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At least 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
NASA NTRS2001

Aeroelastic Response of Nonlinear Wing Section by Functional Series Technique

This paper addresses the problem of the determination of the subcritical aeroelastic response and flutter instability of nonlinear two-dimensional lifting surfaces in an incompressible flow-field via indicial functions and Volterra series approach. The related aeroelastic governing equations are based upon the inclusion of structural and damping nonlinearities in plunging and pitching, of the linear unsteady aerodynamics and consideration of an arbitrary time-dependent external pressure pulse. Unsteady aeroelastic nonlinear kernels are determined, and based on these, frequency and time histories of the subcritical aeroelastic response are obtained, and in this context the influence of the considered nonlinearities is emphasized. Conclusions and results displaying the implications of the considered effects are supplied.

Silva, Walter A.↗
NASA NTRS2000

Aeroelastic Response of Nonlinear Wing Section By Functional Series Technique

This paper addresses the problem of the determination of the subcritical aeroelastic response and flutter instability of nonlinear two-dimensional lifting surfaces in an incompressible flow-field via indicial functions and Volterra series approach. The related aeroelastic governing equations are based upon the inclusion of structural and damping nonlinearities in plunging and pitching, of the linear unsteady aerodynamics and consideration of an arbitrary time-dependent external pressure pulse. Unsteady aeroelastic nonlinear kernels are determined, and based on these, frequency and time histories of the subcritical aeroelastic response are obtained, and in this context the influence of the considered nonlinearities is emphasized. Conclusions and results displaying the implications of the considered effects are supplied.

Marzocca, Piergiovanni↗
NASA NTRS1979

A statistical model for the initial stellar mass function

The nonlinear stages of the fragmentation of a collapsing molecular cloud are modeled by coagulation theory. Several distinct physical processes are discussed, including protostellar fragment coalescence, gas accretion, and binary formation. This work confirms and extends the earlier result of Nakano (1966) that an approximately self-similar limiting form of the mass spectrum develops after several mean initial collision times. An approximate solution to the velocity-averaged coagulation equation is given for an arbitrary power-law dependence of the coalescence rate on mass, with dimensional dependence proportional to m to the power lambda; i.e., the asymptotic mass spectrum varies as m to the -3 lambda/2 power at small masses and cuts off exponentially at large masses, the characteristic mass depending on the number of collision times elapsed. Simple physical arguments suggest that lambda may increase with increasing mass, but is restricted to the range from 2/3 to 4/3. A large fraction of collisions could result in binary formation.

Silk, J.↗
NASA NTRS1977

A Green's function formulation for a nonlinear potential flow solution applicable to transonic flow

Routine determination of inviscid subsonic flow fields about wing-body-tail configurations employing a Green's function approach for numerical solution of the perturbation velocity potential equation is successfully extended into the high subsonic subcritical flow regime and into the shock-free supersonic flow regime. A modified Green's function formulation, valid throughout a range of Mach numbers including transonic, that takes an explicit accounting of the intrinsic nonlinearity in the parent governing partial differential equations is developed. Some considerations pertinent to flow field predictions in the transonic flow regime are discussed.

Baker, A. J.↗
DOE OSTI2023

Topological enhancement of nonlinear transport in unconventional point-node semimetals

The topological singularity of the Bloch states close to the Fermi level significantly enhances nonlinear electric responses in topological semimetals. Here, we systematically characterize this enhancement for a large class of topological nodal-point fermions, including those with linear, linear-quadratic, and quadratic dispersions. Specifically, we determine the leading power-law dependence of the nonlinear response functions on the chemical potential μ defined relative to the nodal point. We identify two characteristics that qualitatively improve nonlinear transports compared to those of conventional Dirac and Weyl fermions. First, the type-II (overtilted) spectrum leads to the log μ enhancement of nonlinear response functions having zero scaling dimension with respect to μ, which is not seen in a type-I (moderately or not tilted) spectrum. Second, the anisotropic linear-quadratic dispersion increases the power of small-μ divergence for the nonlinear response tensors along the linearly dispersing direction. Furthermore, our work reveals new experimental signatures of unconventional nodal points in topological semimetals as well as provides a guiding principle for giant nonlinear electric responses.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1978

Time-domain Green's Function Method for three-dimensional nonlinear subsonic flows

The Green's Function Method for linearized 3D unsteady potential flow (embedded in the computer code SOUSSA P) is extended to include the time-domain analysis as well as the nonlinear term retained in the transonic small disturbance equation. The differential-delay equations in time, as obtained by applying the Green's Function Method (in a generalized sense) and the finite-element technique to the transonic equation, are solved directly in the time domain. Comparisons are made with both linearized frequency-domain calculations and existing nonlinear results.

Tseng, K.↗
NASA NTRS1989

Numerical experience with a class of algorithms for nonlinear optimization using inexact function and gradient information

For optimization problems associated with engineering design, parameter estimation, image reconstruction, and other optimization/simulation applications, low accuracy function and gradient values are frequently much less expensive to obtain than high accuracy values. Here, researchers investigate the computational performance of trust region methods for nonlinear optimization when high accuracy evaluations are unavailable or prohibitively expensive, and confirm earlier theoretical predictions when the algorithm is convergent even with relative gradient errors of 0.5 or more. The proper choice of the amount of accuracy to use in function and gradient evaluations can result in orders-of-magnitude savings in computational cost.

Carter, Richard G.↗
DOE OSTI2021

The impacts of convex piecewise linear cost formulations on AC optimal power flow

Despite strong connections through shared application areas, research efforts on power market optimization (e.g., unit commitment) and power network optimization (e.g., optimal power flow) remain largely independent. A notable illustration of this is the treatment of power generation cost functions, where nonlinear network optimization has largely used polynomial representations and market optimization has adopted piecewise linear encodings. This work combines state-of-the-art results from both lines of research to understand the best mathematical formulations of the nonlinear AC optimal power flow problem with piecewise linear generation cost functions. An extensive numerical analysis of non-convex models, linear approximations, and convex relaxations across fifty-four realistic test cases illustrates that nonlinear optimization methods are surprisingly sensitive to the mathematical formulation of piecewise linear functions. The results indicate that a poor formulation choice can slow down algorithm performance by a factor of ten, increasing the runtime from seconds to minutes. Furthermore, these results provide valuable insights into the best formulations of nonlinear optimal power flow problems with piecewise linear cost functions, an important step towards building a new generation of energy markets that incorporate the nonlinear AC power flow model.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
NASA NTRS1985

Constrained optimization for image restoration using nonlinear programming

The constrained optimization problem for image restoration, utilizing incomplete information and partial constraints, is formulated using nonlinear proramming techniques. This method restores a distorted image by optimizing a chosen object function subject to available constraints. The penalty function method of nonlinear programming is used. Both linear or nonlinear object function, and linear or nonlinear constraint functions can be incorporated in the formulation. This formulation provides a generalized approach to solve constrained optimization problems for image restoration. Experiments using this scheme have been performed. The results are compared with those obtained from other restoration methods and the comparative study is presented.

Yeh, C.-L.↗
NASA NTRS1991

Total recall in distributive associative memories

Iterative error correction of asymptotically large associative memories is equivalent to a one-step learning rule. This rule is the inverse of the activation function of the memory. Spectral representations of nonlinear activation functions are used to obtain the inverse in closed form for Sparse Distributed Memory, Selected-Coordinate Design, and Radial Basis Functions.

Danforth, Douglas G.↗
DOE OSTI2024

Nonlinear susceptibilities for weakly turbulent magnetized plasma: Electrostatic approximation

The plasma weak turbulence theory is a perturbative nonlinear theory, which has been proven to be quite valid in a number of applications. However, the standard weak turbulence theory found in the literature is fully developed for highly idealized unmagnetized plasmas. As many plasmas found in nature and laboratory are immersed in a background static magnetic field, it is necessary to extend the existing discussions to include the effects of ambient magnetic field. Such a task is quite formidable, however, which has prevented fundamental and significant progresses in the subject matter. The central difficulty lies in the formulation of the complete nonlinear response functions for magnetized plasmas. The present paper derives the nonlinear susceptibilities for weakly turbulent magnetized plasmas up to the third order nonlinearity, but in doing so, a substantial reduction in mathematical complexity is achieved by the use of Bessel function addition theorem (or sum rule). The present paper also constructs the weak turbulence wave kinetic equation in a formal sense. For the sake of simplicity, however, the present paper assumes the electrostatic interaction among plasma particles. Fully electromagnetic generalization is a subject of a subsequent paper.

Physics↗