Search NASA⌕ Search

SEARCH · Search NASA

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.

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

At least 1,117 records · Page 62
All sourcesNASA NTRSDOE OSTI
NASA NTRS1999

Electrorheological Fluid Based Force Feedback Device

Parallel to the efforts to develop fully autonomous robots, it is increasingly being realized that there are applications where it is essential to have a fully controlled robot and "feel" its operating conditions, i.e. telepresence. This trend is a result of the increasing efforts to address tasks where humans can perform significantly better but, due to associated hazards, distance, physical limitations and other causes, only robots can be employed to perform these tasks. Such robots need to be assisted by a human that remotely controls the operation. To address the goal of operating robots as human surrogates, the authors launched a study of mechanisms that provide mechanical feedback. For this purpose, electrorheological fluids (ERF) are being investigated for the potential application as miniature haptic devices. This family of electroactive fluids has the property of changing the viscosity during electrical stimulation. Consequently, ERF can be used to produce force feedback haptic devices for tele-operated control of medical and space robotic systems. Forces applied at the robot end-effector due to a compliant environment are reflected to the user using an ERF device where a change in the system viscosity will occur proportionally to the transmitted force. Analytical model and control algorithms are being developed taking into account the non-linearities of these type of devices. This paper will describe the concept and the developed mechanism of ERF based force feedback. The test process and the physical properties of this device will be described and the results of preliminary tests will be presented.

Pfeiffer, Charles↗
NASA NTRS2007

NASA CEV On-Orbit GN&C Analysis

The Orion spacecraft orbit GN&C system will be required to perform both ISS servicing missions and Lunar sortie and outpost crew transportation. While certain aspects of these two missions are complementary, the two missions are also distinct in many ways. Common between the missions is a Low Earth Orbit (LEO) rendezvous, one with the ISS And the other with the LSAM/EDS stack prior to trans-lunar insertion. The lunar missions will additionally require Orion to perform orbit maintenance in LLO, perform contingency lunar orbit operations including RPOD with the LSAM, perform the TEI maneuver sequence, and execute the trans-Earth cruise. The NASA-led team developed a reference configuration orbit GN&C system capable of executing all of these activities with the same navigation sensor suite and control effectors while fully meeting the requirements being developed for System Requirements Review in advance of prime contractor selection. This paper will present an overview of the analyses performed to support system trade studies, demonstrate the feasibility of the NASA reference configuration, and validate the Orion system requirements. These analyses include linear covariance techniques, 3-DOF Monte Carlo simulations, 6-DOF Monte Carlo simulations, and analytical evaluations of GN&C systems performed by the NASA-led Orion team to characterize the sensitivities of Orion s various missions and assess the unique challenges of each. The first part of this paper will describe the trade studies that were performed in order to characterize the RPOD system performance for both the ISS and the lunar missions including development of an RPOD operations concept, RPOD trajectories, contingency scenarios, docking mechanism and associated contact conditions, post-contact thrust issues, relative navigation sensors, relative navigation sensor target infrastructure. The paper will also discuss concepts for both manually-piloted and automatically executed scenarios, as well as the remotely-piloted contingency scenario in LLO. The second part of the paper will discuss the analyses performed for lunar and cislunar GN&C performance including the accuracy of the post-insertion lunar orbit, the ability of Orion to hit a particular Earth return entry corridor, attitude control solutions for long-duration surface operations, and autonomous navigation in support of TEI without ground tracking.

DSouza, Chris↗
DOE OSTI2010

STM Studies of Near-Optimal Doped Bi_2Sr_2CaCu_2O_8 delta

In this paper we summarize our STM studies of the density of electronic states in nearly optimally doped Bi{sub 2}Sr{sub 2}CaCu{sub 2}O{sub 8 + {delta}} in zero field. We report on the inhomogeneity of the gap structure, density of states modulations with four-lattice constant period, and coherence peak modulation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1977

Unsteady flow in a supersonic cascade with strong in-passage shocks

Linearized theory is used to study the unsteady flow in a supersonic cascade with in-passage shock waves. We use the Wiener-Hopf technique to obtain a closed-form analytical solution for the supersonic region. To obtain a solution for the rotational flow in the subsonic region we must solve an infinite set of linear algebraic equations. The analysis shows that it is possible to correlate quantitatively the oscillatory shock motion with the Kutta condition at the trailing edges of the blades. This feature allows us to account for the effect of shock motion on the stability of the cascade. Unlike the theory for a completely supersonic flow, the present study predicts the occurrence of supersonic bending flutter. It therefore provides a possible explanation for the bending flutter that has recently been detected in aircraft-engine compressors at higher blade loadings.

Goldstein, M. E.↗
NASA NTRS1984

On the Kelvin-Helmholtz instabilities of supersonic shear layers

Analytical consideration is given to a Kelvin-Helmholtz instability in a finite width supersonic shear layer with linear and sinusoidal velocity profiles in the transition region. An analogy is explored between the pressure perturbation and the bound and scattering wave states of the one-dimensional Schroedinger equation. A numerical model is obtained for generating contour maps of the real and imaginary parts of the perturbation frequency in the (A,B)-plane. A comparison is made between the numerical results and analytical expressions derived for very small Mach numbers. Two unstable regimes are characterized in the (A,B)-plane. The method is concluded useful for both laboratory and astrophysics problems.

Choudhury, S. R.↗
DOE OSTI2021

Outcomes and Insights From Simplified Analytic Trajectory Optimization for a Tethered Underwater Kite

This letter formulates and solves a periodic trajectory optimization problem for a tethered underwater kite. The goal is to maximize the average mechanical power harvested by the kite. The type of kite considered in this letter extracts electricity from ocean currents by moving cross-current as its reel away from its base station, and consumes electricity to reel back. The problem of optimizing this kite’s trajectory is challenging due to the high dimensionality and nonlinearity of its dynamics. To tackle this challenge, the literature often separates the problem into two subproblems focusing on optimizing the cross-current and the reel-in/reel-out components of the trajectory, respectively, which may be sub-optimal. In contrast, this letter solves for the combined cross-current and reel-in/reel-out trajectory by linearizing the dynamics of the kite around a zero-power reference equilibrium trajectory in spherical coordinates. This allows the trajectory optimization problem to be solved analytically for simple sinusoidal input perturbations from equilibrium. Here we use linear quadratic regulation to enable the nonlinear kite model to track the optimized trajectory. The result is a computationally efficient approach that achieves an attractive Loyd factor of 19.9%, while providing important insights into the nature of the optimal trajectory.

42 ENGINEERING↗
DOE OSTI2018

Isotopic fractionation studies of uranium and plutonium using porous ion emitters as thermal ionization mass spectrometry sources

Investigations of the isotope fractionation behaviors of plutonium and uranium reference standards were conducted employing platinum and rhenium (Pt/Re) porous ion emitter (PIE) sources, a relatively new thermal ionization mass spectrometry (TIMS) ion source strategy. The suitability of commonly employed, empirically developed mass bias correction laws (i.e., the Linear, Power, and Russell's laws) for correcting such isotope ratio data was also determined. Corrected plutonium isotope ratio data, regardless of mass bias correction strategy, were statistically identical to that of the certificate, however, the process of isotope fractionation behavior of plutonium using the adopted experimental conditions was determined to be best described by the Power law. Finally, the fractionation behavior of uranium, using the analytical conditions described herein, is also most suitably modeled using the Power law, though Russell's and the Linear law for mass bias correction rendered results that were identical, within uncertainty, to the certificate value.

07 ISOTOPE AND RADIATION SOURCES↗
NASA NTRS1989

The Jeffcott equations in nonlinear rotordynamics

The solutions of the Jeffcott equations describing the behavior of a rotating shaft are investigated analytically, with a focus on the case where deadband is taken into account. Bounds on the solutions are obtained from those for the linearized equations, and the onset of destructive vibrations is predicted by analyzing the Fourier transforms of the solutions; good agreement with numerical solutions and power-spectrum density plots is demonstrated. It is suggested that the present analytical approach could be applied to determine cryogenic-pump stability margins in flight and hot-fire ground testing of launch vehicles such as the Space Shuttle.

Zalik, R. A.↗
DOE OSTI2020

Verification of local electrostatic gyrokinetic simulation of driftwave instability in field-reversed configuration

Local linear simulations of ion temperature gradient (ITG) instabilities using a gyrokinetic particle code GKD1D have been verified by comparing with the analytic dispersion relation in the slab geometry and by benchmarking with a global gyrokinetic code GTC-X in a realistic field-reversed configuration (FRC). Results of ITG simulations using either adiabatic or kinetic electrons exhibit excellent agreements between the two codes for linear frequencies, growth rates, and mode structures. The ITG modes in the FRC scrape-off layer region are mostly dominated by the poloidal m = 1 harmonic. Kinetic electrons enhance the subdominant m = 2 harmonic and the even parity dominates the ITG mode structure. Kinetic electrons increase the growth rates for the low-n modes, but decrease the growth rates for the high-n modes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Non-Abelian Bremsstrahlung and Azimuthal Asymmetries in High Energy p+A Reactions

Here we apply the GLV reaction operator solution to the Vitev-Gunion-Bertsch (VGB) boundary conditions to compute the all-order in nuclear opacity non-abelian gluon bremsstrahlung of event- by-event uctuating beam jets in nuclear collisions. We evaluate analytically azimuthal Fourier moments of single gluon, v$M\atop{n}$ {1}, and even number 2ℓ gluon, v$M\atop{n}$ {2ℓ} inclusive distributions in high energy p+A reactions as a function of harmonic $n$, target recoil cluster number, $M$, and gluon number, 2ℓ, at RHIC and LHC. Multiple resolved clusters of recoiling target beam jets together with the projectile beam jet form Color Scintillation Antenna (CSA) arrays that lead to character- istic boost non-invariant trapezoidal rapidity distributions in asymmetric B+A nuclear collisions. The scaling of intrinsically azimuthally anisotropic and long range in η nature of the non-Abelian bremsstrahlung leads to v n moments that are similar to results from hydrodynamic models, but due entirely to non-Abelian wave interference phenomena sourced by the fluctuating CSA. Our analytic non-flow solutions are similar to recent numerical saturation model predictions but differ by predicting a simple power-law hierarchy of both even and odd v n without invoking k T factorization. A test of CSA mechanism is the predicted nearly linear η rapidity dependence of the v n (k T η). Non- Abelian beam jet bremsstrahlung may thus provide a simple analytic solution to Beam Energy Scan (BES) puzzle of the near $\sqrt{s}$ independence of v n (pT) moments observed down to 10 AGeV where large-x valence quark beam jets dominate inelastic dynamics. Recoil bremsstrahlung from multiple independent CSA clusters could also provide a partial explanation for the unexpected similarity of v n in p(D) + A and non-central A + A at same dN=dη multiplicity as observed at RHIC and LHC.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2012

Thinking outside the box: effects of modes larger than the survey on matter power spectrum covariance

Accurate power spectrum (or correlation function) covariance matrices are a crucial requirement for cosmological parameter estimation from large scale structure surveys. In order to minimize reliance on computationally expensive mock catalogs, it is important to have a solid analytic understanding of the different components that make up a covariance matrix. Considering the matter power spectrum covariance matrix, it has recently been found that there is a potentially dominant effect on mildly non-linear scales due to power in modes of size equal to and larger than the survey volume. This beat coupling effect has been derived analytically in perturbation theory and while it has been tested with simulations, some questions remain unanswered. Moreover, there is an additional effect of these large modes, which has so far not been included in analytic studies, namely the effect on the estimated average density which enters the power spectrum estimate. In this article, we work out analytic, perturbation theory based expressions including both the beat coupling and this local average effect and we show that while, when isolated, beat coupling indeed causes large excess covariance in agreement with the literature, in a realistic scenario this is compensated almost entirely by the local average effect, leaving only ∼ 10% of the excess. We test our analytic expressions by comparison to a suite of large N-body simulations, using both full simulation boxes and subboxes thereof to study cases without beat coupling, with beat coupling and with both beat coupling and the local average effect. For the variances, we find excellent agreement with the analytic expressions for k < 0.2 hMpc{sup −1} at z = 0.5, while the correlation coefficients agree to beyond k = 0.4 hMpc{sup −1}. As expected, the range of agreement increases towards higher redshift and decreases slightly towards z = 0. We finish by including the large-mode effects in a full covariance matrix description for arbitrary survey geometry and confirming its validity using simulations. This may be useful as a stepping stone towards building an actual galaxy (or other tracer's) power spectrum covariance matrix.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1971

Space Trajectories Error Analysis (STEAP) Programs. Volume 1: Analytic manual, update

Manual revisions are presented for the modified and expanded STEAP series. The STEAP 2 is composed of three independent but related programs: NOMAL for the generation of n-body nominal trajectories performing a number of deterministic guidance events; ERRAN for the linear error analysis and generalized covariance analysis along specific targeted trajectories; and SIMUL for testing the mathematical models used in the navigation and guidance process. The analytic manual provides general problem description, formulation, and solution and the detailed analysis of subroutines. The programmers' manual gives descriptions of the overall structure of the programs as well as the computational flow and analysis of the individual subroutines. The user's manual provides information on the input and output quantities of the programs. These are updates to N69-36472 and N69-36473.

Source record↗
DOE OSTI2022

Representation Learning via Quantum Neural Tangent Kernels

Variational quantum circuits are used in quantum machine learning and variational quantum simulation tasks. Designing good variational circuits or predicting how well they perform for given learning or optimization tasks is still unclear. Here we discuss these problems, analyzing variational quantum circuits using the theory of neural tangent kernels. We define quantum neural tangent kernels, and derive dynamical equations for their associated loss function in optimization and learning tasks. We analytically solve the dynamics in the frozen limit, or lazy training regime, where variational angles change slowly and a linear perturbation is good enough. We extend the analysis to a dynamical setting, including quadratic corrections in the variational angles. We then consider a hybrid quantum classical architecture and define a large-width limit for hybrid kernels, showing that a hybrid quantum classical neural network can be approximately Gaussian. The results presented here show limits for which analytical understandings of the training dynamics for variational quantum circuits, used for quantum machine learning and optimization problems, are possible. These analytical results are supported by numerical simulations of quantum machine-learning experiments.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2010

Molecular isotopic effects on coupled electronic and nuclear fluxes

A full quantum treatment shows that coupled electronic and nuclear fluxes exhibit a strong sensitivity to a small mass change in a vibrating molecule. This has been exemplified with the existing isotopes of H{sub 2}{sup +} as well as few fictitious ones. We find that the fluxes undergo a significant change as one goes from one isotope of reduced mass {mu} to another. Other well-defined observables are likewise affected. It turns out that as a general rule, the heavier the isotope, the larger the flux, the smaller the dispersion, and the longer the revival period. While we were able to confirm analytically that the time at the first turning point scales as {radical}({mu}) and that the revival period changes linearly with {mu}, the mechanism of other observables remains subtle as the result of quantum interference highlighted by the pronounced difference observed on the dispersion pattern.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1995

Estimating the Cramer-Rao bound for restored astronomical observations

This work addresses the problem of assigning confidence intervals to estimated photometry data obtained from astronomical observations. The proposed solution is to estimate the Cramer-Rao bound, which is an analytical expression that describes the minimum obtainable mean square error associated with a given estimate of a parameter. This Letter presents a compact and simple form for the bound associated with a linear estimator such as a Wiener filter estimator. A prescription for estimating the variance associated with each element in a restored object was developed using an analytical model for observed data corrupted by either Poisson or Gaussian noise. Both one- and two-dimensional examples are presented.

Zaccheo, T. S.↗
NASA NTRS1985

Turbine Vane External Heat Transfer. Volume 1: Analytical and Experimental Evaluation of Surface Heat Transfer Distributions with Leading Edge Showerhead Film Cooling

Progress in predictive design capabilities for external heat transfer to turbine vanes was summarized. A two dimensional linear cascade (previously used to obtain vane surface heat transfer distributions on nonfilm cooled airfoils) was used to examine the effect of leading edge shower head film cooling on downstream heat transfer. The data were used to develop and evaluate analytical models. Modifications to the two dimensional boundary layer model are described. The results were used to formulate and test an effective viscosity model capable of predicting heat transfer phenomena downstream of the leading edge film cooling array on both the suction and pressure surfaces, with and without mass injection.

Turner, E. R.↗
NASA NTRS1990

Simultaneous expansion and orthogonalization of measured modes for structure identification

Tests of large structures on-orbit will be performed with measurements at a relatively few structure points. Values for the unmeasured degrees of freedom (dofs) can be estimated based on measured dofs and analytical model dynamic information. These 'expanded' mode shapes are useful for optimal-update identification and damage location as well as test/analysis correlation. A new method of expansion for test mode shape vectors is developed from the orthogonal Procrustes problem from computational linear algebra. A subspace defined by the set of measured dofs is compared to a subspace defined by mode shapes from an analytical model of the structure. The method simultaneously expands and orthogonalizes the mode shape vectors. Two demonstration problems are used to compare the new method to current expansion techniques. One demonstration uses test data from a laboratory scale-model truss structure. Performance of the new method is comparable or superior to that of the previous expansion methods which require separate orthogonalization.

Smith, Suzanne Weaver↗
DOE OSTI2021

Six-dimensional matching of intense beam with linear accelerating structure

Beam matching is a common technique that is routinely employed in accelerator design with the aim of minimizing beam losses and preservation of beam brightness. Despite being widely used, a full theoretical understanding of beam matching in 6D remains elusive. In this work, we present an analytical treatment of 6D beam matching of a high-intensity beam onto an RF structure. We begin our analysis within the framework of a linear model, and apply the averaging method to a set of 3D beam envelope equations. Accordingly, we obtain a matched solution that is comprised of smoothed envelopes and periodic terms, describing envelope oscillations with the period of the focusing structure. We then consider the nonlinear regime, where the beam size is comparable with the separatrix size. Stating with a Hamiltonian analysis in 6D phase space, we attain a self-consistent beam profile and show that it is significantly different from the commonly used ellipsoidal shape. Subsequently, we analyze the special case of an equilibrium with equal space charge depression between all degrees of freedom. Comparison of beam dynamics for equipartitioned, equal space charge depression, and equal emittances beams is given. Finally, we present experimental results on beam matching in the LANSCE linac.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗