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At least 883 records · Page 49

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NASA NTRS1983

A unified mathematical theory of electrophoretic processes

A mathematical theory is presented which shows that each of the four classical electrophoretic modes (zone electrophoresis, moving boundary electrophoresis, isotachophoresis, and isoelectric focusing) is based on the same general principles and can collectively be described in terms of a single set of equations. This model can predict the evolution of the four electrophoretic modes as a function of time. The model system is one-dimensional, neglecting the effects of electroosmosis, temperature gradients, and any bulk flows of liquid. The model is based on equations which express the components' dissociation equilibria, the mass transport due to electromigration and diffusion, electroneutrality, and the conservation of mass and charge. The model consists of a system of coupled partial differential and nonlinear algebraic equations which can be solved numerically by use of a computer. The versatility of this model was verified using an example of a three-component system containing cacodylate, tris hydroxylmethylaminomethane, and histidine. Results show that this model not only correctly predicts the characteristic features of each electrophoretic mode, but also gives details of the concentration, pH, and conductivity profiles not easily amenable to direct experimental measurement.

Bier, M.↗

NASA NTRS1992

An approximately factored incremental strategy for calculating consistent discrete aerodynamic sensitivity derivatives

An incremental strategy is presented for iteratively solving very large systems of linear equations, which are associated with aerodynamic sensitivity derivatives for advanced CFD codes. It is shown that the left-hand side matrix operator and the well-known factorization algorithm used to solve the nonlinear flow equations can also be used to efficiently solve the linear sensitivity equations. Two airfoil problems are considered as an example: subsonic low Reynolds number laminar flow and transonic high Reynolds number turbulent flow.

Korivi, V. M.↗

NASA NTRS1994

Dynamics of Numerics and CFD

This lecture attempts to illustrate the basic ideas of how the recent advances in nonlinear dynamical systems theory (dynamics) can provide new insights into the understanding of numerical algorithms used in solving nonlinear differential equations (DEs). Examples will be given of the use of dynamics to explain unusual phenomena that occur in numerics. The inadequacy of the use of linearized analysis for the understanding of long time behavior of nonlinear problems will be illustrated, and the role of dynamics in studying the nonlinear stability, accuracy, convergence property and efficiency of using time- dependent approaches to obtaining steady-state numerical solutions in computational fluid dynamics (CFD) will briefly be explained.

Yee, H. C.↗

DOE OSTI2023

Analysis of the nonlinear propagation of incoherent pulses

The nonlinear propagation of incoherent optical pulses is studied using a normalized nonlinear Schrödinger equation and statistical analysis, demonstrating various regimes that depend on the field’s coherence time and intensity. The quantification of the resulting intensity statistics using probability density functions shows that, in the absence of spatial effects, nonlinear propagation leads to an increase in the likelihood of high intensities in a medium with negative dispersion, and a decrease in a medium with positive dispersion. In the latter regime, nonlinear spatial self-focusing originating from a spatial perturbation can be mitigated, depending on the coherence time and amplitude of the perturbation. These results are benchmarked against the Bespalov–Talanov analysis applied to strictly monochromatic pulses.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1999

Hierarchical Approach to 'Atomistic' 3-D MOSFET Simulation

We present a hierarchical approach to the 'atomistic' simulation of aggressively scaled sub-0.1 micron MOSFET's. These devices are so small that their characteristics depend on the precise location of dopant atoms within them, not just on their average density. A full-scale three-dimensional drift-diffusion atomistic simulation approach is first described and used to verify more economical, but restricted, options. To reduce processor time and memory requirements at high drain voltage, we have developed a self-consistent option based on a solution of the current continuity equation restricted to a thin slab of the channel. This is coupled to the solution of the Poisson equation in the whole simulation domain in the Gummel iteration cycles. The accuracy of this approach is investigated in comparison to the full self-consistent solution. At low drain voltage, a single solution of the nonlinear Poisson equation is sufficient to extract the current with satisfactory accuracy. In this case, the current is calculated by solving the current continuity equation in a drift approximation only, also in a thin slab containing the MOSFET channel. The regions of applicability for the different components of this hierarchical approach are illustrated in example simulations covering the random dopant-induced threshold voltage fluctuations, threshold voltage lowering, threshold voltage asymmetry, and drain current fluctuations.

Asenov, Asen↗

NASA NTRS1989

Design of optimally smoothing multi-stage schemes for the Euler equations

In this paper, a method is developed for designing multi-stage schemes that give optimal damping of high-frequencies for a given spatial-differencing operator. The objective of the method is to design schemes that combine well with multi-grid acceleration. The schemes are tested on a nonlinear scalar equation, and compared to Runge-Kutta schemes with the maximum stable time-step. The optimally smoothing schemes perform better than the Runge-Kutta schemes, even on a single grid. The analysis is extended to the Euler equations in one space-dimension by use of 'characteristic time-stepping', which preconditions the equations, removing stiffness due to variations among characteristic speeds. Convergence rates independent of the number of cells in the finest grid are achieved for transonic flow with and without a shock. Characteristic time-stepping is shown to be preferable to local time-stepping, although use of the optimally damping schemes appears to enhance the performance of local time-stepping. The extension of the analysis to the two-dimensional Euler equations is hampered by the lack of a model for characteristic time-stepping in two dimensions. Some results for local time-stepping are presented.

Van Leer, Bram↗

NASA NTRS1967

Approximate continuous nonlinear minimal- variance filtering

Valid equations derived for approximate continuous nonlinear minimal variance filtering - mathematical models

MATHEMATICAL MODEL↗

NASA NTRS1980

Theoretical prediction of nonlinear propagation effects on noise signatures generated by subsonic or supersonic propeller or rotor-blade tips

The nonlinear propagation equations for sound generated by a constant speed blade tip are presented. Propagation from a subsonic tip is treated as well as the various cases that can occur at supersonic speeds. Some computed examples indicate that the nonlinear theory correlates with experimental results better than linear theory for large amplitude waves. For swept tips that generate a wave with large amplitude leading expansion, the nonlinear theory predicts a cancellation effect that results in a significant reduction of both amplitude and impulse.

Barger, R. L.↗

NASA NTRS1982

Topics in strong Langmuir turbulence

Progress in two approaches to the study of strong Langmuir turbulence is reported. In two spatial dimensions, numerical solution of the Zakharov equations yields a steady state involving linear growth, linear damping, and a collection of coherent, long-lived entities which might loosely be called solitons. In one spatial dimension, a statistical theory is applied to the cubically nonlinear Schroedinger equation and is solved analytically in a special case.

Nicholson, D. R.↗

NASA NTRS1983

Topics in strong Langmuir turbulence

Nicholson, D. R.↗

NASA NTRS2000

Hierarchical Statistical 3D ' Atomistic' Simulation of Decanano MOSFETs: Drift-Diffusion, Hydrodynamic and Quantum Mechanical Approaches

When MOSFETs are scaled to deep submicron dimensions the discreteness and randomness of the dopant charges in the channel region introduces significant fluctuations in the device characteristics. This effect, predicted 20 year ago, has been confirmed experimentally and in simulation studies. The impact of the fluctuations on the functionality, yield, and reliability of the corresponding systems shifts the paradigm of the numerical device simulation. It becomes insufficient to simulate only one device representing one macroscopical design in a continuous charge approximation. An ensemble of macroscopically identical but microscopically different devices has to be characterized by simulation of statistically significant samples. The aims of the numerical simulations shift from predicting the characteristics of a single device with continuous doping towards estimating the mean values and the standard deviations of basic design parameters such as threshold voltage, subthreshold slope, transconductance, drive current, etc. for the whole ensemble of 'atomistically' different devices in the system. It has to be pointed out that even the mean values obtained from 'atomistic' simulations are not identical to the values obtained from continuous doping simulations. In this paper we present a hierarchical approach to the 'atomistic' simulation of aggressively scaled decanano MOSFETs. A full scale 3D drift-diffusion'atomostic' simulation approach is first described and used for verification of the more economical, but also more restricted, options. To reduce the processor time and memory requirements at high drain voltage we have developed a self-consistent option based on a thin slab solution of the current continuity equation only in the channel region. This is coupled to the Poisson's equation solution in the whole simulation domain in the Gummel iteration cycles. The accuracy of this approach is investigated in comparison with the full self-consistent solution. At low drain voltage only single solution of the nonlinear Poisson equation is sufficient to extract the current with satisfactory accuracy. A pilot version of a hydrodynamic 'atomistic' simulator has been developed in order to study the effect of the nonequilibrium, non local transport in decanano MOSFETs on the random dopant induced current fluctuations. For the first time we have also applied the density gradient approach in 3D to investigate the effect of the quantum confinement on the threshold voltage fluctuations. The developed 'atomistic' simulation techniques have been applied to study various fluctuation resistant MOSFET architectures including epitaxial and delta doped devices.

Asenov, Asen↗

NASA NTRS1976

Microwave remote sensing of a two-layer random medium

A two-variable expansion technique is used to solve for the mean Green's. function from the Dyson equation under the nonlinear approximation. The Bethe-Salpeter equation then gives rise to a set of modified radiative transfer (MRT) equations which accommodate coherent effects essential to bounded media. It is found that the nonlinear approximation, instead of the more popular bilocal approximation, should be used for the case of bounded media. The two approximations yield identical results for unbounded media. The MRT equations are then solved for a two-layer random medium. The MRT equations give rise to simple and useful solutions which are applicable to both active and passive microwave remote sensing.

Tsang, L.↗

NASA NTRS1978

Some new nystrom integrators

Nystrom integrators were self starting integrators used to integrate the second order, vector, differential equations the second derivative of x factorial = f factorial (t, x factorial) and the second derivative of x factorial = f factorial (t, x factorial, first derivative of x factorial). Nystrom integrator parameters were defined by a set of nonlinear constraint equations and frequently there were more parameters than there were equations. Additions are included for higher order integrations when the second derivative of x factorial = f factorial (t).

Lear, W. M.↗

NASA NTRS1978

Finite element concepts in computational aerodynamics

Finite element theory was employed to establish an implicit numerical solution algorithm for the time averaged unsteady Navier-Stokes equations. Both the multidimensional and a time-split form of the algorithm were considered, the latter of particular interest for problem specification on a regular mesh. A Newton matrix iteration procedure is outlined for solving the resultant nonlinear algebraic equation systems. Multidimensional discretization procedures are discussed with emphasis on automated generation of specific nonuniform solution grids and accounting of curved surfaces. The time-split algorithm was evaluated with regards to accuracy and convergence properties for hyperbolic equations on rectangular coordinates. An overall assessment of the viability of the finite element concept for computational aerodynamics is made.

Baker, A. J.↗

NASA NTRS1995

CCD/CID Processors Would Offer Greater Precision

Charge-coupled-device/charge-injection-device (CCD/CID) data processors of proposed type offer advantages of massively parallel computational architecture and high computational speed typical of older CCD/CID data processors, but with increased precision. Useful in performing matrix vector multiplications in variety of applications, including solving partial differential equations, processing signal and image data, control computations, and neural-network simulations. Greater precision of proposed devices help to ensure accuracy in CCD/CID implementations of pseudospectral neural networks - particular class of artificial neural networks especially suited to solving nonlinear differential equations.

Barhen, Jacob↗

NASA NTRS1980

Numerical techniques for solving nonlinear instability problems in smokeless tactical solid rocket motors

The selection of a satisfactory numerical method for calculating the propagation of steep fronted shock life waveforms in a solid rocket motor combustion chamber is discussed. A number of different numerical schemes were evaluated by comparing the results obtained for three problems: the shock tube problems; the linear wave equation, and nonlinear wave propagation in a closed tube. The most promising method--a combination of the Lax-Wendroff, Hybrid and Artificial Compression techniques, was incorporated into an existing nonlinear instability program. The capability of the modified program to treat steep fronted wave instabilities in low smoke tactical motors was verified by solving a number of motor test cases with disturbance amplitudes as high as 80% of the mean pressure.

Baum, J. D.↗

NASA NTRS1992

Computational modeling of femtosecond optical solitons from Maxwell's equations

An algorithm is developed that permits the direct time integration of full-vector nonlinear Maxwell's equations. This capability permits the modeling of both linear and nonlinear instantaneous and dispersive effects in the electric polarization in material media. The modeling of the optical carrier is retained. The fundamental innovation is to notice that it is possible to treat the linear and nonlinear convolution integrals, which describe the dispersion, as new dependent variables. A coupled system of nonlinear second-order ordinary differential equations can then be derived for the linear and nonlinear convolution integrals, by differentiating them in the time domain. These equations, together with Maxwell's equations, are solved to determine the electromagnetic fields in nonlinear dispersive media. Results are presented of calculations in one dimension of the propagation and collision of femtosecond electromagnetic solitons that retain the optical carrier, taking into account as the Kerr and Raman interactions.

Goorjian, Peter M.↗

NASA NTRS1997

Self-Consistent and Time-Dependent Solar Wind Models

We describe the first results from a self-consistent study of Alfven waves for the time-dependent, single-fluid magnetohydrodynamic (MHD) solar wind equations, using a modified version of the ZEUS MHD code. The wind models we examine are radially symmetrical and magnetized; the initial outflow is described by the standard Parker wind solution. Our study focuses on the effects of Alfven waves on the outflow and is based on solving the full set of the ideal nonlinear MHD equations. In contrast to previous studies, no assumptions regarding wave linearity, wave damping, and wave-flow interaction are made; thus, the models naturally account for the back-reaction of the wind on the waves, as well as for the nonlinear interaction between different types of MHD waves. Our results clearly demonstrate when momentum deposition by Alfven waves in the solar wind can be sufficient to explain the origin of fast streams in solar coronal holes; we discuss the range of wave amplitudes required to obtained such fast stream solutions.

Ong, K. K.↗