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At least 451 records · Page 25
All sourcesNASA NTRSDOE 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↗
DOE OSTI2022

Prediction of the energetic particle redistribution by an improved critical gradient model and analysis of the transport threshold

Based on the theory of critical gradient model (CGM) and following the simulation method proposed by Waltz et al., a combination of TGLFEP and EPtran code is employed to predict the energetic particle (EP) transport induced by Alfvén eigenmodes (AEs). To be consistent with the experiment, recent improvements to the simulation method include consideration of threshold evolution and orbit loss due to finite orbit width. The revised CGM is applied to simulate two DIII-D experimental discharges (#142111 and #153071). It well reproduces the experimental profiles with multiple unstable AEs and large-scale EP transport. Discharge #142111 had previously been simulated using a nonlinear MHD-kinetic code MEGA with a transport mechanism based on stochasticity induced by overlapping AE. By comparing the simulated EP profiles, we find that the AE transport threshold is approximated by both the MEGA nonlinear stability threshold and the proposed CGM threshold (error <5% for single n and <17% for multiple n simulation). Both of them are larger than the linear stability threshold of the most unstable AE mode by a quantity of the order of the flux needed to sustain EP transport by the background turbulence. Additionally, we have also applied the improved CGM to simulate the α particle redistribution for a China Fusion Engineering Test Reactor steady state scenario. Because of the clear separation between the AE unstable region and the loss cone, only a moderate α particle loss of ~9.6% is predicted.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Ultrafast nonequilibrium dynamics and high-harmonic generation in two-dimensional quantum spin Hall materials

For this work, we develop the theoretical framework of nonequilibrium ultrafast photonics in monolayer quantum spin Hall insulators supporting a multitude of topological states. In these materials, ubiquitous strong light-matter interactions in the femtosecond scale lead to nonadiabatic quantum dynamics, resulting in topology-dependent nonlinear optoelectronic transport phenomena. We investigate the mechanism driving topological Dirac fermions interacting with strong ultrashort light pulses and uncover various experimentally accessible physical quantities that encode fingerprints of the quantum material's topological electronic state from the high-harmonic generated spectrum. Our work sets the theoretical cornerstones to realize the full potential of time-resolved harmonic spectroscopy for understanding nonequilibrium processes in quantum topological systems and identifying topological invariants in two-dimensional quantum spin Hall solid state systems.

2-dimensional systems↗
DOE OSTI2022

Sierra/SolidMechanics 5.6 User's Manual

Sierra/SolidMechanics (Sierra/SM) is a three-dimensional solid mechanics code with a versatile element library, nonlinear material models, large deformation capabilities, and contact. It is built on the SIERRA Framework. SIERRA provides a data management framework in a parallel computing environment that allows the addition of capabilities in a modular fashion. Contact capabilities are parallel and scalable. This document provides information about the functionality in Sierra/SM and the command structure required to access this functionality in a user input file. This document is divided into chapters based primarily on functionality. For example, the command structure related to the use of various element types is grouped in one chapter; descriptions of material models are grouped in another chapter. Sierra/SM provides both explicit transient dynamics and implicit quasistatics and dynamics capabilities. Both the explicit and implicit modules are highly scalable in a parallel computing environment. In the past, the explicit and implicit capabilities were provided by two separate codes, known as Presto and Adagio, respectively. These capabilities have been consolidated into a single code. The executable is named Adagio, but it provides the full suite of solid mechanics capabilities, for both implicit and explicit. The Presto executable has been disabled as a consequence of this consolidation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Relating Hydro–Mechanical and Elastodynamic Properties of Dynamically Stressed Tensile–Fractured Rock in Relation to Applied Normal Stress, Fracture Aperture, and Contact Area

We exploit nonlinear elastodynamic properties of fractured rock to probe the micro-scale mechanics of fractures and understand the relation between fluid transport and fracture aperture under dynamic stressing. Experiments were conducted on rough, tensile-fractured Westerly granite subject to triaxial stresses. We measure fracture permeability for steady-state fluid flow with deionized water. Pore pressure oscillations are applied at amplitudes ranging from 0.2 to 1 MPa at 1 Hz frequency. During dynamic stressing we transmit ultrasonic signals through the fracture using an array of piezoelectric transducers (PZTs) to monitor evolution of interface properties. We examine the influence of fracture aperture and contact area by conducting measurements at effective normal stresses of 10–20 MPa. Additionally, the evolution of contact area with stress is characterized using pressure sensitive film. These experiments are conducted separately with the same fracture and map contact area at stresses from 9 to 21 MPa. The measurements are a proxy for “true” contact area for the fracture surface and we relate them to elastic properties using the calculated PZT sensor footprints via numerical modeling of Fresnel zones. We compare the elastodynamic response of the fracture using the stress-induced changes in ultrasonic wave velocities for transmitter-receiver pairs to image spatial variations in contact properties. We show that nonlinear elasticity and permeability enhancement decrease with increasing normal stress. Additionally, post-oscillation wave velocity and permeability exhibit quick recoveries toward pre-oscillation values. Estimates of fracture contact area (global and local) demonstrate that the elastodynamic and permeability responses are dominated by fracture topology.

58 GEOSCIENCES↗
NASA NTRS1984

On the '3 kiloparsec arm' - Resonance excitation of linear and nonlinear waves by an oval distortion in the central region

The mechanism responsible for the massive rapidly expanding Galactic feature known as the 3-kpc arm (Rougoor and Oort, 1960) is investigated theoretically in the framework of a density-wave model of the Galaxy. The arm is attributed to outgoing waves excited at the outer Lindblad resonance (OLR) of a small rotating oval distortion near the Galactic center. Linear and nonlinear models are developed, and it is shown that a density crest at 3.5 kpc with expansion velocity 53 km/s can be generated by a distortion turning at 118 km/s kpc with a 10-percent perturbation of the main gravitational field at the OLR (located at 3 kpc). The wave character of the nonlinear solution is found to be the same as that of the linear solution and to give good agreement with the observations in terms of expansion velocity, size, shape, and mass; only the observed asymmetry of the arm is not reproduced.

Yuan, C.↗
NASA NTRS1982

Turbulence in transient solar phenomena

If theta dependence is kept in the Navier-Stokes equations for the solar wind, than a density enhancement will grow. This growth is followed in the nonlinear equations until a streamer is formed. Viscosity stops the streamer's growth when there is a large difference in speeds inside and outside of the streamer. Using classical fluid mechanics and a latitude dependent hydrodynamical model, it is shown that unmagnetized perturbed flow evolves into high and low density regions. The growth mechanisms for density enrichments are discussed along with a nonlinear solution for their large amplitude development. It was found that a higher Reynolds number is needed to start turbulence in the presence of a magnetic field because energy is required to bend the field lines attached to the fluid. If cosmological gas was turbulent shortly after the big bang, then galaxies could have been formed by turbulent eddies.

Cross, M.↗
NASA NTRS1989

Generic element processor (application to nonlinear analysis)

The focus here is on one aspect of the Computational Structural Mechanics (CSM) Testbed: finite element technology. The approach involves a Generic Element Processor: a command-driven, database-oriented software shell that facilitates introduction of new elements into the testbed. This shell features an element-independent corotational capability that upgrades linear elements to geometrically nonlinear analysis, and corrects the rigid-body errors that plague many contemporary plate and shell elements. Specific elements that have been implemented in the Testbed via this mechanism include the Assumed Natural-Coordinate Strain (ANS) shell elements, developed with Professor K. C. Park (University of Colorado, Boulder), a new class of curved hybrid shell elements, developed by Dr. David Kang of LPARL (formerly a student of Professor T. Pian), other shell and solid hybrid elements developed by NASA personnel, and recently a repackaged version of the workhorse shell element used in the traditional STAGS nonlinear shell analysis code. The presentation covers: (1) user and developer interfaces to the generic element processor, (2) an explanation of the built-in corotational option, (3) a description of some of the shell-elements currently implemented, and (4) application to sample nonlinear shell postbuckling problems.

Stanley, Gary↗
DOE OSTI2021

Data-driven learning of Mori–Zwanzig operators for isotropic turbulence

Developing reduced-order models for turbulent flows, which contain dynamics over a wide range of scales, is an extremely challenging problem. In statistical mechanics, the Mori–Zwanzig (MZ) formalism provides a mathematically exact procedure for constructing reduced-order representations of high-dimensional dynamical systems, where the effects due to the unresolved dynamics are captured in the memory kernel and orthogonal dynamics. Turbulence models based on MZ formalism have been scarce due to the limited knowledge of the MZ operators, which originates from the difficulty in deriving MZ kernels for complex nonlinear dynamical systems. In this work, we apply a recently developed data-driven learning algorithm, which is based on Koopman's description of dynamical systems and Mori's linear projection operator, on a set of fully resolved isotropic turbulence datasets to extract the Mori–Zwanzig operators. With data augmentation using known turbulence symmetries, the extracted Markov term, memory kernel, and orthogonal dynamics are statistically converged and the generalized fluctuation–dissipation relation can be verified. The properties of the memory kernel and orthogonal dynamics, and their dependence on the choices of observables are investigated to address the modeling assumptions that are commonly used in MZ-based models. A series of numerical experiments are then constructed using the extracted kernels to evaluate the memory effects on prediction. The results show that the prediction errors are strongly affected by the choice of observables and can be further reduced by including the past history of the observables in the memory kernel.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Instabilities of a vortex-ring-bright soliton in trapped binary three-dimensional Bose-Einstein condensates

Instabilities of vortex-ring-bright coherent structures in harmonically trapped two-component three-dimensional Bose-Einstein condensates are studied numerically within the coupled Gross-Pitaevskii equations and interpreted analytically. Interestingly, the filled vortex core with a sufficiently large amount of the bright component is observed to reduce the parametric interval of stability of the vortex ring. Here, we have identified the mechanisms of several linear instabilities and one nonlinear parametric instability in this connection. Two of the linear instabilities are qualitatively different from ones reported earlier and are associated with azimuthal modes of m = 0 and m = 1, i.e., deviations of the vortex from the stationary ring shape. Our nonlinear parametric resonance instability occurs between the m = 0 and m = 2 modes and signals the exchange of energy between them.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1979

Effect of grazing flow on the nonlinear acoustic behavior of helmholtz resonators

A semi empirical fluid mechanical model is derived of the acoustic behavior of thin walled single orifice Helmholtz resonators in a grazing flow environment. The model assumes that the flow field incident to a resonator orifice consists of a spherical sound particle velocity field superimposed upon a mean grazing flow. The incident and cavity sound fields are connected in terms of an orifice discharge coefficient whose values are determined experimentally using the two microphone method. With regard to its application to rocket motor interiors, the most important finding of this study is that the acoustic impedance of Helmholtz resonators is affected by grazing flow when the product of the amplitude of the sound pressure incident to the resonator orifice and the rocket motor interior mean grazing flow speed are less than 0.5. For values greater than 0.5, the acoustic impedance is independent of the grazing flow.

Hersh, A. S.↗
NASA NTRS1983

Interaction of multiple supersonic jets with a transonic flow field

The influence of multiple high pressure, supersonic, radial or tangential jets, that are injected from the circumference of the base plane of an axisymmetric body, on its longitudinal aerodynamic coefficients in transonic flow is studied experimentally. The interaction of the jets with the body flow field increases the pressures on the forebody, thus altering its lift and static stability characteristics. It is shown that, within the range of parameters studied. This interaction has a stabilizing effect on the body. The contribution to lift and stability is significant at small angles of attack and decreases nonlinearly at higher angles when the crossflow mechanism becomes dominant.

Seginer, A.↗
NASA NTRS1984

A nonlinear structural concept for drag-reducing compliant walls

Two mechanisms of drag reduction for flow over flat plates were investigated. The first mechanism employs Bushnell's hypothesis that compliant walls produce drag reduction by interfering with the formation of the turbulent spots in a turbulent boundary layer. It is shown that the amplitudes and frequencies of compliant wall motions for drag reduction might be achieved by using slightly curved walls and the resulting large amplitude motions of snap buckling. A simple structural model of an arch is used in the analysis, and an asymptotic method is developed. The required wall motions can be obtained by using materials like mylar. In addition, the delay of transition from laminar to turbulent flow by driven walls was studied for Poiseuille channel flow. The walls are driven by a periodic traveling wave. A significant increase in the transitional Reynolds number is obtained by appropriately prescribing the wavelength and phase velocity of the wall motion. Previously developed asymptotic methods are used in the analysis. Previously announced in STAR as N83-11061

Reiss, E. L.↗
NASA NTRS1985

Simulation study of Type 2 counterstreaming electrons along auroral field lines

The production of counterstreaming electrons associated with parallel fields along auroral field lines is examined through the use of computer simulation. A 2 1/2-dimensional (two spatial and three velocity dimensions) electrostatic particle algorithm and auroral boundary conditions are used to set up a self-consistent V potential structure. The simulation produces signatures of counterstreaming electrons resembling those observed by the Dynamics Explorer 1 satellite. The main signatures are as follows: (1) the phase space contours of the electron distribution function are elongated along the V-parallel axis, and (2) the energy of electrons streaming in the upward direction is comparable to the energy of the accelerated electron beam. The simulation indicates that a portion of the accelerated electron beam is trapped by large amplitude electrostatic waves produced through the two-stream instability. Strong wave-particle interactions then thermalize the trapped electrons to produce suprathermal electrons streaming in the direction opposite to that of the accelerated electron beam. These results suggest a possible mechanism of producing counterstreaming electron fluxes through nonlinear processes of the two-stream instability.

Wagner, J. S.↗
NASA NTRS1987

Numerical simulation of transition

The paper presents numerical algorithms for studying the physics of transition and turbulence in simple geometries. The highly nonlinear stages of transition prior to turbulent spot formation are studied in detail. The use of simulations to study the sensitivity of laminar flow control techniques in the nonlinear regime is demonstrated. A new instability mechanism associated with the center modes in channel flows is revealed.

Hussaini, M. Y.↗
NASA NTRS1994

Parameter estimation in a structural acoustic system with fully nonlinear coupling conditions

A methodology for estimating physical parameters in a class of structural acoustic systems is presented. The general model under consideration consists of an interior cavity which is separated from an exterior noise source by an enclosing elastic structure. Piezoceramic patches are bonded to or embedded in the structure; these can be used both as actuators and sensors in applications ranging from the control of interior noise levels to the determination of structural flaws through nondestructive evaluation techniques. The presence and excitation of patches, however, changes the geometry and material properties of the structure as well as involves unknown patch parameters, thus necessitating the development of parameter estimation techniques which are applicable in this coupled setting. In developing a framework for approximation, parameter estimation and implementation, strong consideration is given to the fact that the input operator is unbonded due to the discrete nature of the patches. Moreover, the model is weakly nonlinear. As a result of the coupling mechanism between the structural vibrations and the interior acoustic dynamics. Within this context, an illustrating model is given, well-posedness and approximations results are discussed and an applicable parameter estimation methodology is presented. The scheme is then illustrated through several numerical examples with simulations modeling a variety of commonly used structural acoustic techniques for systems excitations and data collection.

Banks, H. T.↗
NASA NTRS1999

A Novel Shape Parameterization Approach

This paper presents a novel parameterization approach for complex shapes suitable for a multidisciplinary design optimization application. The approach consists of two basic concepts: (1) parameterizing the shape perturbations rather than the geometry itself and (2) performing the shape deformation by means of the soft objects animation algorithms used in computer graphics. Because the formulation presented in this paper is independent of grid topology, we can treat computational fluid dynamics and finite element grids in a similar manner. The proposed approach is simple, compact, and efficient. Also, the analytical sensitivity derivatives are easily computed for use in a gradient-based optimization. This algorithm is suitable for low-fidelity (e.g., linear aerodynamics and equivalent laminated plate structures) and high-fidelity analysis tools (e.g., nonlinear computational fluid dynamics and detailed finite element modeling). This paper contains the implementation details of parameterizing for planform, twist, dihedral, thickness, and camber. The results are presented for a multidisciplinary design optimization application consisting of nonlinear computational fluid dynamics, detailed computational structural mechanics, performance, and a simple propulsion module.

Samareh, Jamshid A.↗