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At least 1,063 records · Page 59
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Photon–photon chemical thermodynamics of frequency conversion processes in highly multimode systems

Abstract Frequency generation in highly multimode nonlinear optical systems is inherently a complex process, giving rise to an exceedingly convoluted landscape of evolution dynamics. While predicting and controlling the global conversion efficiencies in such nonlinear environments has long been considered impossible, here, we formally address this challenge even in scenarios involving a very large number of spatial modes. By utilizing fundamental notions from optical statistical mechanics, we develop a universal theoretical framework that effectively treats all frequency components as chemical reactants/products, capable of undergoing optical thermodynamic reactions facilitated by a variety of multi-wave mixing effects. These photon–photon reactions are governed by conservation laws that directly determine the optical temperatures and chemical potentials of the ensued chemical equilibria for each frequency species. In this context, we develop a comprehensive stoichiometric model and formally derive an expression that relates the chemical potentials to the optical stoichiometric coefficients, in a manner akin to atomic/molecular chemical reactions. This advancement unlocks new predictive capabilities that can facilitate the optimization of frequency generation in highly multimode photonic arrangements, surpassing the limitations of conventional schemes that rely exclusively on nonlinear optical dynamics. Notably, we identify a universal regime of Rayleigh–Jeans thermalization where an optical reaction at near-zero optical temperatures can promote the complete and entropically irreversible conversion of light to the fundamental mode at a target frequency. Our theoretical results are corroborated by numerical simulations in settings where second-harmonic generation, sum-frequency generation and four-wave mixing processes can manifest.

Optics↗
DOE OSTI2022

Closures for multicomponent reacting flows based on dispersion analysis

This work presents algebraic closure models associated with advective transport and nonlinear reactions in a Reynolds-averaged Navier-Stokes context for a system of species subject to binary reactions and transport by advection and diffusion. Expanding upon analysis originally developed for non-reactive transport in the context of Taylor dispersion of scalars, this work extends the modified gradient diffusion model explicated by Peters [N. Peters, Turbulent Combustion, Cambridge Monographs on Mechanics (Cambridge University Press, Cambridge, 2000)] and based on work by Corrsin [S. Corrsin, The reactant concentration spectrum in turbulent mixing with a first-order reaction, J. Fluid Mech. 11, 407 (1961)] beyond single-component transport phenomena and involving nonlinear reactions. The presented model forms, from this weakly nonlinear extension of the original dispersion theory, lead to an analytic expression for the eddy diffusivity matrix that explicitly captures the influence of the reaction kinetics on the closure operators. Furthermore, we demonstrate that the derived model form directly translates between flow topologies through a priori and a posteriori testing of a binary species system subject to homogeneous isotropic turbulence. Using two- and three-dimensional direct numerical simulations involving laminar and turbulent flows, it is shown that this framework improves prediction of mean quantities compared to previous results. Lastly, the presented model form, collapses to the earlier gradient diffusion and its modified version derived by Corrsin in the limits of nonreactive species and linear reactions, respectively.

42 ENGINEERING↗
NASA NTRS1992

Venus tectonic styles and crustal differentiation

Two of the most important constraints are known from Pioneer Venus data: the lack of a system of spreading rises, indicating distributed deformation rather than plate tectonics; and the high gravity/topography ratio, indicating the absence of an asthenosphere. In addition, the high depth/diameter ratios of craters on Venus indicate that Venus probably has no more crust than Earth. The problems of the character of tectonics and crustal formation and recycling are closely coupled. Venus appears to lack a recycling mechanism as effective as subduction, but may also have a low rate of crustal differentiation because of a mantle convection pattern that is more distributed, less concentrated, than Earth's. Distributed convection, coupled with the nonlinear dependence of volcanism on heat flow, would lead to much less magmatism, despite only moderately less heat flow, compared to Earth. The plausible reason for this difference in convective style is the absence of water in the upper mantle of Venus. We have applied finite element modeling to problems of the interaction of mantle convection and crust on Venus. The main emphasis has been on the tectonic evolution of Ishtar Terra, as the consequence of convergent mantle flow. The early stage evolution is primarily mechanical, with crust being piled up on the down-stream side. Then the downflow migrates away from the center. In the later stages, after more than 100 m.y., thermal effects develop due to the insulating influence of the thickened crust. An important feature of this modeling is the entrainment of some crustal material in downflows. An important general theme in both convergent and divergent flows is that of mixing vs. stratification. Models of multicomponent solid-state flow obtain that lower-density crustal material can be entrained and recycled, provided that the ration of low-density to high-density material is small enough (as in subducted slabs on Earth). The same considerations should apply in upflows; a small percent of partial melt may be carried along with its matrix and never escape to the surface. Models that assume melt automatically rising to the crust and no entrainment or other mechanism of recycling lower-density material obtain oscillatory behavior, because it takes a long time for heat to build up enough to overcome a Mg-rich low-density residuum. However, these models develop much thicker crust than consistent with estimates from crater depth/diameter ratios.

Kaula, W. M.↗
NASA NTRS1990

Boundary layer roll circulations during FIRE

The probable mechanism underlying the development of boundary layer roll circulations are studied using wind and temperature profiles measured by the National Center for Atmospheric Research (NCAR) Electra during the stratocumulus phase of the First ISCCP Regional Experiment (FIRE). The expected, or preferred, roll orientations, horizontal wavelengths, and propagation periods are determined by finding the minimum values of the dynamic and thermodynamic forcing parameters, which here are the eddy Reynolds number (Re) and moist Rayleigh number (Ra sub m). These minimum values depend on the height z sub T of the capping temperature inversion and on the values of the Fourier coefficients of the background height-dependent vector wind profile. As input to our nonlinear spectral model, descent and ascent runs by the Electra provide for initial estimates of the inversion height and the wind profiles. In the first phase of the investigation presented here, a mechanism is said to be a probable contributor to the development of roll circulations within the stratocumulus-topped boundary layer if the modeled roll orientation and wavelengths agree with their observed values. Preliminary results using the 14-coefficient model of Haack-Hirschberg (1988) are discussed for the 7 July 1987 Electra Mission 188-A (Flight 5). This mission was flown across a sharp cloud boundary that was within a LANDSAT/SPOT scene. The stratocumulus deck was relatively solid in the eastern part of the scene, while there was a rapid decrease in cloud cover to scattered cumulus clouds aligned in streets to the west. These cloud streets were oriented nearly parallel to the mean wind direction in the layer, which was approximately 340 degrees. The hypothesis that roll circulations occurred in both the relatively clear and the cloudy regions is investigated using as model input a descent profile obtained in the relatively clear air and an ascent profile obtained in the cloudy air. Initial results for the clear air case are that the pure inflection point mode is not possible and the pure thermal mode was oriented 35 degrees to the right of the mean wind direction. The origin of this unacceptably large discrepancy between the observed and modeled results will be investigated further and the conclusions reported at the next FIRE workshop.

Shirer, Hampton N.↗
DOE OSTI2021

Physics-constrained, low-dimensional models for magnetohydrodynamics: First-principles and data-driven approaches

Plasmas are highly nonlinear and multiscale, motivating a hierarchy of models to understand and describe their behavior. However, there is a scarcity of plasma models of lower fidelity than magnetohydrodynamics (MHD), although these reduced models hold promise for understanding key physical mechanisms, efficient computation, and real-time optimization and control. Galerkin models, obtained by projection of the MHD equations onto a truncated modal basis, and data-driven models, obtained by modern machine learning and system identification, can furnish this gap in the lower levels of the model hierarchy. This work develops a reduced-order modeling framework for compressible plasmas, leveraging decades of progress in projection-based and data-driven modeling of fluids. We begin by formalizing projection-based model reduction for nonlinear MHD systems. To avoid separate modal decompositions for the magnetic, velocity, and pressure fields, we introduce an energy inner product to synthesize all of the fields into a dimensionally consistent, reduced-order basis. Next, we obtain an analytic model by Galerkin projection of the Hall-MHD equations onto these modes. We illustrate how global conservation laws constrain the model parameters, revealing symmetries that can be enforced in data-driven models, directly connecting these models to the underlying physics. We demonstrate the effectiveness of this approach on data from high-fidelity numerical simulations of a three-dimensional spheromak experiment. Finally, this manuscript builds a bridge to the extensive Galerkin literature in fluid mechanics and facilitates future principled development of projection-based and data-driven models for plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Micro-tearing mode dominated electron heat transport in DIII-D H-mode pedestal

Abstract A new, comprehensive set of evidence reveals that Micro-Tearing Modes (MTMs) dominate pedestal electron heat transport in an H-mode experiment in the DIII-D tokamak. The experiment investigates the role of MTMs by scanning pedestal collisionality, a main drive of MTM instability, from 0.43 to 0.84 on the pedestal top. Broadband (150–800 kHz) magnetic and density fluctuations originating from the pedestal gradient region and highly consistent with MTMs are observed, with amplitude increasing during the scan. The higher magnetic fluctuation amplitude correlates with a lower pedestal electron temperature gradient, implying MTMs may regulate the pedestal electron heat transport. The collisionality scan results in profile and transport changes consistent with predicted transport capability of MTMs: (1) experimentally-determined electron heat diffusivity increases ∼40% at the location where the broadband density fluctuations peak; (2) ion heat diffusivity has less increase (<20%); and (3) a locally flattened region in the electron temperature pedestal is observed at high collisionality. A local, linear gyrokinetic simulation finds MTMs as the most unstable mode in the pedestal gradient region. In addition, local, nonlinear simulations suggest MTMs can dominate and drive experimentally-relevant, megawatt-level electron heat flux. This result establishes MTMs as an effective transport mechanism in the H-mode pedestal, in particular at high collisionality.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Scalable Multiphysics Block Preconditioning for Low Mach Number Compressible Resistive MHD with Application to Magnetic Confinement Fusion

This study investigates multiphysics block preconditioners that are critical in devising scalable Newton–Krylov iterative solvers for longer time-scale fully implicit fluid plasma models. The specific model of interest is the visco-resistive, low Mach number, compressible magnetohydrodynamics (MHD) model. This model describes the dynamics of conducting fluids in the presence of electromagnetic fields and can be used to study aspects of astrophysical phenomena, important science and technology applications, and basic plasma physics. The specific application of interest that motivates this study is the macroscopic simulation of longer time-scale stability and disruptions of magnetic confinement fusion devices, specifically the ITER Tokamak. The computational solution of the governing balance equations for mass, momentum, heat transfer, and magnetic induction for resistive MHD systems can be extremely challenging. These difficulties arise from both the strong nonlinear, nonsymmetric coupling of fluid and electromagnetic phenomena as well as the significant range of time and length scales that the interactions of these physical mechanisms produce. To handle the range of time and spatial scales of interest, a fully implicit unstructured variational multiscale finite element formulation is employed. For the scalable solution of the Newton linearized systems, fully coupled block preconditioners are designed to leverage algebraic multigrid subsolves. In conclusion, results are presented for the strong and weak scaling of the method as well as the robustness of these techniques for a large range of Lundquist numbers.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1975

Application of Hamilton's law of varying action

The law of varying action enunciated by Hamilton in 1834-1835 permits the direct analytical solution of the problems of mechanics, both stationary and nonstationary, without consideration of force equilibrium and the theory of differential equations associated therewith. It has not been possible to obtain direct analytical solutions to nonstationary systems through the use of energy theory, which has been limited for 140 years to the principle of least action and to Hamilton's principle. It is shown here that Hamilton's law permits the direct analytical solution to nonstationary, initial value systems in the mechanics of solids without any knowledge or use of the theory of differential equations. Solutions are demonstrated for nonconservative, nonstationary particle motion, both linear and nonlinear.

Bailey, C. D.↗
NASA NTRS1985

Perturbations of the Richardson number field by gravity waves

An analytic solution is presented for a stratified fluid of arbitrary constant Richardson number. By computer aided analysis the perturbation fields, including that of the Richardson number can be calculated. The results of the linear analytic model were compared with nonlinear simulations, leading to the following conclusions: (1) the perturbations in the Richardson number field, when small, are produced primarily by the perturbations of the shear; (2) perturbations of in the Richardson number field, even when small, are not symmetric, the increase being significantly larger than the decrease (the linear analytic solution and the nonlinear simulations both confirm this result); (3) as the perturbations grow, this asymmetry increases, but more so in the nonlinear simulations than in the linear analysis; (4) for large perturbations of the shear flow, the static stability, as represented by N2, is the dominating mechanism, becoming zero or negative, and producing convective overturning; and (5) the convectional measure of linearity in lee wave theory, NH/U, is no longer the critical parameter (it is suggested that (H/u sub 0) (du sub 0/dz) takes on this role in a shearing flow).

Wurtele, M. G.↗
NASA NTRS1993

Compression strength failure mechanisms in unidirectional composite laminates containing a hole

Experiments on graphite-epoxy laminated plates containing unloaded small holes show that these laminates are notch insensitive. That is, the uniaxial strength of these laminates with small holes exceeds the strength predicted by a point stress criterion using the stress concentration factor for the in-plane stress field. Laminates containing large holes exhibit notch sensitive behavior and consequently their strength is reasonably well predicted by the stress concentration effect. This hole size effect is manifested both in tension and in compression. Apparently, some mechanism must cause in-plane stress relief for laminates containing small holes. The purpose of this research was to study the influence of geometric nonlinearity on the micromechanical response of a filamentary composite material in the presence of a strain gradient caused by a discontinuity such as a hole. A mathematical model was developed at the micromechanical level to investigate this geometrically nonlinear effect.

Johnson, Eric R.↗
NASA NTRS1993

Femtosecond pulses generated from a synchronously pumped chromium-doped forsterite laser

Kerr lens mode-locking (KLM) has become a standard method to produce femtosecond pulses from tunable solid state lasers. High power inside the laser resonator propagating through the laser-medium with nonlinear index of refraction, coupled with the stability conditions of the laser modes in the resonator, result in a passive amplitude modulation which explains the mechanism for pulse shortening. Recently, chromium doped forsterite was shown to exhibit similar pulse behavior. A successful attempt to generate femtosecond pulses from a synchronously pumped chromium-doped forsterite laser with intracavity dispersion compensation is reported. Stable, transform limited pulses with duration of 105 fs were routinely generated, tunable between 1240 to 1270 nm.

Seas, A.↗
NASA NTRS1995

Material processing of convection-driven flow field and temperature distribution under oblique gravity

A set of mathematical formulation is adopted to study vapor deposition from source materials driven by heat transfer process under normal and oblique directions of gravitational acceleration with extremely low pressure environment of 10(exp -2) mm Hg. A series of time animation of the initiation and development of flow and temperature profiles during the course of vapor deposition has been obtained through the numerical computation. Computations show that the process of vapor deposition has been accomplished by the transfer of vapor through a fairly complicated flow pattern of recirculation under normal direction gravitational acceleration. It is obvious that there is no way to produce a homogeneous thin crystalline films with fine grains under such a complicated flow pattern of recirculation with a non-uniform temperature distribution under normal direction gravitational acceleration. There is no vapor deposition due to a stably stratified medium without convection for reverse normal direction gravitational acceleration. Vapor deposition under oblique direction gravitational acceleration introduces a reduced gravitational acceleration in vertical direction which is favorable to produce a homogeneous thin crystalline films. However, oblique direction gravitational acceleration also induces an unfavorable gravitational acceleration along horizontal direction which is responsible to initiate a complicated flow pattern of recirculation. In other words, it is necessary to carry out vapor deposition under a reduced gravity in the future space shuttle experiments with extremely low pressure environment to process vapor deposition with a homogeneous crystalline films with fine grains. Fluid mechanics simulation can be used as a tool to suggest most optimistic way of experiment with best setup to achieve the goal of processing best nonlinear optical materials.

Hung, R. J.↗
NASA NTRS1995

The nonlinear evolution of inviscid Goertler vortices in three-dimensional boundary layers

The nonlinear development of inviscid Gortler vortices in a three-dimensional boundary layer is considered. We do not follow the classical approach of weakly nonlinear stability problems and consider a mode which has just become unstable. Instead we extend the method of Blackaby, Dando, and Hall (1992), which considered the closely related nonlinear development of disturbances in stratified shear flows. The Gortler modes we consider are initially fast growing and we assume, following others, that boundary-layer spreading results in them evolving in a linear fashion until they reach a stage where their amplitudes are large enough and their growth rates have diminished sufficiently so that amplitude equations can be derived using weakly nonlinear and non-equilibrium critical-layer theories. From the work of Blackaby, Dando and Hall (1993) is apparent, given the range of parameters for the Gortler problem, that there are three possible nonlinear integro-differential evolution equations for the disturbance amplitude. These are a cubic due to viscous effects, a cubic which corresponds to the novel mechanism investigated in this previous paper, and a quintic. In this paper we shall concentrate on the two cubic integro-differential equations and in particular, on the one due to the novel mechanism as this will be the first to affect a disturbance. It is found that the consideration of a spatial evolution problem as opposed to temporal (as was considered in Blackaby, Dando, and Hall, 1992) causes a number of significant changes to the evolution equations.

Blackaby, Nicholas↗
DOE OSTI2020

A collective elastic fluctuation mechanism for decoupling and stretched relaxation in glassy colloidal and molecular liquids

We propose a microscopic theory for the decoupling of self-diffusion and structural relaxation in glass-forming liquids within the Elastically Collective Nonlinear Langevin Equation (ECNLE) activated dynamics framework. Our central hypothesis is that the heterogeneity relevant to this problem is static fluctuations of local density on the scale of 3–4 particle diameters and how this changes local packing correlations. These fluctuations modify the degree of dynamical cage expansion that mechanistically couples intracage large amplitude hopping and longer range collective elasticity in ECNLE theory. Decoupling only emerges in the deeply supercooled regime where the strongly temperature dependent elastic barrier becomes non-negligible relative to its noncooperative local analog. The theory makes predictions for various aspects of the decoupling phenomenon, including apparent fractional power law Stokes-Einstein behavior, that appear to be consistent with experiments and simulations on hard sphere fluids and molecular liquids. Of central importance is a microscopic connection between the barrier fluctuation variance and most probable barrier height. Sensible results are also obtained for the nonexponential stretching of a generic relaxation time correlation function and its temperature evolution. Nonuniversality can arise from the relative importance of the local and collective barriers (related to fragility) and the precise magnitude of the length scale that defines the transition from local cage to elastic physics. Comparison is made with a traplike model based on a Gaussian distribution of barriers.

Xie, Shi-Jie (ORCID:0000000333174720)↗
DOE OSTI2023

Efficient Reformulation of Linear and Nonlinear Solid-Phase Diffusion in Lithium-ion Battery Models using Symmetric Polynomials: Mass Conservation and Computational Efficiency

Lithium-ion batteries are typically modeled using porous electrode theory coupled with various transport and reaction mechanisms, along with suitable discretization or approximations for the solid-phase diffusion equation. The solid-phase diffusion equation represents the main computational burden for typical pseudo-2-dimensional (p2D) models since these equations in the pseudo r -dimension must be solved at each point in the computational grid. This substantially increases the complexity of the model as well as the computational time. Traditional approaches towards simplifying solid-phase diffusion possess certain significant limitations, especially in modeling emerging electrode materials which involve phase changes and variable diffusivities. A computationally efficient representation for solid-phase diffusion is discussed in this paper based on symmetric polynomials using Orthogonal Collocation and Galerkin formulation (weak form). A systematic approach is provided to increase the accuracy of the approximation (p form in finite element methods) to enable efficient simulation with a minimal number of semi-discretized equations, ensuring mass conservation even for non-linear diffusion problems involving variable diffusivities. These methods are then demonstrated by incorporation into the full p2D model, illustrating their advantages in simulating high C-rates and short-time dynamic operation of Lithium-ion batteries.

25 ENERGY STORAGE↗
NASA NTRS1979

Nonlinear singularly perturbed optimal control problems with singular arcs

Singular perturbation techniques are studied for dealing with singular arc problems by analyzing a relatively low-order but otherwise general system. This system encompasses many flight mechanic problems including Goddard's problem and a version of the minimum time-to-climb problem. Boundary layer solutions are constructed which are stable and reach the outer solution in a finite time. A uniformly valid composite solution is then formed from the reduced and boundary layer solutions. The value of the approximate solution is that it is relatively easy to obtain and does not involve singular arcs. To illustrate the utility of the results, the technique is used to obtain an approximate solution of a simplified version of the aircraft minimum time-to-climb problem.

Ardema, M. D.↗
NASA NTRS1985

Electromagnetic radiation and nonlinear energy flow in an electron beam-plasma system

It is shown that the unstable electron-plasma waves of a beam-plasma system can generate electromagnetic radiation in a uniform plasma. The generation mechanism is a scattering of the unstable electron plasma waves off ion-acoustic waves, producing electromagnetic waves whose frequency is near the local plasma frequency. The wave vector and frequency matching conditions of the three-wave mode coupling are experimentally verified. The electromagnetic radiation is observed to be polarized with the electric field parallel to the beam direction, and its source region is shown to be localized to the unstable plasma wave region. The frequency spectrum shows negligible intensity near the second harmonic of the plasma frequency. These results suggest that the observed electromagnetic radiation of type III solar bursts may be generated near the local plasma frequency and observed downstream where the wave frequency is near the harmonic of the plasma frequency.

Whelan, D. A.↗