Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “asymptotic analysis”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Structure and overstability of resistive modes with runaway electrons

In this paper, we investigate the effects of runaway electron current on the dispersion relation of resistive magnetohydrodynamic modes in tokamaks. We present a new theoretical model to derive the dispersion relation, which is based on the asymptotic analysis of the resistive layer structure of the modes. It is found that in addition to the conventional resistive layer, a new runaway current layer can emerge whose properties depend on the ratio of the Alfvén velocity to the runaway electron convection speed. Due to the contribution from this layer, both the tearing mode and kink mode will have a real frequency in addition to a growth rate. The derived dispersion relation has been compared with numerical results using both a simplified eigenvalue calculation and a M3D-C 1 linear simulation, and good agreement is found in both cases.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

A Stochastic Transport Model for the Cumulative Number of Fissions and Deposited Fission Energy

The stochastic theory of neutron transport is extended to describe the cumulative distribution of fission numbers and deposited fission energy in a multiplying assembly. Solutions for the probability distributions are obtained using analytical approximations and Monte Carlo simulation in lumped geometry and in symmetric homogeneous and heterogeneous spheres. The results show the development of a power-law tail in the steady state fission number and deposited energy distributions when the medium is critical, independent of the fission neutron multiplicity distribution and domain heterogeneity. In contrast, the asymptotic decay is faster than exponential in subcritical media due to rapid chain extinction and in supercritical media due to the increasing probability of chain divergence. Here, a formal asymptotic analysis of the problem in lumped geometry with an arbitrary fission neutron multiplicity confirms the existence of power-law tails at critical.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

MATEY: multiscale adaptive transformer models for spatiotemporal physical systems

Accurate representation of the multiscale features in spatiotemporal physical systems using vision transformer architectures requires extremely long, computationally prohibitive token sequences. To address this issue, we propose two novel adaptive tokenization schemes that dynamically adjust patch sizes based on local features: one ensures convergent behavior to uniform patch refinement, while the other offers better computational efficiency. Moreover, we present a set of spatiotemporal attention schemes, where the temporal or axial spatial dimensions are decoupled, to evaluate their baseline computational and data efficiencies and to determine whether adaptive tokenization can improve this performance. We assess the performance of the proposed multiscale adaptive model, MATEY, in a sequence of experiments. Compared to a full spatiotemporal attention scheme or a scheme that decouples only the temporal dimension, we find that fully decoupled axial attention is less efficient and expressive, requiring more training time and model parameters to achieve the same accuracy. The experiments on the adaptive tokenization schemes show that, compared to a uniformly refined model, the proposed schemes achieve comparable or improved accuracy at a much lower cost in the tested two-dimensional settings. While the asymptotic analysis suggests the potential for favorable scaling, empirical validation at substantially longer sequence lengths remains to be performed in future work. Finally, we demonstrate in two fine-tuning tasks featuring different physics that models pretrained on PDEBench data outperform the ones trained from scratch, especially in the low data regime with frozen attention.

adaptive tokenization↗
DOE OSTI2022

Precoder Design for Physical-Layer Security and Authentication in Massive MIMO UAV Communications

Supporting reliable and seamless wireless connectivity for unmanned aerial vehicles (UAVs) has recently become a critical requirement to enable various different use cases of UAVs. Due to their widespread deployment footprint, cellular networks can support beyond visual line of sight (BVLOS) communications for UAVs. In this paper, we consider cellular connected UAVs (C-UAVs) that are served by massive multiple input-multiple-output (MIMO) links to extend coverage range, while also improving physical layer security and authentication. Here, we consider Rician channel and propose a novel linear precoder design for transmitting data and artificial noise (AN). We derive the closed-form expression of the ergodic secrecy rate of CUAVs for both conventional and proposed precoder designs. In addition, we obtain the optimal power splitting factor that divides the power between data and AN by asymptotic analysis. Then, we apply the proposed precoder design in the fingerprint embedding authentication framework, where the goal is to minimize the probability of detection of the authentication tag at an eavesdropper. In simulation results, we show the superiority of the proposed precoder in both secrecy rate and the authentication probability considering moderate and large number of antenna massive MIMO scenarios.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2021

Risk-Adaptive Experimental Design for High-Consequence Systems: LDRD Final Report

Constructing accurate statistical models of critical system responses typically requires an enormous amount of data from physical experiments or numerical simulations. Unfortunately, data generation is often expensive and time consuming. To streamline the data generation process, optimal experimental design determines the 'best' allocation of experiments with respect to a criterion that measures the ability to estimate some important aspect of an assumed statistical model. While optimal design has a vast literature, few researchers have developed design paradigms targeting tail statistics, such as quantiles. In this project, we tailored and extended traditional design paradigms to target distribution tails. Our approach included (i) the development of new optimality criteria to shape the distribution of prediction variances, (ii) the development of novel risk-adapted surrogate models that provably overestimate certain statistics including the probability of exceeding a threshold, and (iii) the asymptotic analysis of regression approaches that target tail statistics such as superquantile regression. To accompany our theoretical contributions, we released implementations of our methods for surrogate modeling and design of experiments in two complementary open source software packages, the ROL/OED Toolkit and PyApprox.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1973

The parallel diffusion of cosmic rays in a random magnetic field.

Within the quasi-linear approximation, the existence of the parallel diffusion coefficient for cosmic rays in a random magnetic field (homogeneous, isotropic), despite the slow decay of the interaction between particles and random field, is demonstrated. As an example, the results of a numerical calculation of the parallel diffusion coefficient for a Gaussian random-field correlation function are presented. The numerical results are corroborated by asymptotic analysis and are compared to those of other theories.

Klimas, A.↗
NASA NTRS1976

Laminar flow at a three-dimensional stagnation point with large rates of injection

Exact calculations of the titled flow are presented and compared to the predictions of an asymptotic analysis for large rates of injection. The inner layer of the boundary layer is found to involve outflow in both orthogonal directions whether the external flow along the y axis is inward or outward. As a result, the flow at a nearly two-dimensional stagnation point involves drastic changes as a weak outflow changes to a weak inflow. It is also found that the velocity profiles in the two directions in the inner layer are quite different.

Libby, P. A.↗
NASA NTRS1982

Observational dispersion relations

Pulse propagation in plasmas has been widely studied in relation to instabilities and their classification as convective or absolute. Such analyses emphasize the importance of considering the summation of a spectrum of modes, rather than simply making deductions from Brillouin dispersion relations plotted either for real frequency and complex wavenumber, or for complex frequency and real wavenumber. In particular, erroneous conclusions may be drawn about the magnitude and direction of propagation of a transient pulse. In this paper, the point of view is taken that an observer remote from the source would measure an 'observational dispersion relation'. The nature of this dispersion relation is examined for absorbing or convectively unstable plasmas by asymptotic analysis, and for different source waveforms. Illustrative results are presented for propagation in cold plasmas and for beam-plasma interaction.

Crawford, F. W.↗
NASA NTRS1982

Stationarity of magnetohydrodynamic fluctuations in the solar wind

Solar wind research and studies of charged particle propagation often assume that the interplanetary magnetic field represents a stationary random process. The extent to which ensemble averages of the solar wind magnetic fields follow the asymptotic behavior predicted by the ergodic theorem was investigated. Several time periods, including a span of nearly two years, are analyzed. Data intervals which span many solar rotations satisfy the conditions of weak stationarity if the effects of solar rotation are included in the asymptotic analysis. Shorter intervals which include a small integral number of interplanetary sectors also satisfy weak stationarity. The results are illustrated using magnetometer data from the ISEE-3, Voyager and IMP spacecraft.

Matthaeus, W. H.↗
NASA NTRS1983

Flow in a differentially rotated cylindrical drop at low Reynolds number

A liquid drop held captive between parallel disks that are differentially rotated is a model for the swirling flows induced by crystal rotation in the floating-zone process for growing semiconductor materials. An asymptotic analysis for a cylindrical drop is presented that elucidates the structure of the axisymmetric cellular motions caused by disk rotation at low Reynolds number. Variations of meniscus shape induced by these flows are described in the limit of small capillary number. Most cellular flow fields break the bifurcation point that corresponds to the Plateau-Rayleigh limit for the length of a static drop into two disjoint shape families and lower the maximum stable drop length. This effect is studied by a singular bifurcation analysis.

Harriott, G. M.↗
NASA NTRS1983

Numerical solution of the Navier-Stokes equations for compressible turbulent two/three dimensional flows in the terminal shock region of an inlet/diffuser

The multidimensional, ensemble-averaged, compressible, time-dependent Navier-Stokes equations in conjunction with mixing length turbulence model and shock capturing technique have been used to study the terminal shock type of flows in various flight regimes occurring in a diffuser/inlet model. The numerical scheme for solving the governing equations is based on a linearized block implicit approach and the following high Reynolds number calculations have been carried out: (1) 2-D, steady, subsonic; (2) 2-D, steady, transonic with normal shock, (3) 2-D, steady, supersonic with terminal shock, (4) 2-D, transient process of shock development and (5) 3-D, steady, transonic with normal shock. The numerical results obtained for the 2-D and 3-D transonic shocked flows have been compared with corresponding experimental data; the calculated wall static pressure distributions agree well with the measured data. The predicted transient responses of the flow to externally applied impulsive disturbance are consistent with results obtained via asymptotic analysis.

Liu, N.-S.↗
NASA NTRS1984

Flow in a differentially rotated cylindrical drop at moderate Reynolds number

Galerkin finite-element approximations are combined with computer-implemented perturbation methods for tracking families of solutions to calculate the steady axisymmetric flows in a differentially rotated cylindrical drop as a function of Reynolds number Re, drop aspect ratio and the rotation ratio between the two end disks. The flows for Reynolds numbers below 100 are primarily viscous and reasonably described by an asymptotic analysis. When the disks are exactly counter-rotated, multiple steady flows are calculated that bifurcate to higher values of Re from the expected solution with two identical secondary cells stacked symmetrically about the axial midplane. The new flows have two cells of different size and are stable beyond the critical value Re sub c. The slope of the locus of Re sub c for drops with aspect ratio up to 3 disagrees with the result for two disks of infinite radius computed assuming the similarity form of the velocity field. Changing the rotation ratio for exact counter-rotation ruptures the junction of the multiple flow fields into two separated flow families.

Harriott, G. M.↗
NASA NTRS1985

Numerical studies of interacting vortices

To get a basic understanding of the physics of flowfields modeled by vortex filaments with finite vortical cores, systematic numerical studies of the interactions of two dimensional vortices and pairs of coaxial axisymmetric circular vortex rings were made. Finite difference solutions of the unsteady incompressible Navier-Stokes equations were carried out using vorticity and stream function as primary variables. Special emphasis was placed on the formulation of appropriate boundary conditions necessary for the calculations in a finite computational domain. Numerical results illustrate the interaction of vortex filaments, demonstrate when and how they merge with each other, and establish the region of validity for an asymptotic analysis.

Liu, G. C.↗
NASA NTRS1985

A panel method study of vortex sheets with special emphasis on sheets of axisymmetric geometry

The self induced evolution of a vortex sheet was simulated by modeling the sheet using an integration of discrete elements of vorticity. Replacing small sections of a vortex sheet by flat panels of constant vorticity is found to reproduce more accurately the initial conditions for the Lagrangian simulation technique than replacement by point vortices. The flat panel method for the vortex sheet was then extended to model axisymmetric vortex sheets. The local and far field velocities induced by the axisymmetric panels were obtained using matched asymptotic analysis, and some of the uncertainties involved in other models of the axisymmetric vortex sheet have been eliminated. One important result of this analysis is the determination of the proper choice of core size for a circular vortex filament which may replace a section of an axisymmetric vortex sheet. Roll-up of both two dimensional and axisymmetric vortex sheets was computed using the panel methods developed in the report.

Sugioka, I.↗
NASA NTRS1984

Heat and mass transfer in combustion - Fundamental concepts and analytical techniques

Fundamental combustion phenomena and the associated flame structures in laminar gaseous flows are discussed on physical bases within the framework of the three nondimensional parameters of interest to heat and mass transfer in chemically-reacting flows, namely the Damkoehler number, the Lewis number, and the Arrhenius number which is the ratio of the reaction activation energy to the characteristic thermal energy. The model problems selected for illustration are droplet combustion, boundary layer combustion, and the propagation, flammability, and stability of premixed flames. Fundamental concepts discussed include the flame structures for large activation energy reactions, S-curve interpretation of the ignition and extinctin states, reaction-induced local-similarity and non-similarity in boundary layer flows, the origin and removal of the cold boundary difficulty in modeling flame propagation, and effects of flame stretch and preferential diffusion on flame extinction and stability. Analytical techniques introduced include the Shvab-Zeldovich formulation, the local Shvab-Zeldovich formulation, flame-sheet approximation and the associated jump formulation, and large activation energy matched asymptotic analysis. Potentially promising research areas are suggested.

Law, C. K.↗
NASA NTRS1987

Damage growth in composite laminates with interleaves

The influence of placing interleaves between fiber reinforced plies in multilayered composite laminates is investigated. The geometry of the composite is idealized as two dimensional, isotropic, linearly elastic media made of a damaged layer bonded between two half planes and separated by thin interleaves of low extensional and shear moduli. The damage in the layer is taken in the form of a symmetric crack perpendicular to the interface and may extend up to the interface. The case of an H-shaped crack in the form of a broken layer with delamination along the interface is also analyzed. The interleaves are modeled as distributed shear and tension springs. Fourier integral transform techniques are used to develop solutions in terms of singular integral equations. An asymptotic analysis of the integral equations based on Muskhelishvili's techniques reveals logarithmically singular axial stresses in the half plane at the crack tips for the broken layer. For the H shaped crack, similar singularities are found to exist in the axial stresses at the interface crack tips in the layer and the half plane. The solution of the equations is found numerically for the stresses and displacements by using the Hadamard's concept of direct differentiation of Cauchy integrals as well as Gaussian integration techniques.

Goree, James G.↗
NASA NTRS1986

Numerical studies of interacting vortices

To get a basic understanding of the physics of flowfields modeled by vortex filaments with finite vortical cores, systematic numerical studies of the interactions of two vortices and pairs of coaxial axisymmetric circular vortex rings were made. Finite difference solutions of the unsteady incompressible Navier-Stokes equations were carried out using vorticity and stream function as primary variables. Special emphasis was placed on the formulation of appropriate boundary conditions necessary for the calculations in a finite computational domain. Numerical results illustrate the interaction of vortex filaments, demonstrate when and how they merge with each other, and establish the region of validity for an asymptotic analysis.

Liu, G. C.↗