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Results for “Analytic linearization”

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.

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At least 1,387 records · Page 77
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

On Concavity and Utilization Analytics of Wide-Area Network Transport Protocols

Wide-area data transfers in high-performance computing infrastructures and big data applications are increasingly carried over dynamically provisioned dedicated network connections, which provide high capacities with no competing traffic. Throughput of TCP and UDT over wide-area connections depends, often in a complex non-linear way, on the congestion control mechanism, buffer sizes, and the number of parallel streams. In addition, our extensive TCP and UDT throughput measurements and time traces over a suite of physical and emulated 10 Gbps connections with 0-366 ms round-trip times (RTTs) show significant statistical and temporal variations. Consequently, parameter selection and optimization for transport methods require data analytics to complement analytical throughput models. We present analytics based on the concavity-convexity of throughput profiles which provide insights into peak throughput and superior/inferior trend compared to linear interpolations based on RTT. In particular, we propose the utilization-concavity coefficient, a scalar metric that incorporates both utilization and concavity profile to characterize the overall performance of a transport protocol. These measurements-based anaytics enable us to select a transport protocol and its parameters for a given host and connection configuration to achieve high throughput with statistical guarantees.

Rao, Nageswara↗
DOE OSTI2010

Evolution of dark energy perturbations in scalar-tensor cosmologies

We solve analytically and numerically the generalized Einstein equations in scalar-tensor cosmologies to obtain the evolution of dark energy and matter linear perturbations. We compare our results with the corresponding results for minimally coupled quintessence perturbations. We find that scalar-tensor dark energy density perturbations are amplified by a factor of about 10{sup 4} compared to minimally coupled quintessence perturbations on scales less than about 1000 h{sup -1} Mpc (sub-Hubble scales). On these scales dark energy perturbations constitute a fraction of about 10% compared to matter density perturbations. Scalar-tensor dark energy density perturbations are anticorrelated with matter linear perturbations on sub-Hubble scales. This anticorrelation of matter with negative pressure perturbations induces a mild amplification of matter perturbations by about 10% on sub-Hubble scales. The evolution of scalar field perturbations on sub-Hubble scales is scale independent and therefore corresponds to a vanishing effective speed of sound (c{sub s{Phi}=}0). We briefly discuss the observational implications of our results, which may include predictions for galaxy and cluster halo profiles that are modified compared to {Lambda}CDM. The observed properties of these profiles are known to be in some tension with the predictions of {Lambda}CDM.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2010

Adiabatic description of capture into resonance and surfatron acceleration of charged particles by electromagnetic waves

We present an analytical and numerical study of the surfatron acceleration of nonrelativistic charged particles by electromagnetic waves. The acceleration is caused by capture of particles into resonance with one of the waves. We investigate capture for systems with one or two waves and provide conditions under which the obtained results can be applied to systems with more than two waves. In the case of a single wave, the once captured particles never leave the resonance and their velocity grows linearly with time. However, if there are two waves in the system, the upper bound of the energy gain may exist and we find the analytical value of that bound. We discuss several generalizations including the relativistic limit, different wave amplitudes, and a wide range of the waves' wavenumbers. The obtained results are used for qualitative description of some phenomena observed in the Earth's magnetosphere.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2013

Alfvén wave collisions, the fundamental building block of plasma turbulence. I. Asymptotic solution

The nonlinear interaction between counterpropagating Alfvén waves is the physical mechanism underlying the cascade of energy to small scales in astrophysical plasma turbulence. Beginning with the equations for incompressible MHD, an asymptotic analytical solution for the nonlinear evolution of these Alfvén wave collisions is derived in the weakly nonlinear limit. The resulting qualitative picture of nonlinear energy transfer due to this mechanism involves two steps: first, the primary counterpropagating Alfvén waves interact to generate an inherently nonlinear, purely magnetic secondary fluctuation with no parallel variation; second, the two primary waves each interact with this secondary fluctuation to transfer energy secularly to two tertiary Alfvén waves. These tertiary modes are linear Alfvén waves with the same parallel wavenumber as the primary waves, indicating the lack of a parallel cascade. The amplitude of these tertiary modes increases linearly with time due to the coherent nature of the resonant four-wave interaction responsible for the nonlinear energy transfer. The implications of this analytical solution for turbulence in astrophysical plasmas are discussed. The solution presented here provides valuable intuition about the nonlinear interactions underlying magnetized plasma turbulence, in support of an experimental program to verify in the laboratory the nature of this fundamental building block of astrophysical plasma turbulence.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Uncertainty propagation in feed-forward neural network models

We develop new uncertainty propagation methods for feed-forward neural network architectures with leaky ReLU activation functions subject to random perturbations in the input vectors. In particular, we derive analytical expressions for the probability density function (PDF) of the neural network output and its statistical moments as a function of the input uncertainty and the parameters of the network, i.e., weights and biases. A key finding is that an appropriate linearization of the leaky ReLU activation function yields accurate statistical results even for large perturbations in the input vectors. This can be attributed to the way information propagates through the network. We also propose new analytically tractable Gaussian copula surrogate models to approximate the full joint PDF of the neural network output. To validate our theoretical results, we conduct Monte Carlo simulations and a thorough error analysis on a multi-layer neural network representing a nonlinear integro-differential operator between two polynomial function spaces. Our findings demonstrate excellent agreement between the theoretical predictions and Monte Carlo simulations.

MLP networks↗
NASA NTRS1992

Loss-cone-driven ion cyclotron waves in the magnetosphere

The study examines the theoretical properties of linear ion cyclotron waves propagating in the magnetosphere at arbitrary angles to the background magnetic field. It is found that in some cases the linear wave growth of modes with oblique propagation can dominate that of the parallel propagating electromagnetic ion cyclotron (EMIC) wave. The growth rate of the loss-cone-driven mode depends strongly on the depth of the loss cone. A simple analytical theory which explains the scaling of the growth rate of the oblique mode with respect to various parameters is presented. The loss-cone-driven mode is an electromagnetic mode which is preferentially nearly linearly polarized. The wave field which results from the oblique mode in its perferentially nearly linearly polarized form are nearly perpendicular to B0 and are such that they may be difficult to distinguish from those of a linearly polarized parallel propgating EMIC wave.

Denton, Richard E.↗
NASA NTRS1976

The dynamics of spin stabilized spacecraft with movable appendages, part 2

The dynamics and stability of a spin stabilized spacecraft with a hinged appendage system are treated analytically and numerically. The hinged system consists of a central hub with masses attached to (assumed) massless booms of fixed length whose orientation relative to the main part can change. The general three dimensional deployment dynamics of such a hinged system is considered without any restriction on the location of the hinge points. The equations of motion for the hinged system, with viscous damping at both hinge points, are linearized about the nominal equilibrium position where the booms are orthogonal to the nominal spin axis for the case of two dimensional and three dimensional motion. Analytic stability criteria are obtained from the necessary condition on the sign of all the coefficients in the system characteristic equation.

Bainum, P. M.↗
NASA NTRS1988

Bounds on the Fourier coefficients for the periodic solutions of non-linear oscillator equations

The differential equations describing nonlinear oscillations (as seen in mechanical vibrations, electronic oscillators, chemical and biochemical reactions, acoustic systems, stellar pulsations, etc.) are investigated analytically. The boundedness of the Fourier coefficients for periodic solutions is demonstrated for two special cases, and the extrapolation of the results to higher-dimensionsal systems is briefly considered.

Mickens, R. E.↗
DOE OSTI2018

Modeling the shape of boundary using NURBS curves directly in modified boundary integral equations for Laplace’s equation

The main purpose of this study is the modification of the parametric integral equations systems (PIES) method, to include the NURBS curves into its mathematical formulas. We want to create an opportunity for defining the boundary shape using NURBS curves without the classical discretization process. We present an inclusion of the NURBS curves into PIES, and its application in process of modeling and solving the boundary value problems, on Laplace’s equation example. The correctness and accuracy of such modeling is confirmed by the examples. Obtained solutions are compared with these obtained using linear segments and B-spline curves. Additionally, we verify the correctness of modeling and modifying the shape using analytical solutions. The NURBS curves significantly expand the possibilities and increase the accuracy of the boundary shape modeling which is an important aspect of the numerical solving of boundary value problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

A compact mechanical power take-off for wave energy converters: Design, analysis, and test verification

Power Take-off (PTO) is one of the most critical components in the ocean wave conversion. This paper introduces an innovative compact mechanical PTO using a ball screw mechanism and a Mechanical Motion Rectifier (MMR) to improve the energy conversion performance. The proposed MMR PTO converts bidirectional oscillatory motion of the ocean waves into unidirectional rotation. The detailed design and working principle of the MMR PTO are explicitly explained. Dynamic analysis is presented for the three most important factors that influence the performance, including the equivalent mass, the equivalent damping, and the excitation frequency. The analytical relationship between these factors and the disengaged freewheeling motion caused by the MMR mechanism is derived, and the analytical solution is verified through dry lab testing. Experimental results in bench tests show that compared with the traditional linear PTO which use the ball screw to drive the generator directly, the MMR PTO is more efficient because of the unique freewheeling motion, achieving a maximum 81.2% energy transfer efficiency. After integrating the prototype PTO with a single-body point absorber type of wave energy converter, testing in a water tank yields total PTO efficiency up to 62.4%, showing a very promising potential for real applications.

16 TIDAL AND WAVE POWER↗
DOE OSTI2021

Lyapunov stability of smart inverters using linearized distflow approximation

Fast-acting smart inverters that utilize preset operating conditions to determine real and reactive power injection/consumption can create voltage instabilities (over-voltage, voltage oscillations and more) in an electrical distribution network if set-points are not properly configured. In this work, linear distribution power flow equations and droop-based Volt–Var and Volt–Watt control curves are used to analytically derive a stability criterion using Lyapunov analysis that includes the network operating condition. The methodology is generally applicable for control curves that can be represented as Lipschitz functions. The derived Lipschitz constants account for smart inverter hardware limitations for reactive power generation. A local policy is derived from the stability criterion that allows inverters to adapt their control curves by monitoring only local voltage, thus avoiding centralized control or information sharing with other inverters. The criterion is independent of the internal time-delays of smart inverters. Simulation results for inverters with and without the proposed stabilization technique demonstrate how smart inverters can mitigate voltage oscillations locally and mitigate real and reactive power flow disturbances at the substation under multiple scenarios. The study concludes with illustrations of how the control policy can dampen oscillations caused by solar intermittency and cyberattacks.

42 ENGINEERING↗
DOE OSTI2011

Scalings of strongly coupled collisionless q = 2 triple tearing modes in a tokamak plasma

Within the framework of a reduced collisionless magnetohydrodynamics (MHD) model containing the effects of electron inertia and electron pressure gradient, scaling laws of the strongly coupled collisionless q=2 triple tearing instabilities with broad linear spectra in a tokamak plasma are studied numerically. It is found that as the poloidal mode number m increases, the scaling power laws of the linear growth rate of triple tearing modes (TTMs) on S{sub Hp}, d{sub e}, and {rho}{sub s} change gradually from the strongly coupled tearing mode scalings to the standard single tearing mode (STM) scalings, where S{sub Hp} is the magnetic Reynolds number, d{sub e} is the electron inertial skin depth, and {rho}{sub s} is the ion sound gyroradius. For example, d{sub e}-scaling of the linear growth rate {gamma}{approx}d{sub e}{sup {alpha}}{sub d} changes gradually from {gamma}{approx}d{sub e}{sup 1} to {gamma}{approx}d{sub e}{sup 3} as the m number increases in the case of {rho}{sub s}<<d{sub e}, while {rho}{sub s}-scaling {gamma}{approx}d{sub e}{sup {alpha}}{sub {rho}} shifts gradually from {gamma}{approx}{rho}{sub s}{sup 2/3} to {gamma}{approx}{rho}{sub s}{sup 1} as m increases in the case of d{sub e}<<{rho}{sub s}. Furthermore, it is observed that the increase of {rho}{sub s} gradually weakens the dependence on d{sub e} in both large and small {Delta}' regimes, such as, {approx}d{sub e}{sup 1{yields}{approx}}d{sub e}{sup 1/3} in the large {Delta}' regime, where {Delta}' is the linear instability parameter of tearing modes. The numerical results about the scaling laws are validated by the previous relevant analytical theories in terms of the similarity of physical characteristics in the same {Delta}' regime. In addition, the effects of d{sub e} and {rho}{sub s} on the spectrum structures of the unstable TTMs are discussed. Finally, the spatial characteristics of the eigenmode structures for different mode numbers are analyzed in detail. It is interestingly found that the structure of the most unstable eigenmode of the TTMs is quite similar to the eigenmode structure of a standard double tearing mode (DTM).

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2013

Eulerian simulations of collisional effects on electrostatic plasma waves

The problem of collisions in a plasma is a wide subject with a huge historical literature. In fact, the description of realistic plasmas is a tough problem to attack, both from the theoretical and the numerical point of view. In this paper, a Eulerian time-splitting algorithm for the study of the propagation of electrostatic waves in collisional plasmas is presented. Collisions are modeled through one-dimensional operators of the Fokker-Planck type, both in linear and nonlinear forms. The accuracy of the numerical code is discussed by comparing the numerical results to the analytical predictions obtained in some limit cases when trying to evaluate the effects of collisions in the phenomenon of wave plasma echo and collisional dissipation of Bernstein-Greene-Kruskal waves. Particular attention is devoted to the study of the nonlinear Dougherty collisional operator, recently used to describe the collisional dissipation of electron plasma waves in a pure electron plasma column [M. W. Anderson and T. M. O'Neil, Phys. Plasmas 14, 112110 (2007)]. Finally, for the study of collisional plasmas, a recipe to set the simulation parameters in order to prevent the filamentation problem can be provided, by exploiting the property of velocity diffusion operators to smooth out small velocity scales.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Modulation of effective damping constant using spin Hall effect

We have investigated modulation of the effective damping constant α{sub eff} via spin currents through the spin Hall effect for Permalloy/Pt bilayer films with various thicknesses. The observed linear and sinusoidal dependences of current density and field direction on α{sub eff} are in agreement with the analytical model. By comparing the thickness dependence of spin Hall angle obtained from the damping modulation with that previously obtained by spin-torque-induced ferromagnetic resonance, we show that there is no clear extrinsic contribution in the present method. We also show the large modulation of the effective damping constant (down to ∼20%) in the high-current-density region.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2015

Quantum efficiency harmonic analysis of exciton annihilation in organic light emitting diodes

Various exciton annihilation processes are known to impact the efficiency roll-off of organic light emitting diodes (OLEDs); however, isolating and quantifying their contribution in the presence of other factors such as changing charge balance continue to be a challenge for routine device characterization. Here, we analyze OLED electroluminescence resulting from a sinusoidal dither superimposed on the device bias and show that nonlinearity between recombination current and light output arising from annihilation mixes the quantum efficiency measured at different dither harmonics in a manner that depends uniquely on the type and magnitude of the annihilation process. We derive a series of analytical relations involving the DC and first harmonic external quantum efficiency that enable annihilation rates to be quantified through linear regression independent of changing charge balance and evaluate them for prototypical fluorescent and phosphorescent OLEDs based on the emitters 4-(dicyanomethylene)-2-methyl-6-(4-dimethylaminostyryl)-4H-pyran and platinum octaethylporphyrin, respectively. We go on to show that, in most cases, it is sufficient to calculate the needed quantum efficiency harmonics directly from derivatives of the DC light versus current curve, thus enabling this analysis to be conducted solely from standard light-current-voltage measurement data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Parameterized anomalous transport model for current-carrying collisionless plasmas in pulsed power inertial confinement fusion

Current delivery in pulsed power inertial confinement fusion is influenced by collisionless current-carrying microturbulent plasmas, which are sourced from electrode surfaces. In this setting, the lower hybrid drift instability—triggered by plasma acceleration—is a leading candidate driver of difficult-to-predict momentum and energy transport. To characterize the nonlinear state of the microturbulent plasma, a parameterized anomalous transport model is developed for the instability, with analytic formulas for anomalous collision frequency, resistivity, and species heating rates. The formulas are expressed in terms of linear-theory variables and four dimensionless parameters that characterize the macroscopic plasma state. The model is built on linear theory analysis, power law analysis, and quasilinear theory analysis, and is validated using a series of nonlinear continuum kinetic Vlasov–Poisson simulations. The theoretical and computational investigation demonstrates that the anomalous collision frequency associated with the instability can be reliably approximated, within about a factor of five or better, by the unscaled linear theory growth rate of the fastest-growing wavenumber mode. This finding enables efficient calculation of anomalous resistivity and species heating rates over a wide range of plasma conditions, resulting in improved predictive capabilities.

Complex functions↗
DOE OSTI2010

COSMOLOGICAL DENSITY FLUCTUATIONS ON 100 Mpc SCALES AND THEIR ISW EFFECT

We measure the matter probability distribution function (PDF) via counts in cells in a volume-limited subsample of the Sloan Digital Sky Survey Luminous Red Galaxy Catalog on scales from 30 h {sup -1} Mpc to 150 h {sup -1} Mpc and estimate the linear Integrated Sachs-Wolfe effect produced by supervoids and superclusters in the tail of the PDF. We characterize the PDF by the variance, S{sub 3}, and S{sub 4}, and study in simulations the systematic effects due to finite volume, survey shape, and redshift distortion. We compare our measurement to the prediction of {Lambda}CDM with linear bias and find a good agreement. We use the moments to approximate the tail of the PDF with analytic functions. A simple Gaussian model for the superstructures appears to be consistent with the claim by Granett et al. that density fluctuations on 100 h {sup -1} Mpc scales produce hot and cold spots with {Delta}T {approx} 10 {mu}K on the cosmic microwave background.

79 ASTRONOMY AND ASTROPHYSICS↗