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At least 469 records · Page 26
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Anti-symmetric and positivity preserving formulation of a spectral method for Vlasov-Poisson equations

We analyze the anti-symmetric properties of a spectral discretization for the one-dimensional Vlasov-Poisson equations. The discretization is based on a spectral expansion in velocity with the symmetrically weighted Hermite basis functions, central finite differencing in space, and an implicit Runge Kutta integrator in time. The proposed discretization preserves the anti-symmetric structure of the advection operator in the Vlasov equation, resulting in a stable numerical method. We apply such discretization to two formulations: the canonical Vlasov-Poisson equations and their continuously transformed square-root representation. The latter preserves the positivity of the particle distribution function. We derive analytically the conservation properties of both formulations, including particle number, momentum, and energy, which are verified numerically on the following benchmark problems: manufactured solution, linear and nonlinear Landau damping, two-stream instability, bump-on-tail instability, and ion-acoustic wave.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1994

The onset of gravothermal oscillations in globular cluster evolution

We have carried out an extensive set of Fokker-Planck simulations of the evolution of globular clusters on very long timescales, up to 600 times the initial core collapse time t(sub cc). We consider an idealized equal mass star cluster, with a wide range of values for the total number of stars, 7000 less than N less than 2 x 10(exp 6). Our models include the heating effect of compact binaries formed in three-body encounters, which halts the initial core collapse and drives a core reexpansion. Postcollapse gravothermal oscillations of the cluster core are found to occur for all N approximately greater than or equal to 8000. For 8000 approximately less than or equal to N approximately less than or equal to 11,000, the oscillation has a simple, regular waveform with a single, well-defined period. For N approximately equals 12,000, the oscillations become nonlinear in a process resembling a period doubling. For N approximately greater than or equal to 14,000, the waveform of the oscillations becomes increasingly more irregular with increasing N, resembling chaotic behavior for N approximately greater than or equal to 15,000. During the oscillations, the core radius and core mass vary dramatically: by more than a factor of 10 for N greater than 15,000, by more than a factor of 100 for N greater than 5 x 10(exp 4), and by more than a factor of 1000 for N greater than 5 x 10(exp 5). However, even during the times of maximum expansion, the core contains only a small fraction of the cluster mass. For most N values, the maximum core mass at any time after core collapse is less than 1% of the cluster mass. The exceptions lie in the range 5 x 10(exp 4) approximately less than or equal to N approximately equal to or less than 2 x 10(exp 5), where the maximum post-collapse core mass reaches approximately 2% of the cluster mass. We discuss the observational implications of these predictions.

Breeden, Joseph L.↗
NASA NTRS1990

A numerical and analytical study of nonlinear bifurcations associated with the morphological stability of two-dimensional single crystals

The nonlinear stability of a two-dimensional single crystal of pure material in an undercooled melt is studied both analytically and numerically. The quasi-steady state approximation is used for the thermal fields, and the effects of different solid and liquid thermal conductivities, isotropic interfacial growth kinetics, and isotropic surface tension are included. The bifurcation analysis is performed by calculating the instantaneous value of the fundamental component of the local normal growth speed for an interface perturbed by a single Fourier shape component. Numerically, the fundamental component of the interfacial growth speed is found by Fourier analysis of the solution to an integrodifferential equation obeyed at the interface. Analytically, an expansion technique is used to derive a solvability condition defining each of these bifurcation points. The analytical and numerical results are in very close agreement. Almost all of the bifurcations are subcritical, and the results are presented by giving values of the Landau coefficient as a function of the different dimensionless parameters used in the model.

Brush, L. N.↗
NASA NTRS1995

Observational and numerical studies of extreme frontal scale contraction

The general objective of this effort is to increase understanding of how frontal scale contraction processes may create and sustain intense mesoscale precipitation along intensifying cold fronts. The five-part project (an expansion of the originally proposed two-part project) employed conventional meteorological data, special mesoscale data, remote sensing measurements, and various numerical models. First an idealized hydrostatic modeling study of the scale contraction effects of differential cloud cover on low-level frontal structure and dynamics was completed and published in a peer-reviewed journal. The second objective was to complete and publish the results from a three dimensional numerical model simulation of a cold front in which differential sensible heating related to cloud coverage patterns was apparently crucial in the formation of a severe frontal squall line. The third objective was to use a nonhydrostatic model to examine the nonlinear interactions between the transverse circulation arising from inhomogeneous cloud cover, the adiabatic frontal circulation related to semi-geostrophic forcing, and diabatic effects related to precipitation processes, in the development of a density current-like microstructure at the leading edge of cold fronts. Although the development of a frontal model that could be used to initialize such a primitive equation model was begun, we decided to focus our efforts instead on a project that could be successfully completed in this short time, due to the lack of prospects for continued NASA funding beyond this first year (our proposal was not accepted for future funding). Thus, a fourth task was added, which was to use the nonhydrostatic model to test tentative hypotheses developed from the most detailed observations ever obtained on a density current (primarily sodar and wind profiler data). These simulations were successfully completed, the findings were reported at a scientific conference, and the results have recently been submitted to a peer-reviewed journal. The fifth objective was to complete the analysis of data collected during the Cooperative Oklahoma Profiler Studies (COPS-91) field project, which was supported by NASA. The analysis of the mesoscale surface and sounding data, Doppler radar imagery, and other remote sensing data from multi frequency wind profiler, microwave radiometer, and the Radio Acoustic Sounding System has been completed. This study is a unique investigation of processes that caused the contraction of a cold front to a microscale zone exhibiting an undular bore-like structure. Results were reported at a scientific conference and are being prepared for publication. In summary, considerable progress has been achieved under NASA funding in furthering our understanding of frontal scale contraction and density current - gravity wave interaction processes, and in utilizing models and remotely sensed data in such studies.

Koch, Steven E.↗
DOE OSTI2023

The saturation mechanism of thermal instability

The literature on thermal instability (TI) reveals that even for a simple homogeneous plasma, the nonlinear outcome ranges from a gentle reconfiguration of the initial state to an explosive one, depending on whether the condensations that form evolve in an isobaric or nonisobaric manner. After summarizing the recent developments on the linear and nonlinear theory of TI, here we derive several general identities from the evolution equation for entropy that reveal the mechanism by which TI saturates; whenever the boundary of the instability region (the Balbus contour) is crossed, a dynamical change is triggered that causes the comoving time derivative of the pressure to change the sign. This event implies that the gas pressure force reverses direction, slowing the continued growth of condensation. For isobaric evolution, this “pressure reversal” occurs nearly simultaneously for every fluid element in condensation and a steady state is quickly reached. For nonisobaric evolution, the condensation is no longer in mechanical equilibrium and the contracting gas rebounds with greater force during the expansion phase that accompanies the gas reaching the equilibrium curve. The cloud then pulsates because the return to mechanical equilibrium becomes wave mediated. We show that both the contraction rebound event and subsequent pulsation behavior follow analytically from an analysis of the new identities. Our analysis also leads to the identification of an isochoric TI zone and makes it clear that unless this zone intersects the equilibrium curve, isochoric modes can only become unstable if the plasma is in a state of thermal non-equilibrium.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Real-time estimation and control of divertor surface heat flux on the DⅢ-D tokamak

We report Future tokamaks will require robust technologies for the mitigation of heat exhaust onto the plasma-facing components. As a first step towards this development, a system has been developed at DIII-D that estimates and controls in real-time the heat flux to the PFCs. Real-time estimation of the peak power flux from this model-based approach is validated with off-line infra-red measurements for various DIII-D plasma discharges. A nonlinear free-boundary simulation code (GSevolve) is used for simulating the closed loop response and for the off-line determination of the control parameters. The implementation and first experimental results of the application during the DIII-D plasma campaign are reported.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

A Bottom-up Approach to Improve the Representation of Deep Convective Clouds in Weather and Climate Models (Final Report)

A fundamental yet outstanding question about deep cumulus convection regards how convective updrafts, downdrafts, and surface-based cold pools are inter-related within organized storms, and how these three convective components are modulated by external and internal factors. We considered this question through numerical model simulations as well as data collected during the MC3E field campaign. One of our basic hypotheses was that deep cold pools are forced by wide downdrafts which arise from wide updrafts. This “bottom-up” perspective required consideration of the external controls on updraft width, and then the internal controls on cold-pool characteristics including depth. Model experiments showed that environmental vertical wind shear (an external factor) exerts a particularly strong control on updraft width; analyses of linear and nonlinear dynamic pressure forcing readily explain this control. The experiments also showed that increases in updraft width are accompanied by corresponding increases in downdraft width and cold-pool depth. The updraft–downdraft connection is through precipitation: the wide area of precipitation that will be initiated in a wide updraft will in turn lead to a wide downdraft. The downdraft–cold pool connection is through mass continuity: at the downdraft terminus, the large downdraft mass flux through a wide downdraft must lead to a deep cold pool. Model experiments also showed that the cold-pool depth and other characteristics can be significantly modulated by microphysical processes (internal factors). Specifically, the cold-pool expansion rate, depth, and intensity was found to depend most strongly on the amount of rain evaporation near the ground. However, the sustenance of the cold pool itself depended upon the downdrafts strengthened by sublimation of graupel higher in the storm. Finally, field campaign data revealed compelling inter-relationships between the cold-pool characteristics, and downdraft transience in terms of the microphysics. For example, pulses of hail and graupel (also internal factors) within downdrafts resulted in short-lived increases in the cold-pool depth. However, the cold-pool speed appeared to be relatively independent of the cold-pool depth and intensity, suggesting limitations of density current theory to convective cold pools in nature.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1990

Estimating short-period dynamics using an extended Kalman filter

An extended Kalman filter (EKF) is used to estimate the parameters of a low-order model from aircraft transient response data. The low-order model is a state space model derived from the short-period approximation of the longitudinal aircraft dynamics. The model corresponds to the pitch rate to stick force transfer function currently used in flying qualities analysis. Because of the model chosen, handling qualities information is also obtained. The parameters are estimated from flight data as well as from a six-degree-of-freedom, nonlinear simulation of the aircraft. These two estimates are then compared and the discrepancies noted. The low-order model is able to satisfactorily match both flight data and simulation data from a high-order computer simulation. The parameters obtained from the EKF analysis of flight data are compared to those obtained using frequency response analysis of the flight data. Time delays and damping ratios are compared and are in agreement. This technique demonstrates the potential to determine, in near real time, the extent of differences between computer models and the actual aircraft. Precise knowledge of these differences can help to determine the flying qualities of a test aircraft and lead to more efficient envelope expansion.

Bauer, Jeffrey E.↗
DOE OSTI2025

TCC in the interior of moduli space and its implications for the string landscape and cosmology

We consider the classical Friedmann-Robertson-Walker solutions that describe a universe undergoing a transition from an accelerating expansion phase in the past to an eternal decelerating expansion phase in the future, driven by a scalar field evolving in a potential energy landscape. We show that any solution for which the accelerating phase violates the Trans-Planckian Censorship Conjecture (TCC), even in the interior of moduli space, never approaches the asymptotic vacuum with zero particles. Based on the assumption that the effective field theory must be valid for the vacuum on the asymptotic boundary, as motivated by holography and string theory, we argue that (multi-field) scalar potentials with such solutions are disallowed, thus strengthening the case for TCC. In particular, assuming the regularity of the future vacuum state in the string landscape, we derive results that imply a new set of highly-nonlinear constraints across the string landscape which in the absence of certain meta-stable vacua make realizing inflation impossible.

Cosmological models↗
NASA NTRS2006

Compressible Flow Toolbox

The Compressible Flow Toolbox is primarily a MATLAB-language implementation of a set of algorithms that solve approximately 280 linear and nonlinear classical equations for compressible flow. The toolbox is useful for analysis of one-dimensional steady flow with either constant entropy, friction, heat transfer, or Mach number greater than 1. The toolbox also contains algorithms for comparing and validating the equation-solving algorithms against solutions previously published in open literature. The classical equations solved by the Compressible Flow Toolbox are as follows: The isentropic-flow equations, The Fanno flow equations (pertaining to flow of an ideal gas in a pipe with friction), The Rayleigh flow equations (pertaining to frictionless flow of an ideal gas, with heat transfer, in a pipe of constant cross section), The normal-shock equations, The oblique-shock equations, and The expansion equations.

Melcher, Kevin J.↗
DOE OSTI2021

Stability and Conservation properties of Hermite-based approximations of the Vlasov-Poisson System

Spectral approximation based on Hermite-Fourier expansion of the Vlasov-Poisson model for a collisionless plasma in the electro-static limit is provided by adding high-order artificial collision operators of Lenard-Bernstein type. These differential operators are suitably designed in order to preserve the physically-meaningful invariants (number of particles, momentum, energy). In view of time-discretization, stability results in appropriate norms are presented. In this study, necessary conditions link the magnitude of the artificial collision term, the number of spectral modes of the discretization, as well as the time-step. The analysis, carried out in full for the Hermite discretization of a simple linear problem in one-dimension, is then partly extended to cover the complete nonlinear Vlasov-Poisson model.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1976

Lattice theory of three-dimensional cracks

The problem of the stability of a three-dimensional crack is analyzed within a lattice-statics approximation. The consequence of introducing a jog into the crack face as well as the effects of various nonlinear-force laws are studied. The phenomenon of lattice trapping (upper and lower bounds on the applied stress for an equilibrium crack of given length) is again obtained. It is possible to obtain some physical insight into which aspects of the force law are critical for crack stability. In particular, the inadequacy of a thermodynamic approach - which relates the critical stress to a surface energy corresponding to the area under the cohesive-force-vs-displacement curve - is demonstrated. Surface energy is a global property of the cohesive-force law. Crack stability is sensitive to much more refined aspects of the cohesive-force law. Crack healing is sensitive to the long-range portion of the cohesive force. Crack expansion is sensitive to the position of the maximum in the cohesive-force relation.

Esterling, D. M.↗
DOE OSTI2025

Two-Frequency RF Fields Induced Multipactor in Coaxial Transmission Lines

Multipactor is a nonlinear discharge phenomenon that occurs in vacuum RF systems, potentially leading to signal distortion, power loss, and even permanent damage to high-power components. This study presents a detailed investigation of two-surface multipactor in coaxial transmission lines under two-frequency excitation, using one-dimensional (1D) Monte Carlo simulations validated by three-dimensional (3D) Particle-in-Cell (PIC) results and experimental data. Introducing a second carrier mode is shown to suppress multipactor by reshaping and shrinking the susceptibility region, with the extent and location of suppression strongly dependent on the device aspect ratio and the relative phase of the second mode. Distinct suppression patterns emerge across different frequency–gap distance (fd) regimes, and in certain cases, susceptibility expansion is also observed. The study identifies and distinguishes pure and mixed multipactor modes in coaxial geometry, where analytical mode boundaries are not readily defined. Unlike planar systems, pure-mode regions in coaxial structures overlap with mixed-mode domains, complicating classification. Image charge forces are found to have minimal effect on susceptibility thresholds but do influence electron growth rates. These findings provide new insights into waveform-driven control of multipactor in high-power RF systems.

43 PARTICLE ACCELERATORS↗
NASA NTRS1986

Resistive ballooning modes in line-tied coronal arcades

The equations describing the linear evolution of resistive ballooning modes are obtained by using a modified WKB expansion in the short perpendicular wavelength, while variations of the perturbations along the field are described by a slowly varying amplitude, on which the tying boundary conditions are imposed. In general, given an equilibrium, there are certain ranges of magnetic surfaces for which the system predicts instability even without dissipation. The main conclusion is that within the resistive MHD approximation cylindrically symmetric arcades with pressure falling with radius are unstable to resistive localized modes; the growth rates, close to ideal marginal stability, are large, so that it would appear that energy could be released during 10 to 100 Alfven times. The wavelength of the modes is expected to be limited by the ion gyroradius, when stabilizing drift effects must be taken into account. The nonlinear evolution of resistive ballooning modes should be studied to assess their overall relevance to the violent and rapidly evolving phenomena observed on the sun.

Velli, Marco↗
DOE OSTI2024

Time propagation of electronic wavefunctions using nonorthogonal determinant expansions

The use of truncated configuration interaction in real-time time-dependent simulations of electron dynamics provides a balance of computational cost and accuracy, while avoiding some of the failures associated with real-time time-dependent density functional theory. However, low-order truncated configuration interaction also has limitations, such as overestimation of polarizability in configuration interaction singles, even when perturbative doubles are included. Increasing the size of the determinant expansion may not be computationally feasible, and so, in this work, we investigate the use of nonorthogonality in the determinant expansion to establish the extent to which higher-order substitutions can be recovered, providing an improved description of electron dynamics. Model systems are investigated to quantify the extent to which different methods accurately reproduce the (hyper)polarizability, including the high-harmonic generation spectrum of H 2 , water, and butadiene.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2006

User Guide for Compressible Flow Toolbox Version 2.1 for Use With MATLAB(Registered Trademark); Version 7

This report provides a user guide for the Compressible Flow Toolbox, a collection of algorithms that solve almost 300 linear and nonlinear classical compressible flow relations. The algorithms, implemented in the popular MATLAB programming language, are useful for analysis of one-dimensional steady flow with constant entropy, friction, heat transfer, or shock discontinuities. The solutions do not include any gas dissociative effects. The toolbox also contains functions for comparing and validating the equation-solving algorithms against solutions previously published in the open literature. The classical equations solved by the Compressible Flow Toolbox are: isentropic-flow equations, Fanno flow equations (pertaining to flow of an ideal gas in a pipe with friction), Rayleigh flow equations (pertaining to frictionless flow of an ideal gas, with heat transfer, in a pipe of constant cross section.), normal-shock equations, oblique-shock equations, and Prandtl-Meyer expansion equations. At the time this report was published, the Compressible Flow Toolbox was available without cost from the NASA Software Repository.

Melcher, Kevin J.↗
DOE OSTI2023

An effective field theory for non-maximal quantum chaos

In non-maximally quantum chaotic systems, the exponential behavior of out-of-time-ordered correlators (OTOCs) results from summing over exchanges of an infinite tower of higher “spin” operators. We construct an effective field theory (EFT) to capture these exchanges in (0 + 1) dimensions. The EFT generalizes the one for maximally chaotic systems, and reduces to it in the limit of maximal chaos. The theory predicts the general structure of OTOCs both at leading order in the 1/N expansion (N is the number of degrees of freedom), and after resuming over an infinite number of higher order 1/N corrections. These general results agree with those previously explicitly obtained in specific models. We also show that the general structure of the EFT can be extracted from the large q SYK model.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Dependence of Solar Wind Proton Temperature on the Polarization Properties of Alfvénic Fluctuations at Ion-kinetic Scales

In this work, we use fluctuating magnetic helicity to investigate the polarization properties of Alfvénic fluctuations at ion-kinetic scales in the solar wind as a function of β p , the ratio of proton thermal pressure to magnetic pressure, and θ vB , the angle between the proton flow and local mean magnetic field, B 0 . Using almost 15 yr of Wind observations, we separate the contributions to helicity from fluctuations with wavevectors, k, quasi-parallel and oblique to B 0 , finding that the helicity of Alfvénic fluctuations is consistent with predictions from linear Vlasov theory. This result suggests that the nonlinear turbulent fluctuations at these scales share at least some polarization properties with Alfvén waves. Furthermore, we also investigate the dependence of proton temperature in the β p –θ vB plane to probe for possible signatures of turbulent dissipation, finding that it correlates with θ vB . The proton temperature parallel to B 0 is higher in the parameter space where we measure the helicity of right-handed Alfvénic fluctuations, and the temperature perpendicular to B 0 is higher where we measure left-handed fluctuations. This finding is inconsistent with the general assumption that by sampling different θ vB in the solar wind we can analyze the dependence of the turbulence distribution on θ kB , the angle between k and B 0 . After ruling out both instrumental and expansion effects, we conclude that our results provide new evidence for the importance of local kinetic processes that depend on θ vB in determining proton temperature in the solar wind.

79 ASTRONOMY AND ASTROPHYSICS↗