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At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

Nonlinear Color–Metallicity Relations of Globular Clusters. VII. Nonlinear Absorption-line Index versus Metallicity Relations and Bimodal Index Distributions of NGC 5128 Globular Clusters

Spectroscopy on the globular cluster (GC) system of NGC 5128 revealed bimodality in absorption-line index distributions of its old GCs. GC division is a widely observed and studied phenomenon whose interpretation has depicted host galaxy formation and evolution such that it harbors two distinct metallicity groups. Such a conventional view of GC bimodality has mainly been based on photometry. The recent GC photometric data, however, presented an alternative perspective in which the nonlinear metallicity-to-color transformation is responsible for color bimodality of GC systems. Here we apply the same line of analysis to the spectral indices and examine the absorption-line index versus metallicity relations for the NGC 5128 GC system. NGC 5128 GCs display nonlinearity in the metallicity-index planes, most prominently for the Balmer lines and by a non-negligible degree for the metallicity-sensitive magnesium line. We demonstrate that the observed spectroscopic division of NGC 5128 GCs can be caused by the nonlinear nature of the metallicity-to-index conversions and thus one does not need to resort to two separate GC subgroups. Our analysis incorporating this nonlinearity provides a new perspective on the structure of NGC 5128's GC system, and a further piece to the global picture of the formation of GC systems and their host galaxies.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Propagation of a finite-amplitude elastic pulse in a bar of Berea sandstone: A detailed look at the mechanisms of classical nonlinearity, hysteresis, and nonequilibrium dynamics: Nonlinear propagation of elastic pulse

Here, we study the propagation of a finite-amplitude elastic pulse in a long thin bar of Berea sandstone. In previous work, this type of experiment has been conducted to quantify classical nonlinearity, based on the amplitude growth of the second harmonic as a function of propagation distance. To greatly expand on that early work, a non-contact scanning 3D laser Doppler vibrometer was used to track the evolution of the axial component of the particle velocity over the entire surface of the bar as functions of the propagation distance and source amplitude. With these new measurements, the combined effects of classical nonlinearity, hysteresis, and nonequilibrium dynamics have all been measured simultaneously. We then show that the numerical resolution of the 1D wave equation with terms for classical nonlinearity and attenuation accurately captures the spectral features of the waves up to the second harmonic. But, for higher harmonics the spectral content is shown to be strongly influenced by hysteresis. This work also shows data which not only quantifies classical nonlinearity but also the nonequilibrium dynamics based on the relative change in the arrival time of the elastic pulse as a function of strain and distance from the source. Finally, a comparison is made to a resonant bar measurement, a reference experiment used to quantify nonequilibrium dynamics, based on the relative shift of the resonance frequencies as a function of the maximum dynamic strain in the sample.

58 GEOSCIENCES↗
DOE OSTI2020

Parametrically driven nonlinear Dirac equation with arbitrary nonlinearity

Here, the damped and parametrically driven nonlinear Dirac equation with arbitrary nonlinearity parameter $\kappa$ is analyzed, when the external force is periodic in space and given by $\mathcal{f(x) = r}$ cos(Kx), both numerically and in a variational approximation using five collective coordinates (time dependent shape parameters of the wave function). Our variational approximation satisfies exactly the low-order moment equations. Because of competition between the spatial period of the external force λ = 2π/K , and the soliton width $l_s$, which is a function of the nonlinearity $\kappa$ as well as the initial frequency ω 0 of the solitary wave, there is a transition (at fixed ω 0 ) from trapped to unbound behavior of the soliton, which depends on the parameters $\mathcal{r}$ and K of the external force and the nonlinearity parameter $\kappa$. We previously studied this phenomena when $\kappa$ = 1 where we showed that for λ $\gg l_s$ the soliton oscillates in an effective potential, while forλ $\ll l_s$ it moves uniformly as a free particle. In this paper we focus on the $\kappa$ dependence of the transition from oscillatory to particle behavior and explicitly compare the curves of the transition regime found in the collective coordinate approximation as a function of $\mathcal{r}$ and K when $\kappa$ = 1/2,1,2 at fixed value of the frequency ω 0 . Since the solitary wave gets narrower for fixed ω 0 as a function of $\kappa$, we expect and indeed find that the regime where the solitary wave is trapped is extended as we increase $\kappa$.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2016

Nonlinear dynamics from the relativistic Boltzmann equation in the Friedmann-Lemaître-Robertson-Walker spacetime

The dissipative dynamics of an expanding massless gas with constant cross section in a spatially flat Friedmann-Lemaître-Robertson-Walker (FLRW) universe is researched. The mathematical problem of solving the full nonlinear relativistic Boltzmann equation is recast into an infinite set of nonlinear ordinary differential equations for the moments of the one-particle distribution function. Momentum-space resolution is determined by the number of nonhydrodynamic modes included in the moment hierarchy, i.e., by the truncation order. We show that in the FLRW spacetime the nonhydrodynamic modes decouple completely from the hydrodynamic degrees of freedom. This results in the system flowing as an ideal fluid while at the same time producing entropy. The solutions to the nonlinear Boltzmann equation exhibit transient tails of the distribution function with nontrivial momentum dependence. The evolution of this tail is not correctly captured by the relaxation time approximation nor by the linearized Boltzmann equation. Yet, the latter probes additional high-momentum details unresolved by the relaxation time approximation. While the expansion of the FLRW spacetime is slow enough for the system to move towards (and not away from) local thermal equilibrium, it is not sufficiently slow for the system to actually ever reach complete local equilibrium. Equilibration is fastest in the relaxation time approximation, followed, in turn, by kinetic evolution with a linearized and a fully nonlinear Boltzmann collision term.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2019

Nonlinearity from stress corrosion cracking as a function of chloride exposure time using the time reversed elastic nonlinearity diagnostic

The Time Reversed Elastic Nonlinearity Diagnostic (TREND) has a long history of successful nondestructive detection of cracks in solids using nonlinear indicators. Recent research implemented TREND to find stress corrosion cracking (SCC) in the heat-affected zone adjacent to welds in stainless steel. SCC development around welds is likely to occur due to the temperature and chemical exposure of steel canisters housing spent nuclear fuel. The ideal SCC detection technique would quantify the size and extent of the SCC, rather than just locating it, as TREND has been used for in the past. The current paper explores TREND's ability to detect an assumed increase in SCC over time using 13 samples exposed to a magnesium chloride (MgCl 2 ) bath for different lengths of time. The samples are then scanned with TREND and nonlinearity is quantified for each scan point and each sample. The results suggest that TREND can be used to not only locate SCC in the heat-affected zone, but also track an increase in nonlinearity, and thereby an increase in damage, in samples exposed to the MgCl 2 solution for a longer duration.

42 ENGINEERING↗
DOE OSTI2019

A Vortex Step Method for Nonlinear Airfoil Polar Data as Implemented in KiteAeroDyn: Preprint

This paper summarizes the underlying theory in the recently developed KiteAeroDyn (KiteAD) module, which is part of KiteFAST (KiteFAST), a numerical simulation tool that is currently being developed at the NREL. KiteFAST is intended for the simulation of airborne wind energy systems (e.g., energy kites). KiteAD implements an innovative vortex step method for the calculation of aerodynamic loads on all of the lifting surfaces of the kite, which is capable of accounting for two-dimensional viscous effects through the use of nonlinear airfoil polars. Considering nonlinear airfoil polar data allows for the modeling of flap or other moving-surface deflections, as well as for the modelling of inflow conditions with larger angles angles of attack. From preliminary verification against other existing codes that can solve for lift distribution on lifting surfaces, the results of the newly implemented method proved to be numerically robust and computationally inexpensive, thus ideal for aeroelastic design and analysis applications.

17 WIND ENERGY↗
NASA NTRS1982

A design methodology for nonlinear systems containing parameter uncertainty: Application to nonlinear controller design

A design methodology capable of dealing with nonlinear systems, such as a controlled ecological life support system (CELSS), containing parameter uncertainty is discussed. The methodology was applied to the design of discrete time nonlinear controllers. The nonlinear controllers can be used to control either linear or nonlinear systems. Several controller strategies are presented to illustrate the design procedure.

Young, G.↗
NASA NTRS1994

Multigrid techniques for nonlinear eigenvalue probems: Solutions of a nonlinear Schroedinger eigenvalue problem in 2D and 3D

This paper presents multigrid (MG) techniques for nonlinear eigenvalue problems (EP) and emphasizes an MG algorithm for a nonlinear Schrodinger EP. The algorithm overcomes the mentioned difficulties combining the following techniques: an MG projection coupled with backrotations for separation of solutions and treatment of difficulties related to clusters of close and equal eigenvalues; MG subspace continuation techniques for treatment of the nonlinearity; an MG simultaneous treatment of the eigenvectors at the same time with the nonlinearity and with the global constraints. The simultaneous MG techniques reduce the large number of self consistent iterations to only a few or one MG simultaneous iteration and keep the solutions in a right neighborhood where the algorithm converges fast.

Costiner, Sorin↗
DOE OSTI2021

Gauge invariance and Ward identities in nonlinear response theory

We present a formal analysis of nonlinear response functions in terms of correlation functions in real- and imaginary-time domains. In particular, we show that causal nonlinear response functions, expressed in terms of nested commutators in real time, can be obtained from the analytic continuation of time-ordered response functions, which are more easily amenable to diagrammatic calculation. This generalizes the well-known result of linear response theory. We then use gauge invariance arguments to derive exact relations between second-order response functions in density and current channels. These identities, which are non-perturbative in the strength of inter-particle interactions, allow us to establish exact connections between nonlinear optics calculations done in different electromagnetic gauges.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Rogue wave solutions for a generalized nonautonomous nonlinear equation in a nonlinear inhomogeneous fiber

In this paper, we investigate a generalized nonautonomous nonlinear equation which describes the ultrashort optical pulse propagating in a nonlinear inhomogeneous fiber. By virtue of the generalized Darboux transformation, the first- and second-order rogue-wave solutions for the generalized nonautonomous nonlinear equation are obtained, under some variable–coefficient constraints. Properties of the first- and second-order rogue waves are graphically presented and analyzed: When the coefficients are all chosen as the constants, we can observe the some functions, the shapes of wave crests and troughs for the first- and second-order rogue waves change. Oscillating behaviors of the first- and second-order rogue waves are observed when the coefficients are the trigonometric functions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

An added-mass partition algorithm for fluid–structure interactions of compressible fluids and nonlinear solids

We describe an added-mass partitioned (AMP) algorithm for solving fluid–structure interaction (FSI) problems involving inviscid compressible fluids interacting with nonlinear solids that undergo large rotations and displacements. The computational approach is a mixed Eulerian–Lagrangian scheme that makes use of deforming composite grids (DCG) to treat large changes in the geometry in an accurate, flexible, and robust manner. The current work extends the AMP algorithm developed in Banks et al. [1] for linearly elasticity to the case of nonlinear solids. To ensure stability for the case of light solids, the new AMP algorithm embeds an approximate solution of a nonlinear fluid–solid Riemann (FSR) problem into the interface treatment. The solution to the FSR problem is derived and shown to be of a similar form to that derived for linear solids: the state on the interface being fundamentally an impedance-weighted average of the fluid and solid states. Numerical simulations demonstrate that the AMP algorithm is stable even for light solids when added-mass effects are large. The accuracy and stability of the AMP scheme is verified by comparison to an exact solution using the method of analytical solutions and to a semi-analytical solution that is obtained for a rotating solid disk immersed in a fluid. The scheme is applied to the simulation of a planar shock impacting a light elliptical-shaped solid, and comparisons are made between solutions of the FSI problem for a neo-Hookean solid, a linearly elastic solid, and a rigid solid. The ability of the approach to handle large deformations is demonstrated for a problem of a high-speed flow past a light, thin, and flexible solid beam.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Nonlinear optical propagation in a tandem structure comprising nonlinear absorption and scattering materials

Laser propagation in a tandem structure comprising carbon nanotubes and phthalocyanines is studied by Z-scan method. Due to the different mechanisms of the two materials, the laser beam can be attenuated with different absorptivities, by changing the sequence of light passing through each material. Numerical simulations considering the effect of path length and the change of nonlinear coefficient within each material are conducted for understanding the distribution of laser intensity in the tandem system and hence, fitting of the asymmetric Z-scan curves. The results are helpful for the design of nonlinear optical devices comprising multiple nonlinear materials and mechanisms.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Nonlinear hybrid simulation of internal kink with beam ion effects in DIII-D

In DIII-D sawteething plasmas, long-lived (1,1) kink modes are often observed between sawtooth crashes. The saturated kink modes have two distinct frequencies. The mode with higher frequency transits to a fishbone-like mode with sufficient on-axis neutral beam power. In this work, hybrid simulations with the global kinetic-magnetohydrodynamic (MHD) hybrid code M3D-K have been carried out to investigate the linear stability and nonlinear dynamics of the n = 1 mode with effects of energetic beam ions for a typical DIII-D discharge where both saturated kink mode and fishbone were observed. Linear simulation results show that the n = 1 internal kink mode is unstable in MHD limit. However, with kinetic effects of beam ions, a fishbone-like mode is excited with mode frequency about a few kHz depending on beam pressure profile. The mode frequency is higher at higher beam power and/or narrower radial profile consistent with the experimental observation. Nonlinear simulations have been performed to investigate mode saturation as well as energetic particle transport. The nonlinear MHD simulations show that the unstable kink mode becomes a saturated kink mode after a sawtooth crash. With beam ion effects, the fishbone-like mode can also transit to a saturated kink mode with a small but finite mode frequency. These results are consistent with the experimental observation of saturated kink mode between sawtooth crashes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2013

NONLINEAR COLOR-METALLICITY RELATIONS OF GLOBULAR CLUSTERS. IV. TESTING THE NONLINEARITY SCENARIO FOR COLOR BIMODALITY VIA HST/WFC3 u-BAND PHOTOMETRY OF M84 (NGC 4374)

Color distributions of globular clusters (GCs) in most massive galaxies are bimodal. Assuming linear color-to-metallicity conversions, bimodality is viewed as the presence of merely two GC subsystems with distinct metallicities, which serves as a critical backbone of various galaxy formation theories. Recent studies, however, revealed that the color-metallicity relations (CMRs) often used to derive GC metallicities (e.g., CMRs of g - z, V - I, and C - T{sub 1}) are in fact inflected. Such inflection can create bimodal color distributions if the underlying GC metallicity spread is simply broad as expected from the hierarchical merging paradigm of galaxy formation. In order to test the nonlinear-CMR scenario for GC color bimodality, the u-band photometry is proposed because the u-related CMRs (e.g., CMRs of u - g and u - z) are theoretically predicted to be least inflected and most distinctive among commonly used optical CMRs. Here, we present Hubble Space Telescope (HST)/WFC3 F336W (u-band) photometry of the GC system in M84, a giant elliptical in the Virgo galaxy cluster. Combining the u data with the existing HST ACS/WFC g and z data, we find that the u - z and u - g color distributions are different from the g - z distribution in a very systematic manner and remarkably consistent with our model predictions based on the nonlinear-CMR hypothesis. The results lend further confidence to the validity of the nonlinear-CMR scenario as an explanation for GC color bimodality. There are some GC systems showing bimodal spectroscopic metallicity, and in such systems the inflected CMRs often create stronger bimodality in the color domain.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Stability of trapped solutions of a nonlinear Schrödinger equation with a nonlocal nonlinear self-interaction potential

This work focuses on the study of the stability of trapped soliton-like solutions of a (1 + 1)-dimensional nonlinear Schrödinger equation (NLSE) in a nonlocal, nonlinear, self-interaction potential of the form [|Ψ(x,t)| 2 +|Ψ(-x,t)| 2 ] κ where κ is an arbitrary nonlinearity parameter. Although the system with κ = 1 (i.e. fully integrable case) was first reported by Yang (2018 Phys. Rev. E 98 042202), here in the present work, we extend this model to the one in which κ is arbitrary. This allows us to compare the stability properties of the now trapped solutions to previously found solutions of the more usual NLSE with κ ≠ 1 which are moving soliton solutions. We show that there is a simple, one-component, nonlocal Lagrangian and corresponding action governing the dynamics of the system. Using a collective coordinate method derived from the action as well as assuming the validity of Derrick's theorem, we find that these trapped solutions are stable for 0 < κ < 2 and unstable when κ > 2. At the critical value of κ, i.e. κ = 2, the solution can either collapse or blowup linearly in time when q 0 = 0, where q 0 is the center of the initial density ρ(x, t = 0) = ψ*ψ of the solution. For q 0 ≠ 0 the displaced solution collapses. When κ > 2 initial small displacements from the origin also lead to collapse of the wave function. This phenomenon is not seen in the usual NLSE.

collective coordinates↗
DOE OSTI2019

Localized States near a Thin Layer with the Nonlinear Properties Separating Nonlinear Focusing and Defocusing Media

Based on the nonlinear Schrödinger equation, new types of localized states near the contact of defocusing and self-focusing media with the Kerr nonlinearity separated by a thin defect layer with the similar nonlinearity have been described. The occurrence of the localized states of two types is demonstrated. The dispersion relations between the excitation localization energy and characteristics of the media and defect layer have been obtained. The localization energy levels for particular cases have been obtained in the explicit analytical form.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗