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At least 199 records · Page 11

Time scales for nonlinear processes in preheating after multifield inflation with nonminimal couplings

We have conducted extensive lattice simulations to study the postinflation dynamics of multifield models involving nonminimal couplings. In this work, we explore the parameter dependence of preheating in these models and describe the various time scales that control such nonlinear processes as energy transfer, rescattering, and the approach to radiation domination and thermalization. In the limit of large nonminimal couplings ($ξ_I$ ~ 100), we find that efficient transfer of energy from the inflaton condensate to radiative degrees of freedom, emergence of a radiation-dominated equation of state, and the onset of thermalization each consistently occur within $N_{\text{reh}} ≲ 3 e$-folds after the end of inflation, largely independent of the values of the other couplings in the models. The exception is the case of negative ellipticity, in which there is a misalignment between the dominant direction in field space along which the system evolves and the larger of the nonminimal couplings $ξ_I$. In those cases, the field-space-driven parametric resonance is effectively shut off. More generally, the competition between the scalar fields’ potential and the field-space manifold structure can yield interesting phenomena such as two-stage resonances. Across many regions of parameter space, we find efficient re-scattering between the distinct fields, leading to a partial memory loss of the shape of the initial fluctuation spectrum. Despite the explosive particle production, which can lead to a quick depletion of the background energy density, the nonlinear processes do not induce any superhorizon correlations after the end of inflation in these models, which keeps predictions for cosmic microwave background observables unaffected by the late-time amplification of isocurvature fluctuations. Hence the excellent agreement between primordial observables and recent observations is preserved for this class of models, even when we consider postinflation dynamics.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Nonlinear optical response of metal-barrier-metal junctions

The optical response of metal-barrier-metal (MBM) junctions is discussed, with emphasis on the nonlinearity of response associated with reversal of polarity as optical intensity is increased. This nonlinear behavior can be used to measure correlation functions of optical pulses or to generate ultrashort electrical pulses. Expressions for the current flowing through the insulating barrier (junction), and for the rectification current, are given. Pulse signal and polarity of the electrical pulse evolves as the junction bias is varied about the null-signal bias. The apparatus used to obtain rectification pulse signals is described; the calculated evolution of the rectified pulse shape is found to correspond to that of pulse signals obtained experimentally. The generation of pulses six orders of magnitude smaller than a previously-obtained instrument-limited 1.6 nanosecond pulse has been observed.

Fan, B.↗

Uncertainty Analysis of Instrument Calibration and Application

Experimental aerodynamic researchers require estimated precision and bias uncertainties of measured physical quantities, typically at 95 percent confidence levels. Uncertainties of final computed aerodynamic parameters are obtained by propagation of individual measurement uncertainties through the defining functional expressions. In this paper, rigorous mathematical techniques are extended to determine precision and bias uncertainties of any instrument-sensor system. Through this analysis, instrument uncertainties determined through calibration are now expressed as functions of the corresponding measurement for linear and nonlinear univariate and multivariate processes. Treatment of correlated measurement precision error is developed. During laboratory calibration, calibration standard uncertainties are assumed to be an order of magnitude less than those of the instrument being calibrated. Often calibration standards do not satisfy this assumption. This paper applies rigorous statistical methods for inclusion of calibration standard uncertainty and covariance due to the order of their application. The effects of mathematical modeling error on calibration bias uncertainty are quantified. The effects of experimental design on uncertainty are analyzed. The importance of replication is emphasized, techniques for estimation of both bias and precision uncertainties using replication are developed. Statistical tests for stationarity of calibration parameters over time are obtained.

Tripp, John S.↗

Modeling heart rate variability by stochastic feedback

We consider the question of how the cardiac rhythm spontaneously self-regulates and propose a new mechanism as a possible answer. We model the neuroautonomic regulation of the heart rate as a stochastic feedback system and find that the model successfully accounts for key characteristics of cardiac variability, including the 1/f power spectrum, the functional form and scaling of the distribution of variations of the interbeat intervals, and the correlations in the Fourier phases which indicate nonlinear dynamics.

Non-NASA Center↗

Proceedings of the Second Annual Symposium for Nondestructive Evaluation of Bond Strength

Ultrasonics, microwaves, optically stimulated electron emission (OSEE), and computational chemistry approaches have shown relevance to bond strength determination. Nonlinear ultrasonic nondestructive evaluation methods, however, have shown the most effectiveness over other methods on adhesive bond analysis. Correlation to changes in higher order material properties due to microstructural changes using nonlinear ultrasonics has been shown related to bond strength. Nonlinear ultrasonic energy is an order of magnitude more sensitive than linear ultrasound to these material parameter changes and to acoustic velocity changes caused by the acoustoelastic effect when a bond is prestressed. Signal correlations between non-linear ultrasonic measurements and initialization of bond failures have been measured. This paper reviews bond strength research efforts presented by university and industry experts at the Second Annual Symposium for Nondestructive Evaluation of Bond Strength organized by the NDE Sciences Branch at NASA Langley in November 1998.

Roberts, Mark J.↗

The topology of fractal universes

It is shown how the genus per unit volume of isodensity surfaces in general nonlinear universes is related to the entire hierarchy of correlation functions. The general relation between the correlation function, the probability distribution of densities at several points, and the probability distributions of density and its derivatives at a point are given. Formulas for the area and genus per unit volume of isodensity surfaces are presented. As an application, after first reviewing the case of Gaussian fields, analytic results are reported for one particular example of a thoroughly nonlinear universe, Mandelbrot's Rayleigh-Levy random-walk fractal. While this fractal bears little resemblance to the real universe of galaxies, it possesses the singular and theoretically interesting property that in it cluster-cluster correlations are identically equal to galaxy-galaxy correlations to all orders.

Hamilton, A. J. S.↗

Proceedings of the First Annual Symposium for Nondestructive Evaluation of Bond Strength

Quantitative adhesive bond strength measurement has been an issue for over thirty years. Utilization of nonlinear ultrasonic nondestructive evaluation methods has shown more effectiveness than linear methods on adhesive bond analysis, resulting in an increased sensitivity to changes in bondline conditions. Correlation to changes in higher order material properties due to microstructural changes using nonlinear ultrasonics has been shown and could relate to bond strength. Nonlinear ultrasonic energy is an order of magnitude more sensitive than linear ultrasound to these material parameter changes and to acoustic velocity changes caused by the acoustoelastic effect when a bond is prestressed. This increased sensitivity will assist in getting closer to quantitative measurement of adhesive bond strength. Signal correlations between non-linear ultrasonic measurements and initialization of bond failures have been successfully measured. This paper reviews nonlinear bond strength research efforts presented by university and industry experts at the First Annual Symposium for Nondestructive Evaluation of Bond Strength organized by the NDE Sciences Branch at NASA Langley in November 1997.

Roberts, Mark J.↗

Multispectral histogram normalization contrast enhancement

A multispectral histogram normalization or decorrelation enhancement which achieves effective color composites by removing interband correlation is described. The enhancement procedure employs either linear or nonlinear transformations to equalize principal component variances. An additional rotation to any set of orthogonal coordinates is thus possible, while full histogram utilization is maintained by avoiding the reintroduction of correlation. For the three-dimensional case, the enhancement procedure may be implemented with a lookup table. An application of the enhancement to Landsat multispectral scanning imagery is presented.

Soha, J. M.↗

Determination of acoustic nonlinearity parameters using thermal modulation of ultrasonic waves

This study presents a test method and its theoretical framework to determine the acoustic nonlinearity parameters (α, β, δ) of material using thermal modulation of ultrasonic waves. Temperature change-induced thermal strain excites the nonlinear response of the material and modulates the ultrasonic wave propagating in it. Experimental results showed a strong correlation between the relative wave velocity change and the temperature change. With a quadratic polynomial model, the acoustic nonlinearity parameters were obtained from the polynomial coefficients by curve fitting the experimental data. Their effects on thermal-induced velocity change were discussed. The parameters α, β, and δ govern the hysteretic gap, average slope, and curvature of the correlation curve, respectively. The proposed theory was validated on aluminum, steel, intact and damaged concrete samples. The obtained nonlinear parameters show reasonable agreement with values reported in the literature. Compared to other nonlinear acoustic methods using vibration or acoustic excitation, the thermal modulation method generates more uniform, slow changing, and larger strain field in the test sample. Employing the thermal effect as the driving force for nonlinearity instead of an undesired influencing factor, this method can measure the absolute values of α, β, and δ with good accuracy using a simple ultrasonic test setup.

Physics↗

Analysis of subgrid models using direct and large-eddy simulations of isotropic turbulence

Direct and large eddy simulations of forced and decaying isotropic turbulence have been performed using a pseudospectral and a finite-difference code. Subgrid models that include a one-equation subgrid kinetic energy model with and without a stochastic backscatter forcing term and a new scale similarity model have been analyzed in both Fourier space and physical space. The Fourier space analysis showed that the energy transfer across the cutoff wavenumber k(sub c) is dominated by local interaction. The correlation between the exact and the modeled (by a spectral eddy viscosity) nonlinear terms and the subgrid energy transfer in physical space was found to be quite low. In physical space, a similar correlation analysis was carried out using top hat filtering. Results show that the subgrid stress and the energy flux predicted by the subgrid models correlates very well with the exact data. The scale similarity model showed very high correlation for reasonable grid resolution. However, with decrease in grid resolution, the scale similarity model became more uncorrelated, when compared to the kinetic energy subgrid model. The subgrid models were then used for large-eddy simulations for a range of Reynolds number. It was determined that the dissipation was modeled poorly and that the correlation with the exact results was quite low for all the models. In general, for coarse grid resolution, the scale similarity model consistently showed very low correlation while the kinetic energy model showed a relatively higher correlation. These results suggest that to use the scale similarity model relatively fine grid resolution may be required, whereas, the kinetic energy model could be used even in coarse grid.

Menon, S.↗

Phenomenological Model of Nonlinear Dynamics and Deterministic Chaotic Gas Migration in Bentonite: Experimental Evidence and Diagnostic Parameters

Understanding gas migration in compacted clay materials, e.g., bentonite and claystone, is important for the design and performance assessment of an engineered barrier system of a radioactive waste repository system, as well as many practical applications. Existing field and laboratory data on gas migration processes in low-permeability clay materials demonstrate the complexity of flow and transport processes, including various types of instabilities, caused by nonlinear dynamics of coupled processes of liquid–gas exchange, dilation, fracturing, fracture healing, etc., which cannot be described by classical models of fluid dynamics in porous media. We here show that the complexity of gas migration processes can be explained using a phenomenological concept of nonlinear dynamics and deterministic chaos theory. To do so, we analyzed gas pressure and gas influx (i.e., input) and outflux (i.e., output), recorded during the gas injection experiment in the compact Mx80-D bentonite sample, and calculated a set of the diagnostic parameters of nonlinear dynamics and chaos, such a global embedding dimension, a correlation dimension, an information dimension, and a spectrum of Lyapunov exponents, as well as plotted 2D and 3D pseudo-phase-space strange attractors, based on the univariate influx and outflux time series data. These results indicate the presence of phenomena of low-dimensional deterministic chaotic behavior of gas migration in bentonite. In particular, during the onset of gas influx in the bentonite core, before the breakthrough, the development of gas flow pathways is characterized by the process of chaotic gas diffusion. After the breakthrough, with inlet-to-outlet movement of gas, the prevailing process is chaotic advection. During the final phase of the experiment, with no influx to the sample, the relaxation pattern of gas outflux is resumed back to a process of chaotic diffusion. The types of data analysis and a proposed phenomenological model can be used to establish the basic principles of experimental data-gathering, modeling predictions, and a research design.

36 MATERIALS SCIENCE↗

Sensitivity Analysis of the Integrated Medical Model for ISS Programs

Sensitivity analysis estimates the relative contribution of the uncertainty in input values to the uncertainty of model outputs. Partial Rank Correlation Coefficient (PRCC) and Standardized Rank Regression Coefficient (SRRC) are methods of conducting sensitivity analysis on nonlinear simulation models like the Integrated Medical Model (IMM). The PRCC method estimates the sensitivity using partial correlation of the ranks of the generated input values to each generated output value. The partial part is so named because adjustments are made for the linear effects of all the other input values in the calculation of correlation between a particular input and each output. In SRRC, standardized regression-based coefficients measure the sensitivity of each input, adjusted for all the other inputs, on each output. Because the relative ranking of each of the inputs and outputs is used, as opposed to the values themselves, both methods accommodate the nonlinear relationship of the underlying model. As part of the IMM v4.0 validation study, simulations are available that predict 33 person-missions on ISS and 111 person-missions on STS. These simulated data predictions feed the sensitivity analysis procedures. The inputs to the sensitivity procedures include the number occurrences of each of the one hundred IMM medical conditions generated over the simulations and the associated IMM outputs: total quality time lost (QTL), number of evacuations (EVAC), and number of loss of crew lives (LOCL). The IMM team will report the results of using PRCC and SRRC on IMM v4.0 predictions of the ISS and STS missions created as part of the external validation study. Tornado plots will assist in the visualization of the condition-related input sensitivities to each of the main outcomes. The outcomes of this sensitivity analysis will drive review focus by identifying conditions where changes in uncertainty could drive changes in overall model output uncertainty. These efforts are an integral part of the overall verification, validation, and credibility review of IMM v4.0.

medical equipment↗

Evaluation of Test/Analysis Correlation Methods for Crash Applications

A project has been initiated to improve crash test and analysis correlation. The work in this paper concentrated on the test and simulation results for a fuselage section. Two drop tests of the section were conducted. The first test was designed to excite the linear structural response for comparison with finite element modal analysis results. The second test was designed to provide data for correlation with crash simulations. An MSC.Dytran model was developed to generate nonlinear transient dynamic results. Following minor modifications, the same model was executed in MSC.Nastran to generate modal analysis results. The results presented in this paper concentrate on evaluation of correlation methodologies for crash test data and finite element simulation results.

Lyle, Karen H.↗

High Strain Rate Deformation Modeling of a Polymer Matrix Composite: Matrix Constitutive Equations - Part 1

Recently applications have exposed polymer matrix composite materials to very high strain rate loading conditions, requiring an ability to understand and predict the material behavior under these extreme conditions. In this first paper of a two part report, background information is presented, along with the constitutive equations which will be used to model the rate dependent nonlinear deformation response of the polymer matrix. Strain rate dependent inelastic constitutive models which were originally developed to model the viscoplastic deformation of metals have been adapted to model the nonlinear viscoelastic deformation of polymers. The modified equations were correlated by analyzing the tensile/ compressive response of both 977-2 toughened epoxy matrix and PEEK thermoplastic matrix over a variety of strain rates. For the cases examined, the modified constitutive equations appear to do an adequate job of modeling the polymer deformation response. A second follow-up paper will describe the implementation of the polymer deformation model into a composite micromechanical model, to allow for the modeling of the nonlinear, rate dependent deformation response of polymer matrix composites.

Goldberg, Robert K.↗

A new effective theory for stochastic relativistic hydrodynamics

Thermal fluctuations are a fundamental feature of dissipative systems that are essential for understanding physics near the expected critical point of QCD and in small systems. When such fluctuations are modeled naively in relativistic systems, strange features can appear such as negative self-correlation functions. We construct an effective theory for nonlinear stochastic relativistic hydrodynamics that ensure a well-posed mathematical formulation. Using Crooks fluctuation theorem, we derive a symmetry of the effective action that incorporates fluctuations through a suitable free energy functional. For divergence type theories, the action can then be fully specified using a single vector generating current. The equations of motion obtained using this procedure are guaranteed to be flux conservative and symmetric hyperbolic when the dynamics is causal. This ensures that these equations are well-posed (for suitable initial data) and are in a form that can easily be simulated, including with Metropolis techniques.

Mullins, Nicki [University of Illinois at Urbana-C↗

A Measurement of the Largest-scale CMB E -mode Polarization with CLASS

We present measurements of large-scale cosmic microwave background E-mode polarization from the Cosmology Large Angular Scale Surveyor 90 GHz data. Using 115 det-yr of observations collected through 2024 with a variable-delay polarization modulator, we achieved a polarization sensitivity of 82 μK arcimin, comparable to Planck at similar frequencies (100 and 143 GHz ). The analysis demonstrates effective mitigation of systematic errors and addresses challenges to large-angular-scale power recovery posed by time-domain filtering in maximum-likelihood map-making. A novel implementation of the pixel-space transfer matrix is introduced, which enables efficient filtering simulations and bias correction in the power spectrum using the quadratic cross-spectrum estimator. Overall, we achieved an unbiased time-domain filtering correction to recover the largest angular scale polarization, with the only power deficit, arising from map-making nonlinearity, being characterized as <3%. Through cross-correlation with Planck, we detected the cosmic reionization at 99.4% significance and measured the reionization optical depth τ = $0.053^{+0.018}_{-0.019}$, marking the first ground-based attempt at such a measurement. At intermediate angular scales (ℓ > 30), our results, both independently and in cross-correlation with Planck, remain fully consistent with Planck’s measurements.

79 ASTRONOMY AND ASTROPHYSICS↗

Postbuckling behavior of selected flat stiffened graphite-epoxy panels loaded in compression

Results of an experimental study of the postbuckling behavior of selected flat stiffened graphite-epoxy panels loaded in compression are presented. The postbuckling response and failure characteristics of undamaged panels and panels damaged by low-speed impact are described. Each panel had four equally-spaced I-spaced stiffeners and 16- or 24-ply quasi-isotropic skins. Panels with three different stiffener spacings were tested. Some undamaged specimens supported as much as three times their initial buckling load before failing. Failure of all panels initiated in a skin-stiffener interface region. Analytical results obtained from a nonlinear general shell finite element analysis computer code correlate well with typical postbuckling test results up to failure. The analytical modeling detail necessary to predict accurately the response of a panel is described. Test results show that low-speed impact damage can reduce the postbuckling strength of a stiffened panel and that the skin-stiffener interface region is more sensitive to impact damage than the skin midway between stiffeners.

Starnes, J. H., Jr.↗

Postbuckling behavior of selected curved stiffened graphite-epoxy panels loaded in axial compression

Results of an experimental and analytical study of the postbuckling behavior of selected curved stiffened graphite-epoxy panels loaded in axial compression are presented. The postbuckling response and failure characteristics of the panels are described. Each panel had four equally-spaced I-shaped stiffeners and 16-ply quasi-isotropic skins. Panels with three different stiffener spacings were tested. Failure of all panels initiated in a skin-stiffener interface region. Analytical results from a nonlinear general shell finite element analysis computer code correlate well with typical postbuckling test results up to failure. The analytical modeling detail necessary to predict accurately the response of the panel is described. Measured initial geometric imperfections were included in the postbuckling analysis.

Knight, N. F., Jr.↗