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At least 1,549 records · Page 86
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

The weakly nonlinear response and nonaffine interpretation of the Johnson–Segalman/Gordon–Schowalter model

We derive new analytical solutions for the non-affine Johnson-Segalman/Gordon-Schowalter (JS/GS) constitutive equation with a general relaxation kernel in medium-amplitude oscillatory shear (MAOS) deformation. The results show time-strain separable (TSS) nonlinearity, therefore providing new physically-meaningful interpretation to the heuristic TSS nonlinear parameter in MAOS. The upper-convected, lower-convected, and corotational Maxwell models are all subsets of the results presented here. The model assumes that the microscale elements causing stress in the material slip compared to the continuum deformation. We introduce a visualization of the non-affine deformation field that acts on stress-generating elements to reinforce the hysical interpretation of the JS/GS class of models. Lastly, a case study is presented where previously published results, from fitting TSS models to MAOS data, can be re-interpreted based on the concept of non-affine motion of the JS/GS framework.

36 MATERIALS SCIENCE↗
NASA NTRS1979

Aeroelastic stability and response of horizontal axis wind turbine blades

Coupled flap-lag-torsion equations of motion of an isolated horizontal axis wind turbine (HAWT) blade have been formulated. The analysis neglects blade-tower coupling. The final nonlinear equations have periodic coefficients. A new and convenient method of generating an appropriate time-dependent equilibrium position, required for the stability analysis, has been implemented and found to be computationally efficient. Steady-state response and stability boundaries for an existing (typical) HAWT blade are presented. Such stability boundaries have never been published in the literature. The results show that the isolated blade under study is basically stable. The tower shadow (wake) has a considerable effect on the out-of-plane response but leaves blade stability unchanged. Nonlinear terms can significantly affect linearized stability boundaries; however, they have a negligible effect on response, thus implying that a time-dependent equilibrium position (or steady-state response), based completely on the linear system, is appropriate for the type of HAWT blades under study.

Kottapalli, S. B. R.↗
NASA NTRSDate not supplied

Quantification of Numerical Uncertainty via Nonlinear Dynamical Approach

Motivations (Ensure a Higher Level of Confidence in the Predictability & Reliability of Numerical Simulation for Multiscale Complex Nonlinear Fluid Problems) - The last two decades have been an era when computation is ahead of analysis & when very large scale practical computations are increasingly used in poorly understood multiscale complex nonlinear physical problems & non-traditional fields (Especially when computations offer the ONLY way of generating this type of data limited simulations). - At present some of the numerical uncertainties can be explained and minimized by traditional numerical analysis and standard CFD practices. However, such practices, usually based on linearized analysis, MIGHT NOT be sufficient for strongly nonlinear and/or stiff problems. - We need a good understanding of the nonlinear behavior of numerical schemes being used as an integral part of code verification, validation and certification.

HEC↗
DOE OSTI2023

Exponential Runge-Kutta Parareal for non-diffusive equations

Parareal is a well-known parallel-in-time algorithm that combines a coarse and fine propagator within a parallel iteration. It allows for large-scale parallelism that leads to significantly reduced computational time compared to serial time-stepping methods. However, like many parallel-in-time methods it can fail to converge when applied to non-diffusive equations such as hyperbolic systems or dispersive nonlinear wave equations. Here, this paper explores the use of exponential integrators within the Parareal iteration. Exponential integrators are particularly interesting candidates for Parareal because of their ability to resolve fast-moving waves, even at the large stepsizes used by coarse propagators. This work begins with an introduction to exponential Parareal integrators followed by several motivating numerical experiments involving the nonlinear Schrödinger equation. These experiments are then analyzed using linear analysis that approximates the stability and convergence properties of the exponential Parareal iteration on nonlinear problems. The paper concludes with two additional numerical experiments involving the dispersive Kadomtsev-Petviashvili equation and the hyperbolic Vlasov-Poisson equation. These experiments demonstrate that exponential Parareal methods offer improved time-to-solution compared to serial exponential integrators when solving certain non-diffusive equations.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1986

Averaging analysis for discrete time and sampled data adaptive systems

Earlier continuous time averaging theorems are extended to the nonlinear discrete time case. Theorems for the study of the convergence analysis of discrete time adaptive identification and control systems are used. Instability theorems are also derived and used for the study of robust stability and instability of adaptive control schemes applied to sampled data systems. As a by product, the effects of sampling on unmodeled dynamics in continuous time systems are also studied.

Fu, Li-Chen↗
DOE OSTI2024

RandONets: Shallow networks with random projections for learning linear and nonlinear operators

Deep neural networks have been extensively used for the solution of both the forward and the inverse problem for dynamical systems. However, their implementation necessitates optimizing a high-dimensional space of parameters and hyperparameters. This fact, along with the requirement of substantial computational resources, pose a barrier to achieving high numerical accuracy, but also interpretability. Here, to address the above challenges, we present Random Projection-based Operator Networks (RandONets): shallow networks with random projections and tailor-made numerical analysis methods that learn accurately and fast linear and nonlinear operators. Building on previous works, we prove that RandOnets are universal approximators of linear and nonlinear operators. Due to their simplicity, RandONets provide a one-step transformation of the input space, facilitating interpretability. For the evaluation of their performance, we focus on operators of PDEs. We show, that RandONets outperform by several orders of magnitude, both in terms of numerical approximation accuracy and computational cost, the “vanilla” DeepONets. Hence, we believe that our method will trigger further developments in the field of scientific machine learning, for the development of new ‘’light”schemes that will provide high accuracy while reducing dramatically the computational cost. A MATLAB toolbox for RandONets, including demos, is available on GitHub at https://github.com/GianlucaFabiani/RandONets.

Interpretable machine learning↗
NASA NTRS1986

Response of symmetric rectangular composite laminates with nonlinear damping subjected to acoustic loading

Effects of both nonlinear damping and large-deflection are included in the analysis in an attempt to explain the experimental phenomena of aircraft panels excited at high sound pressure levels; that is the broadening and flattening out of the strain response peaks and the increasing of the response frequency. A nonlinear damping model is considered in the analysis using a single-mode approach. Root-mean-square (RMS) maximum deflection, RMS strains, spectral density functions of strain, and equivalent linear frequency are obtained for clamped and simply supported rectangular symmetric laminated composite plates. It is demonstrated that nonlinear damping is the one which causes the broadening of the response peaks, and it has great influence on RMS panel deflection, RMS strains, and frequency.

Mei, C.↗
NASA NTRS1994

Some recent results of nonlinear acoustics in combustion chambers

The chief purpose of this paper is to provide a brief review of some recent work on nonlinear acoustics applicable to combustion instabilities, largely in the framework of an approximate analysis. Some connections will be made with the modern theory of nonlinear dynamical systems, including very recent and incomplete attempts by others to assess the possible chaotic behavior observed in laboratory tests.

Culick, F. E. C.↗
NASA NTRS1993

Stability of mixing layers

The research program for the first year of this project (see the original research proposal) consists of developing an explicit marching scheme for solving the parabolized stability equations (PSE). Performing mathematical analysis of the computational algorithm including numerical stability analysis and the determination of the proper boundary conditions needed at the boundary of the computation domain are implicit in the task. Before one can solve the parabolized stability equations for high-speed mixing layers, the mean flow must first be found. In the past, instability analysis of high-speed mixing layer has mostly been performed on mean flow profiles calculated by the boundary layer equations. In carrying out this project, it is believed that the boundary layer equations might not give an accurate enough nonparallel, nonlinear mean flow needed for parabolized stability analysis. A more accurate mean flow can, however, be found by solving the parabolized Navier-Stokes equations. The advantage of the parabolized Navier-Stokes equations is that its accuracy is consistent with the PSE method. Furthermore, the method of solution is similar. Hence, the major part of the effort of the work of this year has been devoted to the development of an explicit numerical marching scheme for the solution of the Parabolized Navier-Stokes equation as applied to the high-seed mixing layer problem.

Tam, Christopher↗
DOE OSTI2021

Microstructural changes and mass transport in cement-based materials: A modeling approach

Highlights: • Concept to relate microstructural changes, mass transport, and chemical reactions in cement-based materials is presented. • Multi-physics modeling approach utilizing an extended version of the PNP equation and the geochemical code IPHREEQC. • Case studies indicate significant changes in mass transport properties due to alterations in the microstructure. • Microstructural changes depend on exposure and interactions between chemical reactions, pore structure, and mass transport. A generic modeling framework is presented to relate microstructural changes, i.e. changes in the pore volume distribution and phase assemblage, and mass transport in cement-based materials. The modeling framework accounts for mass transport and chemical equilibrium between ions in the pore solution and solid hydrates by means of an extended version of the Poisson-Nernst-Planck equation, in which the chemical equilibrium is solved by the external geochemical code IPHREEQC. Results of numerical studies concerning carbonation and leaching of a cement-based material indicate significant changes in mass transport properties due to chemical reactions leading to alterations in the microstructure. The resulting highly non-linear (both spatial and temporal) microstructural changes are thereby depending on the exposure and indicate that interactions between chemical reactions, pore structure changes, and mass transport have to be accounted for as a whole.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Stable Rate of Slip Along the Karakax Section of the Altyn Tagh Fault from Observation of Interglacial and Postglacial Offset Morphology and Surface Dating

Digital elevation maps obtained using TanDEM-X and Pleiades data combined with newly obtained surface age estimates using cosmogenic radionuclide (CRN) and optically simulated luminescence (OSL) methods are used to quantify the slip rate along the western section of the Altyn Tagh Fault in southern Xinjiang. The reconstruction of the conical shape of massive alluvial fans inferred to be from the Eemian (115±7 ka) from CRN dating shows consistent left-lateral offsets of 300±20 m, yielding a slip rate of 2.6±0.3 mm/year. Successive episodes of incision have left cut terraces inset in wide canyons, 10–25 m below the fans' surface. The incision was followed by the deposition of a broad terrace of early Holocene age, which is reincised by modern stream channels. Near the village of Shanxili, a 200 m wide valley is partially dammed by a shutter ridge displaced by the fault. A fill terrace deposited upstream from the ridge has an OSL age of 8.8±0.6 ka. The 23±2 m offset of the riser incising the terrace indicates a minimum postdepositional movement on the fault, yielding a Holocene rate of 2.6±0.5 mm/year, consistent with the 115-ka average slip rate. Furthermore, scarp degradation analysis using mass diffusion reveals a nonlinear relationship between fault displacement and degradation coefficient along the progressively exposed fault scarp, a pattern suggesting either seismic clustering or variable diffusion rate since the Eemian. Together with the Gozha Co-Longmu Co fault to the south, the Karakax section of the Altyn Tagh Fault contributes to the eastward movement of the western corner of Tibet.

58 GEOSCIENCES↗
DOE OSTI2026

Investigation of Causal Relationships of the Cross‐Scale Wave Coupling Through Information Theoretical Approach

On 2015 October 2, MMS spacecraft observed an electron micro-injection event near the southern hemispheric high-altitude cusp, coinciding with intense wave activity across several frequency bands. Here, we investigated the MMS magnetic field and plasma during this event to explore cross-scale coupling among the wave modes. Employing the Hilbert-Huang transform, we perform an empirical mode decomposition to extract frequencies and amplitudes of the intrinsic mode functions (IMFs). In this analysis, we establish both linear and nonlinear relationships and examine the information transfer between the IMFs. Notably, the transfer entropy suggests that high frequency ion cyclotron waves may be driven by the mirror mode structures. Our case study effectively demonstrates the utility of the information theory based tools for studying cross-scale wave coupling phenomena.

Rivera, Elmer C. [Andrews University, Berrien Spri↗
DOE OSTI2026

A tutorial on high-order harmonic generation in atoms, molecules, and condensed matter

This tutorial introduces strong-field-driven high-order harmonics, their experimental generation and characterization techniques, and their main applications including attosecond pulse generation and ultrafast spectroscopy of the target material. We begin from the use of atomic targets, where the first high-order harmonic generation (HHG) experiments were realized in the late 1980s. Then, we briefly discuss the basics of the microscopic generation mechanism and how various steps of the mechanism were exploited in applications such as generating isolated attosecond pulses and probing molecular orbitals. We introduce and describe the standard experimental approaches for condensed phase HHG, where we discuss unique technical challenges of the use of solid-state materials, such as the mitigation of plasma formation and laser damage. We cover the fundamentals of high-harmonic spectroscopy in condensed matter systems, such as wide bandgap dielectrics, semiconductors, liquid media, and 2D-crystals. We provide some examples of rapidly emerging spectroscopic capabilities, such as for probing crystal symmetries, Berry phases, and associated non-trivial topological properties of the source material. Finally, we provide an overview of the research field, including some of the challenges, opportunities, and open questions.

Attosecond pulses↗
NASA NTRS1966

Calculated blade response at high tip-speed ratios

This paper presents the initial results of a digital computer study of helicopter rotor-blade-motion stability for a broad range of forward speeds encompassing proposed conventional and compound helicopter designs. The analysis treats the general case of nonlinear, coupled flapping and lagging motions of hinged rigid blades. The results of the study to date indicate that blade-motion stability boundaries cannot be specified for a given blade design in terms of a fixed value of rotor tip-speed ratio. The stability boundaries can shift significantly within the desired operational speed range, with the stability limits depending upon the rotor loading, the mag­nitude of the disturbance encountered by the blade, and the blade position at the instant the external disturbance is encountered. The sample methods suggested for improving blade-motion stability include increasing the effec­tive hinge spring restraint by incorporating pitch-flap coupling or by using hingeless or teetering rotor systems. Reducing rotor loading also has a beneficial effect on the blade-motion stability. The results indi­cate that methods used to deal with the blade-motion stability problem can be expected to diminish the overall vibration levels of the helicopter rotor system across the entire design speed range.

TIP SPEED↗