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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 1,477 records · Page 82
All sourcesNASA NTRSDOE OSTI
NASA NTRS1990

The impedance of a tubular electrode - A model for a porous electrode

A cylindrical tube is used as the basis for a two-dimensional mathematical model to calculate the impedance of a flooded porous electrode. The model incorporates charge-transfer, mass-transfer, and ohmic resistances to obtain the axial and radial dependencies of the concentration and potential profiles. A linearized Butler-Volmer kinetic expression for a simple redox reaction O + e yielding R is used, in conjuction with analytical expressions for the surface concentration and overpotential, to compute the open-circuit impedance. The results of the two-dimensional model, which omits double-layer charging, are compared with the results of a more standardly applied one-dimensional model in which radial variations are neglected, with and without double-layer charging. The simpler-to-apply one-dimensional model is found to be satisfactory when mass-transfer and ohmic resistances are small with respect to charge-transfer resistance. The omission of double-layer charging does not introduce error into the two-dimensional model in the frequency range in which capacitive-like effects are caused by mass-transfer limitations.

Viner, Andrew S.↗
DOE OSTI2013

A new indirect measure of diffusion model error

We define a new indirect measure of the diffusion model error called the diffusion model error source. When this model error source is added to the diffusion equation, the transport solution for the angular-integrated intensity is obtained. This source represents a means by which a transport code can be used to generate information relating to the adequacy of diffusion theory for any given problem without actually solving the diffusion equation. The generation of this source does not relate in any way to acceleration of the iterative convergence of transport solutions. Perhaps the most well-known indirect measure of the diffusion model error is the variable-Eddington tensor. This tensor provides a great deal of information about the angular dependence of the angular intensity solution, but it is not always simple to interpret. In contrast, our diffusion model error source is a scalar that is conceptually easy to understand. In addition to defining the diffusion model error source analytically, we show how to generate this source numerically relative to the S{sub n} radiative transfer equations with linear-discontinuous spatial discretization. This numerical source is computationally tested and shown to reproduce the Sn solution for a Marshak-wave problem. (authors)

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Simulating dielectric spectra: A demonstration of the direct electric field method and a new model for the nonlinear dielectric response

Here we demonstrate a method to compute the dielectric spectra of fluids in molecular dynamics (MD) by directly applying electric fields to the simulation. We obtain spectra from MD simulations with low magnitude electric fields (≈0.01 V/Å) in agreement with spectra from the fluctuation–dissipation method for water and acetonitrile. We examine this method’s trade-off between noise at low field magnitudes and the nonlinearity of the response at higher field magnitudes. We then apply the Booth equation to describe the nonlinear response of both fluids at low frequency (0.1 GHz) and high field magnitude (up to 0.5 V/Å). We develop a model of the frequency-dependent nonlinear response by combining the Booth description of the static nonlinear dielectric response of fluids with the frequency-dependent linear dielectric response of the Debye model. We find good agreement between our model and the MD simulations of the nonlinear dielectric response for both acetonitrile and water.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1987

A comparison of active vibration control techniques - Output feedback vs optimal control

The paper presents analytical and experimental comparison of two control laws for a laboratory structure designed to simulate large space structures. The first control law is the standard linear quadratic law, which is optimal but requires model reduction for practical implementation. The second control law is a new simple direct feedback control law designed to minimize control forces while guaranteeing stability. The optimal control law was found to be only slightly better than the direct feedback law even in terms of the quadratic performance index. Moreover, the optimal control law provided almost no margin of stability for the unmodeled modes while the direct feedback law provided significant stability margins to all modes. The above results were verified experimentally using a digital implementation of the control laws. Excellent agreement between the analytical prediction and experimental measurements was observed.

Martinovic, Zoran N.↗
DOE OSTI2023

Prediction of hemiwicking dynamics in micropillar arrays

Dynamic hemiwicking behavior is observable in both nature and a wide range of industrial applications ranging from biomedical devices to thermal management. We present a semi-analytical modeling framework (without empirical fitting coefficients) to predict transient capillary-driven hemiwicking behavior of a liquid through a nano/microstructured surface, specifically a micropillar array. In our model framework, the liquid domain is discretized into micropillar unit cells to enable the time marching of the hemiwicking front. A simplified linear pressure drop is assumed along the hemiwicking length such that the local meniscus curvature, contact angle, and effective liquid height are determined at each time step in our transient model. This semi-analytical model is validated with experimental data from our own experiments and from published literature for different fluids. Our model predicts hemiwicking dynamics with <20% error over a broad range of micropillar geometries with height-to-pitch ratio ranging between ≈0.34 and 6.7 and diameter-to-pitch ratio in the range of ≈0.25–0.7 and without any fitting parameters. For lower diameter-to-pitch ratio data points related to sparse micropillar array arrangements, we suggest modifications to the semi-analytical model. This work sheds light on complex and dynamic solid–liquid–vapor interfacial interactions which could serve as a guide for the design of textured surfaces for wicking enhancement in multi-phase thermal and mass transport technologies and applications.

Mechanics↗
NASA NTRS1972

On the analytic lunar and solar perturbations of a near earth satellite

The disturbing function of the moon (sun) is expanded as a sum of products of two harmonic functions, one depending on the position of the satellite and the other on the position of the moon (sun). The harmonic functions depending on the position of the perturbing body are developed into trigonometric series with the ecliptic elements l, l', F, D, and Gamma of the lunar theory which are nearly linear with respect to time. Perturbation of elements are in the form of trigonometric series with the ecliptic lunar elements and the equatorial elements omega and Omega of the satellite so that analytic integration is simple and the results accurate over a long period of time.

Estes, R. H.↗
DOE OSTI2016

On the inward drift of runaway electrons during the plateau phase of runaway current

The well observed inward drift of current carrying runaway electrons during runaway plateau phase after disruption is studied by considering the phase space dynamic of runaways in a large aspect ratio toroidal system. We consider the case where the toroidal field is unperturbed and the toroidal symmetry of the system is preserved. The balance between the change in canonical angular momentum and the input of mechanical angular momentum in such a system requires runaways to drift horizontally in configuration space for any given change in momentum space. The dynamic of this drift can be obtained by integrating the modified Euler-Lagrange equation over one bounce time. It is then found that runaway electrons will always drift inward as long as they are decelerating. This drift motion is essentially non-linear, since the current is carried by runaways themselves, and any runaway drift relative to the magnetic axis will cause further displacement of the axis itself. A simplified analytical model is constructed to describe such inward drift both in the ideal wall case and no wall case, and the runaway current center displacement as a function of parallel momentum variation is obtained. The time scale of such displacement is estimated by considering effective radiation drag, which shows reasonable agreement with the observed displacement time scale. Furthermore, this indicates that the phase space dynamic studied here plays a major role in the horizontal displacement of runaway electrons during plateau phase. (C) 2016 AIP Publishing LLC.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1974

On the analytic lunar and solar perturbations of a near earth satellite

The disturbing function of the moon (sun) is expanded as a sum of products of two harmonic functions, one depending on the position of the satellite and the other on the position of the moon (sun). The harmonic functions depending on the position of the perturbing body are developed into trigonometric series with the ecliptic elements l, l prime, F, D and Gamma of the lunar theory which are nearly linear with respect to time. Perturbation of elements are in the form of trigonometric series with the ecliptic lunar elements and the equatorial elements omega and Omega of the satellite, so that analytic integration is simple and the results are accurate over a long period of time.-

Estes, R. H.↗
DOE OSTI2015

Lepton number violation as a key to low-scale leptogenesis

We explore the possibility of having a successful leptogenesis through oscillations between new sterile fermion states added to the Standard Model field content in a well motivated framework, naturally giving rise to the required mass splitting between the sterile states through a small total lepton number violation. We propose a framework with only two sterile states forming a pseudo-Dirac state, in which their mass difference as well as the smallness of the neutrino masses are due to two sources of lepton number violation with ΔL=2, corresponding to an Inverse Seesaw framework extended by a Linear Seesaw mass term. We also explore the pure Inverse Seesaw mechanism in its minimal version, requiring at least four new sterile states in order to comply with neutrino data. Our analytical and numerical studies reveal that one can have a successful leptogenesis at the temperature of the electroweak scale through oscillations between the two sterile states with a “natural” origin of the strong degeneracy in their mass spectrum. We also revisit the analytical expression of the baryon asymmetry of the Universe in the weak washout regime of this framework.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Why Conventional Design Rules for C–H Activation Fail for Open-Shell Transition-Metal Catalysts

The design of selective and active C–H activation catalysts for direct methane-to-methanol conversion is challenging. Bioinspired complexes that form high-valent metal–oxo intermediates capable of hydrogen abstraction and rebound hydroxylation are promising candidates. This promise has made them a target for computational high-throughput screening, typically simplified through the use of linear free energy relationships (LFERs). However, their mid-row transition-metal centers have numerous accessible spin and oxidation states that increase the combinatorial scale of design efforts. Here, we carry out a computational design screen of over 2500 mid-row 3d transition-metal complexes with four metals in numerous spin and oxidation states. We demonstrate the importance of spin/oxidation state in dictating design principles, limiting the generalization of strategies derived for widely studied high-spin Fe(II) catalysts to other metals or spin/oxidation states. Combined assessment of the effect of ligand-field tuning on reaction step energetics and on the identity of the ground state allows us to propose refined design strategies for spin-allowed methane-to-methanol catalysis. We observe weak coupling of energetics and design principles between reaction steps (e.g., oxo formation vs methanol release), meaning that LFERs do not generalize across our larger catalyst set. To rationalize relative reactivity in known catalysts, we instead compute independent reaction energies and propose strategies for further improvements in catalyst design.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

A note on the S-matrix bootstrap for the 2d O(N) bosonic model

In this work we apply the S-matrix bootstrap maximization program to the 2d bosonic O ( N ) integrable model which has N species of scalar particles of mass m and no bound states. Since in previous studies theories were defined by maximizing the coupling between particles and their bound states, the main problem appears to be to find what other functional can be used to define this model. Instead, we argue that the defining property of this integrable model is that it resides at a vertex of the convex space determined by the unitarity and crossing constraints. Thus, the integrable model can be found by maximizing any linear functional whose gradient points in the general direction of the vertex, namely within a cone determined by the normals to the faces intersecting at the vertex. This is a standard problem in applied mathematics, related to semi-definite programming and solvable by fast available numerical algorithms. The information provided by the numerical solution is enough to reproduce the known analytical solution without using integrability, namely the Yang-Baxter equation. This situation seems quite generic so we expect that other theories without continuous parameters can also be found by maximizing linear functionals in the convex space of allowed S-matrices.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Analytical Energy Dispersive X-Ray Fluorescence Measurements with a Scanty Amounts of Plant and Soil Materials

Elemental evaluations in scanty powdered material have been made using energy dispersive X-ray fluorescence (EDXRF) measurements, for which formulations along with specific procedure for sample target preparation have been developed. Fractional amount evaluation involves an itinerary of steps; (i) collection of elemental characteristic X-ray counts in EDXRF spectra recorded with different weights of material, (ii) search for linearity between X-ray counts and material weights, (iii) calculation of elemental fractions from the linear fit, and (iv) again linear fitting of calculated fractions with sample weights and its extrapolation to zero weight. Thus, elemental fractions at zero weight are free from material self absorption effects for incident and emitted photons. The analytical procedure after its verification with known synthetic samples of macro-nutrients, potassium and calcium, was used for wheat plant/ soil samples obtained from a pot experiment.

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

Oxidation kinetics of a continuous carbon phase in a nonreactive matrix

Analytical solutions of and experimental results on the oxidation kinetics of carbon in a pore are presented. Reaction rate, reaction sequence, oxidant partial pressure, total system pressure, pore/crack dimensions, and temperature are analyzed with respect to the influence of each on an overall linear-parabolic rate relationship. Direct measurement of carbon recession is performed using two microcomposite model systems oxidized in the temperature range of 700 to 1200 C, and for times to 35 h. Experimental results are evaluated using the derived analytical solutions. Implications on the oxidation resistance of continuous-fiber-reinforced ceramic-matrix composites containing a carbon constituent are discussed.

Eckel, Andrew J.↗
DOE OSTI2015

The tokamak density limit: A thermo-resistive disruption mechanism

The behavior of magnetic islands with 3D electron temperature and the corresponding 3D resistivity effects on growth are examined for islands with near-zero net heating in the island interior. We refer to the resulting class of non-linearities as thermo-resistive effects. In particular, the effects of varying impurity mix on the previously proposed local island onset threshold [Gates and Delgado-Aparicio, Phys. Rev. Lett. 108, 165004 (2012)] are examined and shown to be consistent with the well established experimental scalings for tokamaks at the density limit. A surprisingly simple semi-analytic theory is developed which imposes the effects of heating/cooling in the island interior as well as the effects of island geometry. For the class of current profiles considered, it is found that a new term that accounts for the thermal effects of island asymmetry is required in the modified Rutherford equation. The resultant model is shown to exhibit a robust onset of a rapidly growing tearing mode—consistent with the disruption mechanism observed at the density limit in tokamaks. A fully non-linear 3D cylindrical calculation is performed that simulates the effect of net island heating/cooling by raising/suppressing the temperature in the core of the island. In both the analytic theory and the numerical simulation, the sudden threshold for rapid growth is found to be due to an interaction between three distinct thermal non-linearities which affect the island resistivity, thereby modifying the growth dynamics.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Nonlinear harmonics coupled by parallel wave propagations in a time-dependent plasma flow

In a time-dependent flow, nonlinear harmonics can be excited by coupling between linear waves and flow-induced harmonic waves. Examining the dispersion relations and selection rules for the coupling, we investigate nonlinearly coupled harmonics for waves propagating along the magnetic field line in a magnetized plasma, as well as waves in an unmagnetized plasma. The coupled harmonics in a plasma flow are described by analytic dispersion relations and selection rules. This nonlinear coupling is corroborated by the particle-in-cell simulation. Here, the coupled-harmonics model describes a mechanism for the excitation of nonlinear harmonics from linear waves in a time-dependent flow. The spectral analysis of the dispersion relation provides a useful way to evaluate the spatiotemporal behavior of a plasma flow.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2010

Complete solution for unambiguous discrimination of three pure states with real inner products

Complete solutions are given in a closed analytic form for unambiguous discrimination of three general pure states with real mutual inner products. For this purpose, we first establish some general results on unambiguous discrimination of n linearly independent pure states. The uniqueness of solution is proved. The condition under which the problem is reduced to an (n-1)-state problem is clarified. After giving the solution for three pure states with real mutual inner products, we examine some difficulties in extending our method to the case of complex inner products. There is a class of set of three pure states with complex inner products for which we obtain an analytical solution.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Dynamics of a single polyampholyte chain

Polymers that feature both positive and negative charges along chains, known as polyampholytes, represent a class of materials that hold promise for a new generation of energy storage devices, the design of which will require knowledge of the underlying structure and dynamics. Here, we develop a theory based on the Rouse model for the dynamic structure factor of a single polyampholyte chain in the weak coupling regime (negligible intramolecular electrostatics) or subjected to weak external electric fields (governed by linear response). Neglecting effects of small ions, we find deviations in scaling from the classic Rouse theory and make predictions for scattering experiments performed on polyampholytes. We find that, under weak coupling with arbitrarily strong fields, the dynamics are highly dependent on the charge distribution and consequently look at two representative examples—random charge densities and periodic charge densities—with different scaling properties. Additionally, under weak fields, the dynamics are largely independent of charge distribution. Finally, we investigate the influence of hydrodynamic effects and the implications of including inertial effects in the model.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1965

Human Tracking Performance in Uncoupled and Coupled Two-Axis Systems

This report presents tile results of an experimental and analytical study of human performance in uncoupled and coupled control systems. Human pilot performance in single and two-axis systems was mathematically modeled by linear second-order describing functions. Model parameters were determined using model matching techniques. Analysis of the models showed that the amplitude ratio and phase lead of the describing function increased with training indicating an increase in open loop bandwidth. The phase margin also decreased with training. Increasing the plant lag time constant resulted in an increase in the model lead time constant and a decrease in the zero frequency gain. No significant difference was found to exist in the normalized tracking error per axis between the two-axis tasks and the single-axis tasks. However tile model lead time constant was significantly greater in two-axis tracking. Manual tracking of two-axis systems with cross-coupling was studied experimentally and analytically. Approximate methods for modeling two-axis performance were developed and checked using a precise spectral analysis approach. Coupled and uncoupled, symmetrical and asymmetrical two-axis performance was compared. The results show that modeling of cross-coupled systems is feasible and that trained subjects are capable of decoupling the axes of some systems. A methodology study compared the identification performance of continuous, iterative, and extrapolation model matching techniques. An iterative technique employing sensitivity equations for the generation of influence coefficients was found to be the best technique due to its excellent identification accuracy and ease of implementation. Convergence in iterative techniques can be improved substantially by equalizing the parameter adjustment rates and limiting the maximum correction per iteration.

Todosiev, E. P.↗