SEARCH · Search NASA

Results for “Nonlinear approximation”

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,711 records · Page 95

All sources NASA NTRS DOE OSTI

NASA NTRS1982

An electrostatic parabolic density drift instability

Assuming a uniform magnetic field and using the local approximation, the Vlassov theory for an electrostatic instability driven by a parabolic density gradient is considered. It is found that the instability grows only in the case of a sufficiently large, positive second derivative of the density. Linear growth rate parametric dependences are given, in addition to weakly nonlinear calculations on wave-particle transport due to this instability.

Gary, S. P.↗

NASA NTRS1983

A model of mean zonal flows in the major planets

The linear theory of deep zonal flows developed by Busse (1976) for the origins of deep motions of the atmospheres of Jupiter and Saturn is extended into the nonlinear regime. Relationships for the relative magnitudes of convective heat and momentum transports are formulated. A perturbation approach is taken to the problem, with the amplitude of the convection serving as the small parameter, and the basic equations being expanded in terms of the Prandtl number. The Boussinesq approximation is employed, together with an assumption of a low Rossby number for the Jovian and Saturn atmospheres. Differences in the amplitude of the Jovian equatorial jet relative to that of Saturn are explored in terms of a low equatorial convective heat flux on Jupiter.

Busse, F. H.↗

NASA NTRS1986

Multiple grid problems on concurrent-processing computers

Three computer codes were studied which make use of concurrent processing computer architectures in computational fluid dynamics (CFD). The three parallel codes were tested on a two processor multiple-instruction/multiple-data (MIMD) facility at NASA Ames Research Center, and are suggested for efficient parallel computations. The first code is a well-known program which makes use of the Beam and Warming, implicit, approximate factored algorithm. This study demonstrates the parallelism found in a well-known scheme and it achieved speedups exceeding 1.9 on the two processor MIMD test facility. The second code studied made use of an embedded grid scheme which is used to solve problems having complex geometries. The particular application for this study considered an airfoil/flap geometry in an incompressible flow. The scheme eliminates some of the inherent difficulties found in adapting approximate factorization techniques onto MIMD machines and allows the use of chaotic relaxation and asynchronous iteration techniques. The third code studied is an application of overset grids to a supersonic blunt body problem. The code addresses the difficulties encountered when using embedded grids on a compressible, and therefore nonlinear, problem. The complex numerical boundary system associated with overset grids is discussed and several boundary schemes are suggested. A boundary scheme based on the method of characteristics achieved the best results.

Eberhardt, D. S.↗

NASA NTRS1985

An evaluation of foldable elastic tubes for application in space structures

An experimental investigation and design study has been performed on one type of foldable elastic tube in order to assess its suitability as a member of deployable space structures. It is demonstrated that one or more slots inserted longitudinally in the center of the tube to alleviate strain serves to prevent collapse of the tube. The nonlinear spring characteristics of the tube that are required for computer-based deployment dynamic analysis of space structures are determined, and it is shown that strain energy levels over a certain range are realizable for tubes representing space structure members in the 15-20 ft length range. Approximate strain energy/geometric parameter relationships are developed which may be useful for preliminary design or concept studies.

Jones, I. W.↗

NASA NTRS1989

New computing systems and their impact on structural analysis and design

A review is given of the recent advances in computer technology that are likely to impact structural analysis and design. The computational needs for future structures technology are described. The characteristics of new and projected computing systems are summarized. Advances in programming environments, numerical algorithms, and computational strategies for new computing systems are reviewed, and a novel partitioning strategy is outlined for maximizing the degree of parallelism. The strategy is designed for computers with a shared memory and a small number of powerful processors (or a small number of clusters of medium-range processors). It is based on approximating the response of the structure by a combination of symmetric and antisymmetric response vectors, each obtained using a fraction of the degrees of freedom of the original finite element model. The strategy was implemented on the CRAY X-MP/4 and the Alliant FX/8 computers. For nonlinear dynamic problems on the CRAY X-MP with four CPUs, it resulted in an order of magnitude reduction in total analysis time, compared with the direct analysis on a single-CPU CRAY X-MP machine.

Noor, Ahmed K.↗

NASA NTRS1991

Lateral modes of broad area semiconductor lasers - Theory and experiment

Calculations of the lateral modes of an ideal broad area laser, including the nonlinear interaction between the carriers and the optical field, are made. The results include periodically modulated near fields and single- and double-lobed far fields similar to those previously measured. The unsaturable losses are higher and quantum efficiencies are lower than those determined from plane-wave approximations. Broad area InGaAs-GaAlAs-GaAs quantum-well lasers were fabricated and measured and found to closely agree with the theory in near, far, and spectrally resolved near fields. An occultation experiment on the far field confirms previously predicted unstable resonatorlike modes with V-shaped fronts.

Lang, Robert J.↗

NASA NTRS2012

UQTools: The Uncertainty Quantification Toolbox - Introduction and Tutorial

UQTools is the short name for the Uncertainty Quantification Toolbox, a software package designed to efficiently quantify the impact of parametric uncertainty on engineering systems. UQTools is a MATLAB-based software package and was designed to be discipline independent, employing very generic representations of the system models and uncertainty. Specifically, UQTools accepts linear and nonlinear system models and permits arbitrary functional dependencies between the system s measures of interest and the probabilistic or non-probabilistic parametric uncertainty. One of the most significant features incorporated into UQTools is the theoretical development centered on homothetic deformations and their application to set bounding and approximating failure probabilities. Beyond the set bounding technique, UQTools provides a wide range of probabilistic and uncertainty-based tools to solve key problems in science and engineering.

Kenny, Sean P.↗

NASA NTRS2018

Development of an Integrated Nonlinear Aeroservoelastic Flight Dynamic Model of the NASA Generic Transport Model

This paper describes a recent development of an integrated fully coupled aeroservoelastic flight dynamic model of the NASA Generic Transport Model (GTM). The integrated model couples nonlinear flight dynamics to a nonlinear aeroelastic model of the GTM. The nonlinearity includes the coupling of the rigid-body aircraft states in the partial derivatives of the aeroelastic angle of attack. Aeroservoelastic modeling of the control surfaces which are modeled by the Variable Camber Continuous Trailing Edge Flap is also conducted. The R.T. Jones' method is implemented to approximate unsteady aerodynamics. Simulations of the GTM are conducted with simulated continuous and discrete gust loads..

Aeroservoelasticit↗

DOE OSTI2024

A Hierarchical OPF Algorithm with Improved Gradient Evaluation in Three-Phase Networks

Linear approximation commonly used in solving alternating-current optimal power flow (AC-OPF) simplifies the system models but incurs accumulated voltage errors in large power networks. Such errors will make the primal-dual type gradient algorithms converge to solutions with voltage violation. In this paper, we improve a recent hierarchical OPF algorithm that rested on primal-dual gradients evaluated with a linearized distribution power flow model. Specifically, we propose a more accurate gradient evaluation method based on an unbalanced three-phase nonlinear distribution power flow model to mitigate the errors arising from linearization. The resultant gradients feature a blocked structure that enables our development of an improved hierarchical primal-dual algorithm to solve the OPF problem. Numerical results on the IEEE 123-bus test feeder and a 4,518-node test feeder show that the proposed method can enhance voltage safety at comparable computational efficiency with the linearized algorithm.

approximation algorithms↗

DOE OSTI2024

Robust Tensor Hypercontraction of the Particle–Particle Ladder Term in Equation-of-Motion Coupled Cluster Theory

One method of representing a high-rank tensor as a (hyper-)product of lower-rank tensors is the tensor hypercontraction (THC) method of Hohenstein et al. This strategy has been found to be useful for reducing the polynomial scaling of coupled-cluster methods by representation of a four-dimensional tensor of electron-repulsion integrals in terms of five two-dimensional matrices. Pierce et al. have already shown that the application of a robust form of THC to the particle–particle ladder (PPL) term reduces the cost of this term in couple-cluster singles and doubles (CCSD) from O(N 6 ) to O(N 5 ) with negligible errors in energy with respect to the density-fitted variant. In this work, we have implemented the least-squares variant of THC (LS-THC) which does not require a nonlinear tensor factorization, including the robust form (R-LS-THC), for the calculation of the excitation and electron attachment energies using equation-of-motion coupled cluster methods EOMEE-CCSD and EOMEA-CCSD, respectively. We have benchmarked the effect of the R-LS-THC-PPL approximation on excitation energies using the comprehensive QUEST database and the accuracy of electron attachment energies using the NAB22 database. Here, we find that errors on the order of 1 meV are achievable with a reduction in total calculation time of approximately 5x.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2017

Analytical trial functions for modelling a two-dimensional Bose condensate

Approximate analytical solutions to the time-independent two-dimensional Gross–Pitaevsky equation are obtained by a variational method. The solutions found are compared with the results of direct numerical calculations. The accuracy of analytical solutions is determined under various conditions of the problem, primarily the degree of nonlinear interaction of atoms in a Bose condensate. (paper)

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

Iteration-based Linearized Distribution-level Locational Marginal Price for Three-phase Unbalanced Distribution Systems

Distributed energy resources (DERs) are rocking the utilities’ business landscape. It calls for competitive market environments that incentivize DERs to form maximum operating efficiency. Among proposed pricing schemes, distribution-level locational marginal price (DLMP) is effective in signaling the marginal generation cost differences driven by energy losses and network constraints. It can be derived from a distribution-level optimal power flow (OPF) framework, as it essentially presents the sensitivity of optimized generation cost towards incremental loads. However, due to the high resistance-to-inductance ratio and unbalanced characteristics of distribution networks, computational affordable DLMPs are highly challenged. This article provides a linear-approximated DLMP that can be solved efficiently and generalized to account for reactive power flow, three-phase unbalanced loads and meshed network structure. The successive linear programming technique is introduced to enhance the model accuracy. Case studies on an IEEE 123-Bus system validate its accuracy against a nonlinear benchmark and capability in offering proper incentives.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2022

Space-Time Block Preconditioning for Incompressible Flow

Parallel-in-time methods have become increasingly popular in the simulation of time-dependent numerical PDEs, allowing for the efficient use of additional message passing interface processes when spatial parallelism saturates. Most methods treat the solution and parallelism in space and time separately. In contrast, all-at-once methods solve the full space-time system directly, largely treating time as simply another spatial dimension. All-at-once methods offer a number of benefits over separate treatment of space and time, most notably significantly increased parallelism and faster time to solution (when applicable). However, the development of fast, scalable all-at-once methods has largely been limited to time-dependent (advection-)diffusion problems. This paper introduces the concept of space-time block preconditioning for the all-at-once solution of incompressible flow. By extending well-known concepts of spatial block preconditioning to the space-time setting, we develop a block preconditioner whose application requires the solution of a space-time (advection-)diffusion equation in the velocity block, coupled with a pressure Schur complement approximation consisting of independent spatial solves at each time-step, and a space-time matrix-vector multiplication. The new method is tested on four classical models in incompressible flow. Finally, the results indicate perfect scalability in refinement of spatial and temporal mesh spacing, perfect scalability in nonlinear Picard iteration count when applied to a nonlinear Navier--Stokes problem, and minimal overhead in terms of number of preconditioner applications compared with sequential time-stepping.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Shadow of a laser beam

Light, being massless, casts no shadow; under ordinary circumstances, photons pass right through each other unimpeded. Here, we demonstrate a laser beam acting like an object — the beam casts a shadow upon a surface when the beam is illuminated by another light source. We observe a regular shadow in the sense it can be seen by the naked eye, it follows the contours of the surface it falls on, and it follows the position and shape of the object (the laser beam). Specifically, we use a nonlinear optical process involving four atomic levels of ruby. We are able to control the intensity of a transmitted laser beam by applying another perpendicular laser beam. We experimentally measure the dependence of the contrast of the shadow on the power of the laser beam, finding a maximum of approximately 22%, similar to that of a shadow of a tree on a sunny day. We provide a theoretical model that predicts the contrast of the shadow. This work opens new possibilities for fabrication, imaging, and illumination.

47 OTHER INSTRUMENTATION↗

NASA NTRS1972

Research in nonlinear optics

A theoretical investigation revealed that a steady state mode-locked solution appropriate to ultrashort pulses is induced by Kerr liquids. An experimental investigation using a Q-switched ruby laser passively mode-locked by the insertion of a Kerr liquid verified the theory. Pulses of about 10 to the -11th power sec were generated when the relaxation time of the liquid was temperature tuned to approximately 10 to the -11th power sec.

Yariv, A.↗

NASA NTRS1982

An efficient full potential implicit method based on characteristics for analysis of supersonic flows

A nonlinear aerodynamic prediction technique based on the full potential equation in conservation form has been developed for the treatment of supersonic flows. The method uses the theory of characteristic signal propagation to accurately simulate the flow structure, which includes shock waves and mixed elliptic-hyperbolic crossflow. An implicit approximate factorization scheme is employed to solve the finite-differenced equation. The necessary body-fitted grid system in every marching plane is generated numerically, using an elliptic grid solver. Results are shown for conical and nonconical wing-body combinations and compared with experimental data and Euler calculations. The method demonstrates an enormous savings in execution time and memory requirements over Euler methods.

Shankar, V.↗

NASA NTRS1987

Aeroelastic modeling of swept tip rotor blades using finite elements

A special finite element for the modeling of a swept tip rotor blade is derived. The swept tip blade undergoes moderate deflections in flap, lag and torsion. The nonlinear, partial differential equations of motion are discretized using a Galerkin finite element method. Tip sweep introduces flap-torsion and lag-axial couplings, and may lead to aeroelastic instabilities associated with frequency coalescence. When frequency coalescence does not occur, sweep is usually stabilizing. A comparison of the approximate model of a swept tip blade, using a blade with straight elastic axis and offsets of aerodynamic centers of gravity, with the exact swept tip model developed in this paper indicates that the approximate model can produce inaccurate results for the case of hingeless rotor blades.

Celi, R.↗

NASA NTRS1989

Kinetic theory model for the flow of a simple gas from a two-dimensional nozzle

A system of nonlinear integral equations equivalent to the Krook kinetic equation for the steady state is the mathematical basis used to develop a computer code to model the flowfields for low-thrust two-dimensional nozzles. The method of characteristics was used to solve numerically by an iteration process the approximated Boltzmann equation for the number density, temperature, and velocity profiles of a simple gas as it exhausts into a vacuum. Results predict backscatter and show the effect of the inside wall boundary layer on the flowfields external to the nozzle.

Riley, B. R.↗