

Reduced basis approximations of parameterized dynamical partial differential equations via neural networks

Projection-based reduced order models are effective at approximating parameter-dependent differential equations that are parametrically separable. When parametric separability is not satisfied, which occurs in both linear and nonlinear problems, projection-based methods fail to adequately reduce the computational complexity. Devising alternative reduced order models is crucial for obtaining efficient and accurate approximations to expensive high-fidelity models. In this work, we develop a timestepping procedure for dynamical parameter-dependent problems, in which a neural-network is trained to propagate the coefficients of a reduced basis expansion. This results in an online stage with a computational cost independent of the size of the underlying problem. Here, we demonstrate our method on several parabolic partial differential equations, including a problem that is not parametrically separable.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1992

Size-reduction techniques for the determination of efficient aeroservoelastic models

Size-reduction techniques for determining efficient time-domain state-space aeroservoelastic models are presented. Various rational function approximation methods of the unsteady aerodynamic force coefficients are brought to a common motion, emphasizing their differences. Among these, the classic Roger's method is the easier to apply but its resulting number of aerodynamic states is typically equal to or larger than the number of structural states. On the other hand, the minimum-state (MS) method, which typically reduces the number of aerodynamic states by 70 percent or more, requires the solution of an iterative nonlinear least-square solution. The MS computational efforts are reduced significantly when three approximation constraints are applied.

Karpel, Mordechay↗

NASA NTRS1987

Structural optimization of an alternate design for the Space Shuttle solid rocket booster field joint

A structural optimization procedure is used to determine the shape of an alternate design for the Shuttle's solid rocket booster field joint. In contrast to the tang and clevis design of the existing joint, this alternate design consists of two flanges bolted together. Configurations with 150 studs of 1 1/8 in diameter and 135 studs of 1 3/16 in diameter are considered. Using a nonlinear programming procedure, the joint weight is minimized under constraints on either von Mises or maximum normal stresses, joint opening and geometry. The procedure solves the design problem by replacing it by a sequence of approximate (convex) subproblems; the pattern of contact between the joint halves is determined every few cycles by a nonlinear displacement analysis. The minimum weight design has 135 studs of 1 3/16 in diameter and is designed under constraints on normal stresses. It weighs 1144 lb per joint more than the current tang and clevis design.

Barthelemy, Jean-Francois M.↗

NASA NTRS1988

Modifying PASVART to solve singular nonlinear 2-point boundary problems

To study the buckling and post-buckling behavior of shells and various other structures, one must solve a nonlinear 2-point boundary problem. Since closed-form analytic solutions for such problems are virtually nonexistent, numerical approximations are inevitable. This makes the availability of accurate and reliable software indispensable. In a series of papers Lentini and Pereyra, expanding on the work of Keller, developed PASVART: an adaptive finite difference solver for nonlinear 2-point boundary problems. While the program does produce extremely accurate solutions with great efficiency, it is hindered by a major limitation. PASVART will only locate isolated solutions of the problem. In buckling problems, the solution set is not unique. It will contain singular or bifurcation points, where different branches of the solution set may intersect. Thus, PASVART is useless precisely when the problem becomes interesting. To resolve this deficiency we propose a modification of PASVART that will enable the user to perform a more complete bifurcation analysis. PASVART would be combined with the Thurston bifurcation solution: as adaptation of Newton's method that was motivated by the work of Koiter 3 are reinterpreted in terms of an iterative computational method by Thurston.

Fulton, James P.↗

NASA NTRS1988

Parameter estimation in moving boundary problems

An approximation scheme which can be used to estimate unknown parameters in moving boundary problems is described. The model equations are fairly general nonlinear diffusion/reaction equations of one spatial variable. Conditions on the parameter sets and model equations are given. It is shown that the estimates obtained using the approximations will converge to best-fit parameters for the original model equations.

Murphy, K. A.↗

NASA NTRS1971

Approximate optimal atmospheric entry trajectories.

For a reentry glider, approximate solutions are found in closed form for the problem of maximizing a function of the terminal velocity, altitude, flight-path angle and heading angle subject to, at most, three terminal nonlinear constraints. The results given here extend the previous results in two important ways: (1) the second-order approximation of the entry dynamics of Loh is used instead of the first-order approximation of Allen and Eggers. This approximation is found to compare extremely well with an exact numerical optimal path. (2) A three-dimensional optimization problem is solved which includes Loh's second-order approximation where the roll angle as well as the lift coefficient are determined subject to constraints which include the terminal heading angle. Furthermore, closed-form solutions can also be obtained subject to in-flight constraints on the lift coefficient and roll angle.

Speyer, J. L.↗

DOE OSTI2018

New discretization of Caputo–Fabrizio derivative

We derive a numerical approximation, namely L1–2 formula, to the Caputo–Fabrizio derivative by using a quadratic interpolation. Quadratic and cubic convergence rates are achieved for L1 and L1–2 formulas using Lagrange interpolation, respectively. We compute Caputo–Fabrizio derivatives of some known functions both theoretically and numerically. In addition, we solve non/linear sub-diffusion equations to test theoretical findings. Numerical results confirm the theoretically observed convergence rates.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Partitioned exponential methods for coupled multiphysics systems

Multiphysics problems involving two or more coupled physical phenomena are ubiquitous in science and engineering. This work develops a new partitioned exponential approach for the time integration of multiphysics problems. After a possible semi-discretization in space, the class of problems under consideration is modeled by a system of ordinary differential equations where the right-hand side is a summation of two component functions, each corresponding to a given set of physical processes. The partitioned-exponential methods proposed herein evolve each component of the system via an exponential integrator, and information between partitions is exchanged via coupling terms. Here, the traditional approach to constructing exponential methods, based on the variation-of-constants formula, is not directly applicable to partitioned systems. Rather, our approach to developing new partitioned-exponential families is based on a general-structure additive formulation of the schemes. Two method formulations are considered, one based on a linear-nonlinear splitting of the right hand component functions, and another based on approximate Jacobians. The paper develops classical (non-stiff) order conditions theory for partitioned exponential schemes based on particular families of T-trees and B-series theory. Several practical methods of third order are constructed that extend the Rosenbrock-type and EPIRK families of exponential integrators. Several implementation optimizations specific to the application of these methods to reaction-diffusion systems are also discussed. Numerical experiments reveal that the new partitioned-exponential methods can perform better than traditional unpartitioned exponential methods on some problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Dynamics of McMillan mappings I. McMillan multipoles

In this article, we consider two dynamical systems: the McMillan sextupole and octupole integrable mappings, originally proposed by Edwin McMillan. Both represent the simplest symmetric McMillan maps, characterized by a single intrinsic parameter. While these systems find numerous applications across various domains of mathematics and physics, some of their dynamical properties remain unexplored. We aim to bridge this gap by providing a comprehensive description of all stable trajectories, including the parametrization of invariant curves, Poincaré rotation numbers, and canonical action–angle variables. In the second part, we establish connections between these maps and general chaotic maps in standard form. Our investigation reveals that the McMillan sextupole and octupole serve as first-order approximations of the dynamics around the fixed point, akin to the linear map and quadratic invariant (known as the Courant–Snyder invariant in accelerator physics), which represents zeroth-order approximations (referred to as linearization). Furthermore, we propose a novel formalism for nonlinear Twiss parameters, which accounts for the dependence of rotation number on amplitude. This stands in contrast to conventional betatron phase advance used in accelerator physics, which remains independent of amplitude. Notably, in the context of accelerator physics, this new formalism demonstrates its capability in predicting dynamical aperture around low-order resonances for flat beams, a critical aspect in beam injection/extraction scenarios.

43 PARTICLE ACCELERATORS↗

DOE OSTI2026

How Silica Surface Chemistry Modulates Interfacial Water: Insights from Machine Learning Molecular Dynamics

Controlling water structure and dynamics at silica interfaces are central to a wide range of technologies, including protective oxide layers for solar water splitting and nanoporous membranes. In this work, we develop a machine learning interatomic potential, trained via active learning, to achieve ab initio accuracy for water confined between hydroxylated silica surfaces over a range of silanol coverages and slit widths. We find that partially hydroxylated surfaces (50 and 75% OH) support stronger water−surface hydrogen bonding and more extended interfacial density profiles than fully hydroxylated (100% OH) surfaces, indicating that increasing OH coverage does not necessarily strengthen interfacial hydrogenbond networks. Translational diffusion decreases approximately linearly with slit width and OH coverage, whereas rotational dynamics respond nonlinearly. In particular, at the smallest slit width of 5 Å, 75% OH coverage produces an enhanced local tetrahedral ordered interfacial network that strongly suppresses reorientation, while 100% coverage yields a crowded, disordered interfacial layer that also hinders rotation. In contrast, the 50% OH coverage is sufficiently sparse that it does not markedly alter water structure or dynamics under confinement. These results show that coupled control of pore size and surface chemistry enables nonlinear tuning of interfacial water structure and transport, providing a design strategy for optimizing porous silica for either enhanced interfacial stability and controlled reactivity or rapid and selective transport.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Machine-learning-based spectral methods for partial differential equations

Spectral methods are an important part of scientific computing’s arsenal for solving partial differential equations (PDEs). However, their applicability and effectiveness depend crucially on the choice of basis functions used to expand the solution of a PDE. The last decade has seen the emergence of deep learning as a strong contender in providing efficient representations of complex functions. In the current work, we present an approach for combining deep neural networks with spectral methods to solve PDEs. In particular, we use a deep learning technique known as the Deep Operator Network (DeepONet) to identify candidate functions on which to expand the solution of PDEs. We have devised an approach that uses the candidate functions provided by the DeepONet as a starting point to construct a set of functions that have the following properties: (1) they constitute a basis, (2) they are orthonormal, and (3) they are hierarchical, i.e., akin to Fourier series or orthogonal polynomials. We have exploited the favorable properties of our custom-made basis functions to both study their approximation capability and use them to expand the solution of linear and nonlinear time-dependent PDEs. The proposed approach advances the state of the art and versatility of spectral methods and, more generally, promotes the synergy between traditional scientific computing and machine learning.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Effects of artificial collisions, filtering, and nonlocal closure approaches on Hermite-based Vlasov–Poisson simulations

Kinetic simulations of collisionless plasmas are computationally challenging due to phase-space mixing and filamentation, resulting in fine-scale velocity structures. This study compares three methods developed to reduce artifacts related to limited velocity resolution in Hermite-based Vlasov–Poisson simulations: artificial collisions, filtering, and nonlocal closure approaches. We evaluate each method's performance in approximating the linear kinetic response function and suppressing recurrence in linear and nonlinear regimes. Numerical simulations of Landau damping demonstrate that artificial collisions, particularly higher orders of the Lenard-Bernstein collisional operator, most effectively recover the correct damping rate across a range of wavenumbers. Moreover, Hou-Li filtering and nonlocal closures underdamp high wavenumber modes in linear simulations, and the Lenard-Bernstein collisional operator overdamps low wavenumber modes in both linear and nonlinear simulations. This study demonstrates that hypercollisions offer a robust approach to kinetic simulations, accurately capturing collisionless dynamics with limited velocity resolution.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

Halo formation from Yukawa forces in the very early Universe

If long-range attractive forces exist and are stronger than gravity then cosmic halo formation can begin in the radiation-dominated era. We study a simple realization of this effect in a system where dark matter fermions have Yukawa interactions mediated by scalar particles, analogous to the Higgs boson in the standard model. We develop a self-consistent description of the system including exact background dynamics of the scalar field, and precise modeling of the fermion density fluctuations. For the latter, we provide accurate approximations for the linear growth as well as quantitative modeling of the nonlinear evolution using N-body simulations. We find that halo formation occurs exponentially fast and on scales substantially larger than simple estimates predict. Here, the final fate of these halos remains uncertain, but could be annihilation, dark stars, primordial black holes, or even the existence of galaxy-sized halos at matter-radiation equality. More generally, our results demonstrate the importance of mapping scalar-mediated interactions onto structure formation outcomes and constraints for beyond the standard model theories.

79 ASTRONOMY AND ASTROPHYSICS↗