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At least 343 records · Page 19

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NASA NTRS2008

Transient Effects in Planar Solidification of Dilute Binary Alloys

The initial transient during planar solidification of dilute binary alloys is studied in the framework of the boundary integral method that leads to the non-linear Volterra integral governing equation. An analytical solution of this equation is obtained for the case of a constant growth rate which constitutes the well-known Tiller's formula for the solute transient. The more physically relevant, constant ramping down temperature case has been studied both numerically and analytically. In particular, an asymptotic analytical solution is obtained for the initial transient behavior. A numerical technique to solve the non-linear Volterra equation is developed and the solution is obtained for a family of the governing parameters. For the rapid solidification condition, growth rate spikes have been observed even for the infinite kinetics model. When recirculating fluid flow is included into the analysis, the spike feature is dramatically diminished. Finally, we have investigated planar solidification with a fluctuating temperature field as a possible mechanism for frequently observed solute trapping bands.

Mazuruk, K.↗

NASA NTRS2008

Transient Effects in Planar Solidification of Dilute Binary Alloys

Mazuruk, Konstantin↗

DOE OSTI2015

Analysis of unstable periodic orbits and chaotic orbits in the one-dimensional linear piecewise-smooth discontinuous map

In this paper, we analytically examine the unstable periodic orbits and chaotic orbits of the 1-D linear piecewise-smooth discontinuous map. We explore the existence of unstable orbits and the effect of variation in parameters on the coexistence of unstable orbits. Further, we show that this structuring is different from the well known period adding cascade structure associated with the stable periodic orbits of the same map. Further, we analytically prove the existence of chaotic orbit for this map.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2014

Aspect ratio effects on limited scrape-off layer plasma turbulence

The drift-reduced Braginskii model describing turbulence in the tokamak scrape-off layer is written for a general magnetic configuration with a limiter. The equilibrium is then specified for a circular concentric magnetic geometry retaining aspect ratio effects. Simulations are then carried out with the help of the global, flux-driven fluid three-dimensional code GBS [Ricci et al., Plasma Phys. Controlled Fusion 54, 124047 (2012)]. Linearly, both simulations and simplified analytical models reveal a stabilization of ballooning modes. Nonlinearly, flux-driven nonlinear simulations give a pressure characteristic length whose trends are correctly captured by the gradient removal theory [Ricci and Rogers, Phys. Plasmas 20, 010702 (2013)], that assumes the profile flattening from the linear modes as the saturation mechanism. More specifically, the linear stabilization of ballooning modes is reflected by a 15% increase in the steady-state pressure gradient obtained from GBS nonlinear simulations when going from an infinite to a realistic aspect ratio.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

Lattice strains and diffraction elastic constants of cubic polycrystals

In situ synchrotron X-ray and neutron diffraction experiments provide a powerful approach to measure lattice strains in bulk polycrystalline materials. They are being increasingly used for quantitative characterization of microscale deformation within and between grains and phases. Here we use a self-consistent micromechanics model to obtain a general analytic solution of the grain-level lattice strains and diffraction elastic constants for a broad class of elastically isotropic polycrystals with cubic crystal symmetry. This analytic solution reveals a direct linear relationship between the reciprocal of the elastic diffraction constant and the orientation index parameter along the direction of any diffraction vector, including tensile loading and transverse directions. The straightforward numerical implementation of this solution provides diffraction elastic constants for 26 representative cubic polycrystals. Finally, analytic solutions of this kind can serve to benchmark in situ diffraction measurements of lattice strains and also facilitate high-throughput studies of microscale stresses and diffraction elastic constants in polycrystalline materials.

36 MATERIALS SCIENCE↗

DOE OSTI2015

Regular and chaotic dynamics of a piecewise smooth bouncer

The dynamical properties of a particle in a gravitational field colliding with a rigid wall moving with piecewise constant velocity are studied. The linear nature of the wall's motion permits further analytical investigation than is possible for the system's sinusoidal counterpart. We consider three distinct approaches to modeling collisions: (i) elastic, (ii) inelastic with constant restitution coefficient, and (iii) inelastic with a velocity-dependent restitution function. We confirm the existence of distinct unbounded orbits (Fermi acceleration) in the elastic model, and investigate regular and chaotic behavior in the inelastic cases. We also examine in the constant restitution model trajectories wherein the particle experiences an infinite number of collisions in a finite time, i.e., the phenomenon of inelastic collapse. We address these so-called “sticking solutions” and their relation to both the overall dynamics and the phenomenon of self-reanimating chaos. Additionally, we investigate the long-term behavior of the system as a function of both initial conditions and parameter values. We find the non-smooth nature of the system produces novel bifurcation phenomena not seen in the sinusoidal model, including border-collision bifurcations. The analytical and numerical investigations reveal that although our piecewise linear bouncer is a simplified version of the sinusoidal model, the former not only captures essential features of the latter but also exhibits behavior unique to the discontinuous dynamics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS2011

Demagnetization Tests Performed on a Linear Alternator for a Stirling Power Convertor

Demagnetization temperature of a linear alternator (LA) can be accurately predicted through an analytical Maxwell model. The M-H characteristics of the alternator magnets must be known. Vendor data are given for cube-shaped magnets, and the shape of a LA magnet may affect its magnetic properties. At GRC, M-H data are directly measured for each LA magnet. This method was validated using TDC alternator tests on the Alternator Test Rig. The analytical Maxwell modeling was utilized on a different style linear alternator to predict demagnetization temperatures for the Advanced Stirling Convertor.

Geng, Steven M.↗

NASA NTRS2019

A Communication Channel Density Estimating Generative Adversarial Network

Autoencoder-based communication systems use neural network channel models to backwardly propagate message reconstruction error gradients across an approximation of the physical communication channel. In this work, we develop and test a new generative adversarial network (GAN) architecture for the purpose of training a stochastic channel approximating neural network. In previous research, investigators have focused on additive white Gaussian noise (AWGN) channels and/or simplified Rayleigh fading channels, both of which are linear and have well defined analytic solutions. Given that training a neural network is computationally expensive, channel approximation networks— and more generally the autoencoder systems—should be evaluated in communication environments that are traditionally difficult. To that end, our investigation focuses on channels that contain a combination of non-linear amplifier distortion, pulse shape filtering, intersymbol interference, frequency-dependent group delay, multipath, and non-Gaussian statistics. Each of our models are trained without any prior knowledge of the channel. We show that the trained models have learned to generalize over an arbitrary amplifier drive level and constellation alphabet. We demonstrate the versatility of our GAN architecture by comparing the marginal probability density function of several channel simulations with that of their corresponding neural network approximations

Smith, Aaron↗

NASA NTRS1979

VTOL controls for shipboard landing

The problem of landing a VTOL aircraft on a small ship in rough seas using an automatic controller is examined. The controller design uses the linear quadratic Gaussian results of modern control theory. Linear time invariant dynamic models are developed for the aircraft, ship, and wave motions. A hover controller commands the aircraft to track position and orientation of the ship deck using only low levels of control power. Commands for this task are generated by the solution of the steady state linear quadratic gaussian regulator problem. Analytical performance and control requirement tradeoffs are obtained. A landing controller commands the aircraft from stationary hover along a smooth, low control effort trajectory, to a touchdown on a predicted crest of ship motion. The design problem is formulated and solved as an approximate finite-time linear quadratic stochastic regulator. Performance and control results are found by Monte Carlo simulations.

Mcmuldroch, C. G.↗

NASA NTRS1986

Circuit transients due to negative bias arcs-II

Two new models of negative-bias arcing on a solar cell power system in Low Earth Orbit are presented. One is an extended, analytical model and the other is a non-linear, numerical model. The models are based on an earlier analytical model in which the interactions between solar cell interconnects and the space plasma as well as the parameters of the power circuit are approximated linearly. Transient voltages due to arcs struck at the negative thermal of the solar panel are calculated in the time domain. The new models treat, respectively, further linear effects within the solar panel load circuit and non-linear effects associated with the plasma interactions. Results of computer calculations with the models show common-mode voltage transients of the electrically floating solar panel struck by an arc comparable to the early model but load transients that differ substantially from the early model. In particular, load transients of the non-linear model can be more than twice as great as those of the early model and more than twenty times as great as the extended, linear model.

Metz, R. N.↗

DOE OSTI2013

Weakly nonlinear incompressible Rayleigh-Taylor instability growth at cylindrically convergent interfaces

A weakly nonlinear (WN) model has been developed for the incompressible Rayleigh-Taylor instability (RTI) in cylindrical geometry. The transition from linear to nonlinear growth is analytically investigated via a third-order solutions for the cylindrical RTI initiated by a single-mode velocity perturbation. The third-order solutions can depict the early stage of the interface asymmetry due to the bubble-spike formation, as well as the saturation of the linear (exponential) growth of the fundamental mode. The WN results in planar RTI [Wang et al., Phys. Plasmas 19, 112706 (2012)] are recovered in the limit of high-mode number perturbations. The difference between the WN growth of the RTI in cylindrical geometry and in planar geometry is discussed. It is found that the interface of the inward (outward) development spike/bubble is extruded (stretched) by the additional inertial force in cylindrical geometry compared with that in planar geometry. For interfaces with small density ratios, the inward growth bubble can grow fast than the outward growth spike in cylindrical RTI. Moreover, a reduced formula is proposed to describe the WN growth of the RTI in cylindrical geometry with an acceptable precision, especially for small-amplitude perturbations. Using the reduced formula, the nonlinear saturation amplitude of the fundamental mode and the phases of the Fourier harmonics are studied. Thus, it should be included in applications where converging geometry effects play an important role, such as the supernova explosions and inertial confinement fusion implosions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2015

Convergence analysis of two-node CMFD method for two-group neutron diffusion eigenvalue problem

In this paper, the nonlinear coarse-mesh finite difference method with two-node local problem (CMFD2N) is proven to be unconditionally stable for neutron diffusion eigenvalue problems. The explicit current correction factor (CCF) is derived based on the two-node analytic nodal method (ANM2N), and a Fourier stability analysis is applied to the linearized algorithm. It is shown that the analytic convergence rate obtained by the Fourier analysis compares very well with the numerically measured convergence rate. It is also shown that the theoretical convergence rate is only governed by the converged second harmonic buckling and the mesh size. It is also noted that the convergence rate of the CCF of the CMFD2N algorithm is dependent on the mesh size, but not on the total problem size. This is contrary to expectation for eigenvalue problem. The novel points of this paper are the analytical derivation of the convergence rate of the CMFD2N algorithm for eigenvalue problem, and the convergence analysis based on the analytic derivations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1993

Testing approximations for non-linear gravitational clustering

The accuracy of various analytic approximations for following the evolution of cosmological density fluctuations into the nonlinear regime is investigated. The Zel'dovich approximation is found to be consistently the best approximation scheme. It is extremely accurate for power spectra characterized by n = -1 or less; when the approximation is 'enhanced' by truncating highly nonlinear Fourier modes the approximation is excellent even for n = +1. The performance of linear theory is less spectrum-dependent, but this approximation is less accurate than the Zel'dovich one for all cases because of the failure to treat dynamics. The lognormal approximation generally provides a very poor fit to the spatial pattern.

Coles, Peter↗

NASA NTRS1987

Analysis of implicit local linearization techniques for upwind and TVD algorithms

An attempt is made to investigate local time linearization techniques for implicit flux-difference splitting and flux-vector splitting schemes in the simplest settings (i.e., first-order spatial schemes and one-dimensional Euler flows). It is noted that first-order spatial schemes provide the simplest examples of schemes which are collective extensions of scalar TVD schemes. Simple analytical results concerning the local linearizations are highlighted and subsequently verified using a numerical fixed-point analysis on selected problems. It is noted that while primary emphasis is on asymptotic behavior, many of the results have implications for time-accurate calculations as well.

Barth, Timothy J.↗

DOE OSTI2015

A molecularly based theory for electron transfer reorganization energy

Using field-theoretic techniques, we develop a molecularly based dipolar self-consistent-field theory (DSCFT) for charge solvation in pure solvents under equilibrium and nonequilibrium conditions and apply it to the reorganization energy of electron transfer reactions. The DSCFT uses a set of molecular parameters, such as the solvent molecule’s permanent dipole moment and polarizability, thus avoiding approximations that are inherent in treating the solvent as a linear dielectric medium. A simple, analytical expression for the free energy is obtained in terms of the equilibrium and nonequilibrium electrostatic potential profiles and electric susceptibilities, which are obtained by solving a set of self-consistent equations. With no adjustable parameters, the DSCFT predicts activation energies and reorganization energies in good agreement with previous experiments and calculations for the electron transfer between metallic ions. Because the DSCFT is able to describe the properties of the solvent in the immediate vicinity of the charges, it is unnecessary to distinguish between the inner-sphere and outer-sphere solvent molecules in the calculation of the reorganization energy as in previous work. Furthermore, examining the nonequilibrium free energy surfaces of electron transfer, we find that the nonequilibrium free energy is well approximated by a double parabola for self-exchange reactions, but the curvature of the nonequilibrium free energy surface depends on the charges of the electron-transferring species, contrary to the prediction by the linear dielectric theory.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2012

Laser Phase Errors in Seeded Free Electron Lasers

Harmonic seeding of free electron lasers has attracted significant attention as a method for producing transform-limited pulses in the soft x-ray region. Harmonic multiplication schemes extend seeding to shorter wavelengths, but also amplify the spectral phase errors of the initial seed laser, and may degrade the pulse quality and impede production of transform-limited pulses. In this paper we consider the effect of seed laser phase errors in high gain harmonic generation and echo-enabled harmonic generation. We use simulations to confirm analytical results for the case of linearly chirped seed lasers, and extend the results for arbitrary seed laser envelope and phase.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1990

Semigroup theory and numerical approximation for equations in linear viscoelasticity

A class of abstract integrodifferential equations used to model linear viscoelastic beams is investigated analytically, applying a Hilbert-space approach. The basic equation is rewritten as a Cauchy problem, and its well-posedness is demonstrated. Finite-dimensional subspaces of the state space and an estimate of the state operator are obtained; approximation schemes for the equations are constructed; and the convergence is proved using the Trotter-Kato theorem of linear semigroup theory. The actual convergence behavior of different approximations is demonstrated in numerical computations, and the results are presented in tables.

Fabiano, R. H.↗

DOE OSTI2015

Relativistic MHD simulations of collision-induced magnetic dissipation in Poynting-flux-dominated jets/outflows

The question of the energy composition of the jets/outflows in high-energy astrophysical systems, e.g. GRBs, AGNs, is taken up first: Matter-flux-dominated (MFD), σ < 1, and/or Poynting-flux-dominated (PFD), σ >1? The standard fireball IS model and dissipative photosphere model are MFD, while the ICMART (Internal-Collision-induced MAgnetic Reconnection and Turbulence) model is PFD. Motivated by ICMART model and other relevant problems, such as “jets in a jet” model of AGNs, the author investigates the models from the EMF energy dissipation efficiency, relativistic outflow generation, and σ evolution points of view, and simulates collisions between high-σ blobs to mimic the situation of the interactions inside the PFD jets/outflows by using a 3D SRMHD code which solves the conservative form of the ideal MHD equations. σ b,f is calculated from the simulation results (threshold = 1). The efficiency obtained from this hybrid method is similar to the efficiency got from the energy evolution of the simulations (35.2%). Efficiency is nearly σ independent, which is also confirmed by the hybrid method. σ b,i - σ b,f provides an interesting linear relationship. Results of several parameter studies of EMF energy dissipation efficiency are shown.

79 ASTRONOMY AND ASTROPHYSICS↗