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All sources NASA NTRS DOE OSTI

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↗

NASA NTRS1991

Nonlinear response of resin matrix laminates using endochronic theory

The nonlinear response of laminated, resin matrix fibrous composites is modeled using orthotropic endochronic theory. The theory is formulated in terms of elastic constants and endochronic parameters characterizing the linear and nonlinear response, respectively, of unidirectional composites. All constants and parameters can be determined from normal (tension and/or compression) and shear tests on unidirectional and off-axis specimens. The nonlinear constitutive response relations for the unidirectional lamina are presented and the procedure for determining constants and parameters from test is described. The results are then used to predict the nonlinear response of unidirectional laminae and angle-ply laminates. Comparison between theory and experiment for compression loading of AS4/3502 graphite-epoxy, angle-ply laminates shows excellent correlation.

Mathison, S. R.↗

DOE OSTI2021

Hydrodynamic nonlinear response of interacting integrable systems

In this work, we develop a formalism for computing the nonlinear response of interacting integrable systems. Our results are asymptotically exact in the hydrodynamic limit where perturbing fields vary sufficiently slowly in space and time. We show that spatially resolved nonlinear response distinguishes interacting integrable systems from noninteracting ones, exemplifying this for the Lieb–Liniger gas. We give a prescription for computing finite-temperature Drude weights of arbitrary order, which is in excellent agreement with numerical evaluation of the third-order response of the XXZ spin chain. We identify intrinsically nonperturbative regimes of the nonlinear response of integrable systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Mixed higher-order anisotropic flow and nonlinear response coefficients of charged particles in $\mathrm {PbPb}$ collisions at $\sqrt{\smash [b]{s_{_{\mathrm {NN}}}}} = 2.76$ and 5.02$\,\text {TeV}$

Anisotropies in the initial energy density distribution of the quark-gluon plasma created in high energy heavy ion collisions lead to anisotropies in the azimuthal distributions of the final-state particles known as collective anisotropic flow. Fourier harmonic decomposition is used to quantify these anisotropies. The higher-order harmonics can be induced by the same order anisotropies (linear response) or by the combined influence of several lower order anisotropies (nonlinear response) in the initial state. The mixed higher-order anisotropic flow and nonlinear response coefficients of charged particles are measured as functions of transverse momentum and centrality in $\mathrm {PbPb}$ collisions at nucleon-nucleon center-of-mass energies $\sqrt{\smash [b]{s_{_{\mathrm {NN}}}}} = 2.76$ and 5.02$\,\text {TeV}$ with the CMS detector. The results are compared with viscous hydrodynamic calculations using several different initial conditions, as well as microscopic transport model calculations. None of the models provides a simultaneous description of the mixed higher-order flow harmonics and nonlinear response coefficients.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRS1995

Numerical simulation of the nonlinear response of composite plates under combined thermal and acoustic loading

A time-domain study of the random response of a laminated plate subjected to combined acoustic and thermal loads is carried out. The features of this problem also include given uniform static inplane forces. The formulation takes into consideration a possible initial imperfection in the flatness of the plate. High decibel sound pressure levels along with high thermal gradients across thickness drive the plate response into nonlinear regimes. This calls for the analysis to use von Karman large deflection strain-displacement relationships. A finite element model that combines the von Karman strains with the first-order shear deformation plate theory is developed. The development of the analytical model can accommodate an anisotropic composite laminate built up of uniformly thick layers of orthotropic, linearly elastic laminae. The global system of finite element equations is then reduced to a modal system of equations. Numerical simulation using a single-step algorithm in the time-domain is then carried out to solve for the modal coordinates. Nonlinear algebraic equations within each time-step are solved by the Newton-Raphson method. The random gaussian filtered white noise load is generated using Monte Carlo simulation. The acoustic pressure distribution over the plate is capable of accounting for a grazing incidence wavefront. Numerical results are presented to study a variety of cases.

Mei, Chuh↗

NASA NTRS1989

Linear and nonlinear responses to middle latitude surface temperature anomalies

Nonlinear responses to fixed and seasonally varying surface temperature anomalies in a two-level hemispheric time-dependent coupled atmosphere-surface mixed layer model are described. Linear stationary models that are equivalent to the nonlinear time-dependent model are used to analyze these responses. A model linearized around the climatological zonal state of the time dependent model and forced by anomalous surface temperatures does not provide a reasonable estimate for the anomalous reponses, which are considerably underestimated. Better responses are obtained when the anomalous stationary nonlinear eddy fluxes are included in a model linearized around the full climatology. However, this latter model is overly sensitive, and anomalous responses are a small residual balance to the forcing by the surface temperature anomalies and the anomalous transient eddy fluxes. To better understand these linear responses, an eigenanalysis of the climatological state is performed. Seasonal anomalies appear to be dominated by one characteristic pattern near resonance which can be associated with a slowly growing coupled atmosphere-ocean instability.

Roads, John O.↗

NASA NTRS1990

Nonlinear response of unidirectional boron/aluminum

Experimental results obtained for unidirectional boron/aluminum subjected to combined loading using off-axis tension, compression and Iosipescu shear specimens are correlated with a nonlinear micromechanics model. It is illustrated that the nonlinear response in the principal material directions is markedly influenced by the different loading modes and different ratios of the applied stress components. The observed nonlinear response under pure and combined loading is discussed in terms of initial yielding, subsequent hardening, stress-interaction effects and unloading-reloading characteristics. The micromechanics model is based on the concept of a repeating unit cell representative of the composite-at-large and employs the unified theory of Bodner and Partom to model the inelastic response of the matrix. It is shown that the employed micromechanics model is sufficiently general to predict the observed nonlinear response of unidirectional boron/aluminum with good accuracy.

Pindera, M.-J.↗

NASA NTRS1973

Nonlinear response of boron/aluminum angleplied laminates under cyclic tensile loading: Contributing mechanisms and their effects

The nonlinear response of boron/aluminum angleplied laminates subjected to cyclic loads was investigated. A procedure is outlined and criteria are proposed which can be used to assess the nonlinear response. The procedure consists of testing strategically selected laminate configurations and analyzing the results using composite mechanics. Results from the investigation show the contributions to nonlinear behavior are from: premature random fiber breaks where the ply orientation angle is small relative to the load direction, ply relative rotation at intermediate values of the ply orientation angle, and nonlinear aluminum matrix behavior at large values of the orientation angle. Premature fiber breaks result in progressively more compliant material; large ply relative rotations result in progressively stiffer material; and pronounced matrix nonlinear behavior results in no significant change in the stiffness of the initial load portion.

Chamis, C. C.↗

NASA NTRS1973

Nonlinear response of boron/aluminum angleplied laminates under cyclic tensile loading - Contributing mechanisms and their effects

Chamis, C. C.↗

DOE OSTI2021

Nonlinear Response of Atmospheric Blocking to Early Winter Barents–Kara Seas Warming: An Idealized Model Study

Wintertime Ural blocking (UB) has been shown to play an important role in cold extremes over Eurasia, and thus it is useful to investigate the impact of warming over the Barents–Kara Seas (BKS) on the behavior of Ural blocking. In our study the response of UB to stepwise tropospheric warming over the BKS is examined using a dry dynamic core model. Nonlinear responses are found in the frequency and local persistence of UB. The frequency and local persistence of the UB increase with the strength of BKS warming in a less strong range and decrease with the further increase of BKS warming, which is linked to the UB propagation influenced by upstream background atmospheric circulation. For a weak BKS warming, the UB becomes more persistent due to its less westward movement associated with intensified upstream zonal wind and meridional potential vorticity gradient (PVy) in the North Atlantic mid-high latitudes, which corresponds to a negative height response over the North Atlantic high latitudes. When BKS warming is strong, a positive height response appears in the early winter stratosphere, and its subsequent downward propagation leads to a negative NAO response or increased Greenland blocking events, which reduces zonal wind and PVy in the high latitudes from North Atlantic to Europe, thus enhancing the westward propagation of UB and reducing its local persistence. The transition to the negative NAO phase and the retrogression of UB are not found when numerically suppressing the downward influence of weakened stratospheric polar vortex, suggesting a crucial role of the stratospheric pathway in nonlinear responses of UB to the early winter BKS warming.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Experimental Investigation of Elastodynamic Nonlinear Response of Dry Intact, Fractured and Saturated Rock

Nonlinear elastodynamic response of fractured rocks carries crucial information on fracture features that can be exploited to forecast flow properties, friction constitutive behavior and poromechanical response. Well-controlled laboratory experiments are designed to measure the nonlinear elastodynamic response of Westerly granite in three states: dry intact, dry fractured and saturated fractured. We study the effect of fracturing and saturation in modifying the elastodynamic response of the rock. Each sample is tested at a normal stress level of 15 MPa. We measure the elastodynamic response of an intact L-shaped sample of Westerly Granite subjected to normal stress oscillations of prescribed amplitudes (0.2–1 MPa) and frequencies (0.1, 1, 10 Hz). Ultrasonic waves transmitted across the sample are used to monitor the evolution of wave velocity before, during and after dynamic stressing. Furthermore, the nonlinearity of the elastodynamic response is measured in terms of: (1) the offset in normalized wave velocity; (2) the amplitude of wave velocity fluctuation during the oscillations; and (3) recovery rate of the wave velocity post-oscillation. We observe that the three nonlinearity parameters show a similar trend. Irrespective of the parameter, the nonlinearity measures higher for sample in dry-intact condition than that for dry-fractured and the saturated-fractured sample exhibits smaller nonlinearity than the dry-fractured sample. As expected, the saturated sample exhibits less nonlinearity than the dry intact and fractured samples due to the presence of interstitial fluid and the resulting increased interface stiffness. Conversely, the dry intact rock shows a higher nonlinearity than the dry fractured. We use numerical simulations to show that the presence of fracture significantly alters the strain distribution across the bulk of the sample and only the contacting asperities are highly strained, thus resulting in a decrease in the measured elastodynamic nonlinearity.

58 GEOSCIENCES↗

DOE OSTI2023

False Indications of Dose-Response Nonlinearity in Large Epidemiologic Cancer Radiation Cohort Studies; A Simulation Exercise

This study explores the likely prevalence of false indications of dose-response nonlinearity in large epidemiologic cancer radiation cohort studies (A-bomb survivors, INWORKS, Techa River). Reasons: Increasing numbers of tests of nonlinearity are being made in studies. Hypothesized nonlinear dose-response models have been justified to policy makers by analyses that rely in part on isolated findings that could be statistical fluctuations. After removing dose nonlinearity (linearization) by adjusting person-years of observation at each dose category, indications of nonlinearity, necessarily false, were counted in 5,000 randomized replications of six datasets. The average frequency of any false positive for five indicators of nonlinearity tested against a linear null was roughly 25% in Monte Carlo simulations per study, consistent with binomial calculations, increasing to ~50% within 6 studies assessed. Comparable frequencies were found using Akaike's information criterion (AIC) for model selection or multi-model averaging. False above-zero threshold doses were found more than 50% of the time, averaging to 0.05 Gy, consistent with findings in the 6 studies. Such bias, uncorrected, could distort meta-analyses of multiple studies, because meta-analyses can incorporate high P value findings. AIC-based correction for the extra threshold parameter lowered these false occurrences to 8 to 19%. Given the simulation rates, the possibility of false positives might be noted when isolated findings of nonlinearity are discussed in a regulatory context. When reporting a threshold dose with a P value > 0.05, it would be informative to note the expected high false prevalence rate due to bias.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

NASA NTRS1998

Nonlinear Response of Thin Cylindrical Shells with Longitudinal Cracks and Subjected to Internal Pressure and Axial compression Loads

The results of an analytical study of the nonlinear response of a thin unstiffened aluminum cylindrical shell with a longitudinal crack are presented. The shell is analyzed with a nonlinear shell analysis code that maintains the shell in a nonlinear equilibrium state while the crack is grown. The analysis accurately accounts for global and local structural response phenomena. Results are presented for internal pressure, axial compression, and combined internal pressure and axial compression loads. The effects of varying crack length on the nonlinear response of the shell subjected to internal pressure are described. The effects of varying crack length on the prebuckling, buckling and postbuckling responses of the shell subjected to axial compression, and subjected to combined internal pressure and axial compression are also described. The results indicate that the nonlinear interaction between the in-plane stress resultants and the out-of-plane displacements near a crack can significantly affect the structural response of the shell. The results also indicate that crack growth instabilities and shell buckling instabilities can both affect the response of the shell as the crack length is increased.

Starnes, James H.↗

NASA NTRS1973

Nonlinear response of plates subjected to inplane and lateral pressure pulses.

The nonlinear response of a rectangular plate exposed to a far-field sonic boom disturbance is studied. The plate is subjected to both lateral and in-plane disturbances. The lateral disturbance is in the form of an N-shaped pressure pulse, and the in-plane disturbance is represented by a sinusoidal pulse. The equations of motion are reduced to a set of nonlinear coupled ordinary differential equations using Galerkin's method. These equations are solved numerically using Hamming's (1959) modified predictor-corrector integration method. The effects of in-plane boundary conditions and in-plane inertia are investigated. The nonlinear results, when compared to the linear theory, serve to delineate the realm of validity of the linear theory.

Knapp, L. J.↗

DOE OSTI2020

Effect of Berry phase on nonlinear response of two-dimensional fermions

We develop a theory of nonlinear response to an electric field of two-dimensional (2D) fermions with topologically nontrivial wave functions characterized by the Berry phase Φ n = n π , n = 1 , 2 , ... . In particular, we find that owing to the suppression of backscattering at odd n , Hall field-induced resistance oscillations, which stem from elastic electron transitions between Hall field-tilted Landau levels, are qualitatively distinct from those at even n : Their amplitude decays with the electric field and their extrema are phase shifted by a quarter cycle. The theory unifies the cases of graphene ( n = 1 ) and graphite bilayer ( n = 2 ) with the case of conventional 2D electron gas ( n = 0 ) and suggests another method to probe backscattering in topological 2D systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS1969

Nonlinear response of a cylindrical shell to an impulsive pressure.

Circular cylindrical shell nonlinear response to uniform radial impulsive pressure, noting inextensionality constraint and equations of motion roles

Lovell, E. G.↗

NASA NTRS1991

Nonlinear response of infinitely long circular cylindrical shells to subharmonic radial loads

The nonlinear response of infinitely long circular cylindrical shells (thin circular rings) in the presence of a two-to-one internal (autoparametric) resonance to a subharmonic excitation of order one-half of the higher mode is analyzed with the multiple-scale method. Four autonomous first-order ordinary differential equations are derived for the modulation of the amplitudes and phases of the interacting models. These modulation equations are used to determine the fixed points and their stability. The fixed points correspond to periodic oscillations of the shell, whereas the limit-cycle solutions of the modulation equations correspond to amplitude and phase-modulated oscillations of the shell. The force response curves exhibit saturation, jumps, and Hopf bifurcation. As excitation frequency changes, all limit cycles deform and lose stability through either pitchfork or cyclic-fold (saddle-node) bifurcations. Some of these saddle-node bifurcations cause a transition to chaos. The pitchfork bifurcations break the symmetry of the limit cycles.

Nayfeh, Ali H.↗

NASA NTRS1986

Nonlinear response - A time domain approach

The present paper reviews the basic concepts of nonlinear response of panels to surface flow and acoustic pressures, simulation of random processes, time domain solutions and the Monte Carlo Method. Applications of this procedure to the orbit-on-demand space vehicles, acoustic fatigue and composite materials are discussed. Numerical examples are included for a variety of nonlinear problems to illustrate the applicability of this method.

Vaicaitis, R.↗