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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 361 records · Page 20
All sourcesNASA NTRSDOE OSTI
DOE OSTI2010

Charged anisotropic matter with linear or nonlinear equation of state

Ivanov pointed out substantial analytical difficulties associated with self-gravitating, static, isotropic fluid spheres when pressure explicitly depends on matter density. Simplifications achieved with the introduction of electric charge were noticed as well. We deal with self-gravitating, charged, anisotropic fluids and get even more flexibility in solving the Einstein-Maxwell equations. In order to discuss analytical solutions we extend Krori and Barua's method to include pressure anisotropy and linear or nonlinear equations of state. The field equations are reduced to a system of three algebraic equations for the anisotropic pressures as well as matter and electrostatic energy densities. Attention is paid to compact sources characterized by positive matter density and positive radial pressure. Arising solutions satisfy the energy conditions of general relativity. Spheres with vanishing net charge contain fluid elements with unbounded proper charge density located at the fluid-vacuum interface. Notably the electric force acting on these fluid elements is finite, although the acting electric field is zero. Net charges can be huge (10{sup 19}C) and maximum electric field intensities are very large (10{sup 23}-10{sup 24} statvolt/cm) even in the case of zero net charge. Inward-directed fluid forces caused by pressure anisotropy may allow equilibrium configurations with larger net charges and electric field intensities than those found in studies of charged isotropic fluids. Links of these results with charged strange quark stars as well as models of dark matter including massive charged particles are highlighted. The van der Waals equation of state leading to matter densities constrained by cubic polynomial equations is briefly considered. The fundamental question of stability is left open.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1988

An invariant asymptotic formula for solutions of second-order linear ODE's

An invariant-matrix technique for the approximate solution of second-order ordinary differential equations (ODEs) of form y-double-prime = phi(x)y is developed analytically and demonstrated. A set of linear transformations for the companion matrix differential system is proposed; the diagonalization procedure employed in the final stage of the asymptotic decomposition is explained; and a scalar formulation of solutions for the ODEs is obtained. Several typical ODEs are analyzed, and it is shown that the Liouville-Green or WKB approximation is a special case of the present formula, which provides an approximation which is valid for the entire interval (0, infinity).

Gingold, H.↗
NASA NTRS2020

A Sensitive Quantitative Analysis of Abiotically Synthesized Short Homopeptides using Ultraperformance Liquid Chromatography and Time-of-Flight Mass Spectrometry

In the origins of life field understanding the abiotic polymerization of simple organic monomers (e.g., amino acids) into larger biomolecules (e.g., oligopeptides), remains a seminal challenge. Recently, preliminary observations showed a limited set of peptides formed in the presence of the plausible prebiotic phosphorylating agent, diamidophosphate (DAP), highlighting the need for an analytical tool to critically evaluate the ability of DAP to induce oligomerization of simple organics under aqueous conditions. However, performing accurate and precise, targeted analyses of short oligopeptides remains a distinct challenge in the analytical chemistry field. Here, we developed a new technique to detect and quantitate amino acids and their homopeptides in a single run using ultraperformance liquid chromatography-fluorescence detection/time of flight mass spectrometry. Over an 8-minute retention time window, 18 target analytes were identified and quantitated, 16 of which were chromatographically separated at, or near baseline resolution. Compound identity was confirmed by accurate mass analysis using a 10 ppm mass tolerance window. This method featured limits of detection < 5 nM (< 1 fmol on column) and limits of quantitation (LOQs) <15 nM (< 3 fmol on column). The LODs and LOQs were upwards of ∼28x and ∼788x lower, respectively, than previous methods for the same analytes, highlighting the quantifiable advantages of this new method. Both detectors provided good quantitative linearity (R(exp 2) > 0.985) for all analytes spanning concentration ranges ∼3 - 4 orders of magnitude. We performed a series of laboratory experiments to investigate DAP-mediated oligomerization of amino acids and peptides and analyzed experimental products with the new method. DAP readily polymerized amino acids and peptides under a range of simulated environmental conditions. This research underscores the potential of DAP to have generated oligopeptides on the primordial Earth, enhancing prebiotic chemical diversity and complexity at or near the origin of life.

Prebiotic Chemistry and Analytical Chemistry↗
DOE OSTI2015

The double-gradient magnetic instability: Stabilizing effect of the guide field

The role of the dawn-dusk magnetic field component in stabilizing of the magnetotail flapping oscillations is investigated in the double-gradient model framework (Erkaev et al., Phys. Rev. Lett. 99, 235003 (2007)), extended for the magnetotail-like configurations with non-zero guide field B{sub y}. Contribution of the guide field is examined both analytically and by means of linearized 2-dimensional (2D) and non-linear 3-dimensional (3D) MHD modeling. All three approaches demonstrate the same properties of the instability: stabilization of current sheet oscillations for short wavelength modes, appearing of the typical (fastest growing) wavelength λ{sub peak} of the order of the current sheet width, decrease of the peak growth rate with increasing B{sub y} value, and total decay of the mode for B{sub y}∼0.5 in the lobe magnetic field units. Analytical solution and 2D numerical simulations claim also the shift of λ{sub peak} toward the longer wavelengths with increasing guide field. This result is barely visible in 3D simulations. It may be accounted for the specific background magnetic configuration, the pattern of tail-like equilibrium provided by approximated solution of the conventional Grad-Shafranov equation. The configuration demonstrates drastically changing radius of curvature of magnetic field lines, R{sub c}. This, in turn, favors the “double-gradient” mode (λ > R{sub c}) in one part of the sheet and classical “ballooning” instability (λ < R{sub c}) in another part, which may result in generation of a “combined” unstable mode.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1989

Control of flexible beams using a free-free active truss

An analytical and experimental study involving controlling flexible beams using a free-free active truss is presented. This work extends previous work in controlling flexible continua with active trusses which were configured with fixed-free boundary conditions. The following describes the Lagrangian approach used to derive the equations of motion for the active truss and the beams attached to it. A partial-state feedback control law is derived for this system based on a full-state feedback Linear Quadratic Regulator method. The analytical model is examined via numerical simulations and the results are compared to a similar experimental apparatus described herein. The results show that control of a flexible continua is possible with a free-free active truss.

Clark, W. W.↗
NASA NTRS1984

Large deflection, large amplitude vibrations and random response of symmetrically laminated rectangular plates

An analytical method is presented for determining large-deflection static bending, large-amplitude free and forced vibrations, and large-amplitude random response of a clamped, symmetrically laminated, rectangular, thin plate subjected to a uniformly distributed transverse loading. Both movable and immovable inplane boundary conditions are considered. Numerical results for bending deflections and strains, frequency ratios, mean-square center deflections and mean-square maximum strains are presented showing the parametric effects of plate length-to-width ratio, orientation of layers, and intensities of applied force for both the linear and nonlinear cases. The analytical results for large-deflection random response are verified through comparison with experimental data.

Gray, C. E., Jr.↗
DOE OSTI2014

Pneumatic Microvalve-Based Hydrodynamic Sample Injection for High-Throughput, Quantitative Zone Electrophoresis in Capillaries

A hybrid microchip/capillary CE system was developed to allow unbiased and lossless sample loading and high throughput repeated injections. This new hybrid CE system consists of a polydimethylsiloxane (PDMS) microchip sample injector featuring a pneumatic microvalve that separates a sample introduction channel from a short sample loading channel and a fused silica capillary separation column that connects seamlessly to the sample loading channel. The sample introduction channel is pressurized such that when the pneumatic microvalve opens briefly, a variable-volume sample plug is introduced into the loading channel. A high voltage for CE separation is continuously applied across the loading channel and the fused silica capillary separation column. Analytes are rapidly separated in the fused silica capillary with high resolution. High sensitivity MS detection after CE separation is accomplished via a sheathless CE/ESI-MS interface. The performance evaluation of the complete CE/ESI-MS platform demonstrated that reproducible sample injection with well controlled sample plug volumes could be achieved by using the PDMS microchip injector. The absence of band broadening from microchip to capillary indicated a minimum dead volume at the junction. The capabilities of the new CE/ESI-MS platform in performing high throughput and quantitative sample analyses were demonstrated by the repeated sample injection without interrupting an ongoing separation and a good linear dependence of the total analyte ion abundance on the sample plug volume using a mixture of peptide standards. The separation efficiency of the new platform was also evaluated systematically at different sample injection times, flow rates and CE separation voltages.

Eletrophoresis↗
DOE OSTI2015

Model reduction for stochastic chemical systems with abundant species

Biochemical processes typically involve many chemical species, some in abundance and some in low molecule numbers. We first identify the rate constant limits under which the concentrations of a given set of species will tend to infinity (the abundant species) while the concentrations of all other species remains constant (the non-abundant species). Subsequently, we prove that, in this limit, the fluctuations in the molecule numbers of non-abundant species are accurately described by a hybrid stochastic description consisting of a chemical master equation coupled to deterministic rate equations. This is a reduced description when compared to the conventional chemical master equation which describes the fluctuations in both abundant and non-abundant species. We show that the reduced master equation can be solved exactly for a number of biochemical networks involving gene expression and enzyme catalysis, whose conventional chemical master equation description is analytically impenetrable. We use the linear noise approximation to obtain approximate expressions for the difference between the variance of fluctuations in the non-abundant species as predicted by the hybrid approach and by the conventional chemical master equation. Furthermore, we show that surprisingly, irrespective of any separation in the mean molecule numbers of various species, the conventional and hybrid master equations exactly agree for a class of chemical systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Optimization of transformer ratio and beam loading in a plasma wakefield accelerator with a structure-exploiting algorithm

Plasma-based acceleration has emerged as a promising candidate as an accelerator technology for a future linear collider or a next-generation light source. We consider the plasma wakefield accelerator (PWFA) concept where a plasma wave wake is excited by a particle beam and a trailing beam surfs on the wake. For a linear collider, the energy transfer efficiency from the drive beam to the wake and from the wake to the trailing beam must be large, while the emittance and energy spread of the trailing bunch must be preserved. One way to simultaneously achieve this when accelerating electrons is to use longitudinally shaped bunches and nonlinear wakes. In the linear regime, there is an analytical formalism to obtain the optimal shapes. In the nonlinear regime, however, the optimal shape of the driver to maximize the energy transfer efficiency cannot be precisely obtained because currently no theory describes the wake structure and excitation process for all degrees of nonlinearity. In addition, the ion channel radius is not well defined at the front of the wake where the plasma electrons are not fully blown out by the drive beam. We present results using a novel optimization method to effectively determine a current profile for the drive and trailing beam in PWFA that provides low energy spread, low emittance, and high acceleration efficiency. We parameterize the longitudinal beam current profile as a piecewise-linear function and define optimization objectives. For the trailing beam, the algorithm converges quickly to a nearly inverse trapezoidal trailing beam current profile similar to that predicted by the ultrarelativistic limit of the nonlinear wakefield theory. For the drive beam, the beam profile found by the optimization in the nonlinear regime that maximizes the transformer ratio also resembles that predicted by linear theory. Furthermore, the current profiles found from the optimization method provide higher transformer ratios compared with the linear ramp predicted by the relativistic limit of the nonlinear theory.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2018

Single-mode perturbation growth in an idealized spherical implosion

This paper considers a dense imploding spherical shell, where perturbations on the inner surface grow due to hydrodynamic instabilities, geometric convergence and compression. A low-convergence implosion with a single spherical harmonic mode perturbation with mode numbers in the range from $\ell$ = 5 to $\ell$ = 100 and at three different amplitudes is considered. The linear theory of Epstein [1] is extended to incorporate reshock, making it applicable to the full implosion process (while perturbations are linear). Linear theory is employed to choose modes such that quantified geometric convergence and compression effects contribute significantly to perturbation growth at the lower mode number, while at the higher mode number the contribution from Rayleigh–Taylor instability dominates. Simulation results from four independent simulation codes (FLASH, HYDRA, Miranda and Flamenco) are presented. The simulation predictions are validated against linear theory pre-reshock and employed to validate the extended theory across the reshock. The simulations continue to substantially non-linear perturbation amplitudes, beyond the limits of the analytical approach, and the presented perturbation amplitudes can inform future non-linear modeling. In this work, the simulated perturbation amplitudes agree to within approximately 10% for most cases, with isolated cases having differences of greater than 50% from the simulated ensemble-mean. This occurs in the case of a low mode number perturbation with a very small amplitude, where the growth of secondary small-scale instabilities leads to substantial differences between the codes after re-shock.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1988

The analysis of non-linear dynamic behavior (including snap-through) of postbuckled plates by simple analytical solution

Static postbuckling and nonlinear dynamic analysis of plates are usually accomplished by multimode analyses, although the methods are complicated and do not give straightforward understanding of the nonlinear behavior. Assuming single-mode transverse displacement, a simple formula is derived for the transverse load displacement relationship of a plate under in-plane compression. The formula is used to derive a simple analytical expression for the static postbuckling displacement and nonlinear dynamic responses of postbuckled plates under sinusoidal or random excitation. Regions with softening and hardening spring behavior are identified. Also, the highly nonlinear motion of snap-through and its effects on the overall dynamic response can be easily interpreted using the single-mode formula. Theoretical results are compared with experimental results obtained using a buckled aluminum panel, using discrete frequency and broadband point excitation. Some important effects of the snap-through motion on the dynamic response of the postbuckled plates are found.

Ng, C. F.↗
NASA NTRS1981

A model for the acoustic impedance of linear suppressor materials bonded on perforated plate

An analytical model is developed for the acoustic impedance of a composite made of a fine screen bonded to a perforated plate, the resistance having been modeled using steady flow theory and data, and including both linear and nonlinear components. The model of the screen resistance alone is derived first, and it is then extended to include a perforated plate bonded to the screen. Quantities such as effective open ratio and pressure recovery are evaluated. Conclusions are presented, including: (1) when the screen is bonded to a perforated plate, the linear resistance increases as the inverse of the perforate open area, (2) the nonlinearity in the screen resistance depends on the square of the screen wire diameter, and (3) when the resistance is considered as a function of approach velocity, the screen nonlinear term increases as the inverse of the square of the perforated plate open area ratio. The general theory can be applied to any screen structure, but final results are limited to a twilled square weave screen. Results can be applied to the study of sound absorbing materials used for lining the walls of aircraft engine duct suppressors.

Rice, E. J.↗
NASA NTRS1959

The Synthesis of Optimum Homing Missile Guidance Systems with Statistical Inputs

An analytical approach is presented which is applicable to the optimization of homing navigation guidance systems which are forced to operate in the presence of radar noise. The two primary objectives are to establish theoretical minimum miss distance performance and a method of synthesizing the optimum control system. The factors considered are: (1) target evasive maneuver, (2) radar glint noise, (3) missile maneuverability, and (4) the inherent time-varying character of the kinematics. Two aspects of the problem are considered. In the first, consideration is given only to minimization of the miss distance. The solution given cannot be achieved in practice because the required accelerations are too large. In the second, results are extended to the practical case where the limited acceleration capabilities of the missile are considered by placing a realistic restriction on the mean-square acceleration so that system operation is confined to the linear range. Although the exact analytical solution of the latter problem does not appear feasible, approximate solutions utilizing time-varying control systems can be found. One of these solutions - a range multiplication type control system - is studied in detail. It is shown that the minimum obtainable miss distance with a realistic restriction on acceleration is close to the absolute minimum for unlimited missile maneuverability. Furthermore, it is shown that there is an equivalence in performance between the homing and beam-rider type guidance systems. Consideration is given to the effect of changes in target acceleration, noise magnitude, and missile acceleration on the minimum miss distance.

Stewart, Elwood C.↗
NASA NTRS1979

Space shuttle active-pogo-suppressor control design using linear quadratic regulator techniques

Two methods of active pogo suppression (stabilization) for the space shuttle vehicle were studied analytically. The basis for both approaches was the linear quadratic regulator, state space technique. The first approach minimized root-mean-square pump inlet pressure by using either fullstate feedback, partial-state feedback, or output feedback with a Kalman filter. The second approach increased the modal damping associated with the critical structural modes by using either full-state feedback or reconstructed state feedback. A number of implementable controls were found by both approaches. The designs were analyzed with respect to sensitivity, complexity, and controller energy requirements, as well as controller performance. Practical controllers resulting from the two design approaches tended to use pressure and flow as feedback variables for the minimum-rms method and structural accelerations or velocities for the modal control method. Both approaches are suitable for the design of active pogo-suppression controllers.

Lehtinen, B.↗
NASA NTRS1981

Analytical performance prediction for large antennas

A linear mathematical modeling of the static and dynamic characteristics of a deployable offset wrap rib antenna was attempted using small motions in an effort to simulate the surface distortion resulting from thermal loading and transient oscillations from control. Both cyclic symmetry and model synthesis were used for parametric analysis. Although the ribs can be modeled as slender beams varying cross sections and equivalent linear material properties, the mesh poses a problem since its equivalent stress strain relations are highly nonlinear and sensitive to the biaxial prestressed state. Consequently, the macroscopic material properties were measured experimentally in the neighborhood of the design prestress. An equivalent tangent modulus technique was then adopted about this equilibrium state and assumed to be valid within a small range of incremental stresses.

El-Raheb, M.↗
NASA NTRS1990

Inhomogeneous electric field effects in a linear RF quadruple trap

The exact potential corresponding to confining fields inside a linear rf quadrupole particle trap of finite length is presented. The analytic expressions for the trapping potential is derived by introducing a linear trap employing a relatively simple cylindrical geometry and solving Laplace's equation for the trap electrodes. The finite length of linear traps results in field distortion near the trap ends. An exact analytic determination of the fields is useful because the profile of the trapped ion cloud is highly dependent on the fields confining it. It is shown that near the ends of the trap, the effective potential arising from the rf fields acts to propel particles out of the trap, and further, that the addition of a dc bias generates an inhomogeneous in the trap that influences the particles both perpendicularly to and along the trap's long axis.

Melborne, R. K.↗