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At least 685 records · Page 38
All sourcesNASA NTRSDOE OSTI
NASA NTRS1958

Drag Minimization for Wings and Bodies in Supersonic Flow

The minimization of inviscid fluid drag is studied for aerodynamic shapes satisfying the conditions of linearized theory, and subject to imposed constraints on lift, pitching moment, base area, or volume. The problem is transformed to one of determining two-dimensional potential flows satisfying either Laplace's or Poisson's equations with boundary values fixed by the imposed conditions. A general method for determining integral relations between perturbation velocity components is developed. This analysis is not restricted in application to optimum cases; it may be used for any supersonic wing problem.

Heaslet, Max A↗
NASA NTRS1995

Algorithms for parallel and vector computations

This is a final report on work performed under NASA grant NAG-1-1112-FOP during the period March, 1990 through February 1995. Four major topics are covered: (1) solution of nonlinear poisson-type equations; (2) parallel reduced system conjugate gradient method; (3) orderings for conjugate gradient preconditioners, and (4) SOR as a preconditioner.

Ortega, James M.↗
NASA NTRS1995

A comparison of two algorithms for simulating collisionless systems

Two completely different simulation algorithms are compared by applying them to the same stellar dynamical problems: one is a self-consistent field (SCF) method for solving Poisson's equation and the other is a phase-space method for integrating the collisionless Boltzmann equation. We consider simulations of spherical stellar systems which are initially far from equilibrium and relax to their final states by gravitational collapse. The initial conditions consist of either uniform-density spheres or nonequilibrium models having Plummer density profiles, in which velocity dispersions are assigned according to given virial ratios. If a few tens of radial expansion terms with hundreds of thousands of particles are used in the SCF code, excellent agreement is found between the results it generates and those obtained with the phase-space solver, provided that a sufficiently large number of grid cells are employed with the latter. These findings imply that for simulating collisionless systmes over many dynamical times, the SCF approach based on sampling phase space is competitive with the approach treating phase space as a continuous fluid. The results of our tests make it possible to estimate the number of particles and basis functions required in situations like those modeled. Limitations of the SCF method and the choice of an optimal set of basis functions are also discussed.

Hozumi, Shunsuke↗
NASA NTRS1996

Multiple Coarse Grid Multigrid Methods for Solving Elliptic Problems

In this paper we describe some classes of multigrid methods for solving large linear systems arising in the solution by finite difference methods of certain boundary value problems involving Poisson's equation on rectangular regions. If parallel computing systems are used, then with standard multigrid methods many of the processors will be idle when one is working at the coarsest grid levels. We describe the use of Multiple Coarse Grid MultiGrid (MCGMG) methods. Here one first constructs a periodic set of equations corresponding to the given system. One then constructs a set of coarse grids such that for each grid corresponding to the grid size h there are four grids corresponding to the grid size 2*h. Multigrid operations such as restriction of residuals and interpolation of corrections are done in parallel at each grid level. For suitable choices of the multigrid operators the MCGMG method is equivalent to the Parallel Superconvergent MultiGrid (PSMG) method of Frederickson and McBryan. The convergence properties of MCGMG methods can be accurately analyzed using spectral methods.

Xiao, Shengyou↗
NASA NTRS1998

Locations of Halide Ions in Tetragonal Lysozyme Crystals

Anions play an important role in the crystallization of lysozyme, and are known to bind to the crystalline protein. Previous studies employing X-ray crystallography had found one chloride ion binding site in the tetragonal crystal form of the protein and four nitrate ion binding sites in the monoclinic form. Studies using other approaches have reported more chloride ion binding sites, but their locations were not known. Knowing the precise location of these anions is also useful in determining the correct electrostatic fields surrounding the protein. In the first part of this study the anion positions in the tetragonal form were determined from the difference Fourier map obtained from the lysozyme crystals grown in bromide and chloride solutions under identical conditions. The anion locations were then obtained from standard crystallographic methods and five possible anion binding sites were found in this manner. The sole chloride ion binding site found in previous studies was confirmed. The remaining four sites were new ones for tetragonal lysozyme crystals. However, three of these new sites and the previously found one corresponded to the four unique binding sites found for nitrate ions in monoclinic crystals. This suggests that most of the anion binding sites in lysozyme remain unchanged, even when different anions and different crystal forms of lysozyme are employed. It is unlikely that there are many more anions in the tetragonal lysozyme crystal structure. Assuming osmotic equilibrium it can be shown that there are at most three more anions in the crystal channels. Some of the new anion binding sites found in this study were, as expected, in pockets containing basic residues. However, some of them were near neutral, but polar, residues. Thus, the study also showed the importance of uncharged, but polar groups, on the protein surface in determining its electrostatic field. This was important for the second part of this study where the electrostatic field surrounding the protein was accurately determined. This was achieved by solving the linearized version of the Poisson-Boltzmann equation for the protein in solution. The solution was computed employing the commercial code Delphi which uses a finite difference technique. This has recently become available as a module in the general protein visualization code Insight II. Partial charges were assigned to the polar groups of lysozyme for the calculations done here. The calculations showed the complexity of the electrostatic field surrounding the protein. Although most of the region near the protein surface had a positive field strength, the active site cleft was negatively charged and this was projected a considerable distance. This might explain the occurrence of "head-to-side" interactions in the formation of lysozyme aggregates in solution. Pockets of high positive field strength were also found in the vicinity of the anion locations obtained from the crystallographic part of this study, confirming the validity of these calculations. This study clearly shows not only the importance of determining the counterion locations in protein crystals and the electrostatic fields surrounding the protein, but also the advantage of performing them together.

Lim, Kap↗
NASA NTRS2000

Statistically Reliable 'Atomistic' Simulation of Sub 100 nm MOSFETs

A 3D 'atomistic' simulation technique to study random impurity induced threshold voltage lowering and fluctuations in sub 0. 1 micron MOSFETs is presented. It allows statistical analysis of random impurity effects down to the individual impurity level-Efficient algorithms based on a single solution of Poisson's equation, followed by the solution of a simplified current continuity equation are used in the simulations.

Asenov, Asen↗
NASA NTRS1998

Efficient 3D 'Atomistic' Simulation Technique for Studying of Random Dopant Induced Threshold Voltage Lowering and Fluctuations in Decanano MOSFETs

A 3D 'atomistic' simulation technique to study random dopant induced threshold voltage lowering and fluctuations in sub 0.1 micron MOSFETs is presented. It allows statistical analysis of random impurity effects down to the individual impurity level. Efficient algorithms based on a single solution of Poisson's equation, followed by the solution of a simplified current continuity equation are used in the simulations.

Asenov, Asen↗
NASA NTRS2001

Plasma Reactor Modeling and Validation Experiments

Plasma processing is a key processing stop in integrated circuit manufacturing. Low pressure, high density plum reactors are widely used for etching and deposition. Inductively coupled plasma (ICP) source has become popular recently in many processing applications. In order to accelerate equipment and process design, an understanding of the physics and chemistry, particularly, plasma power coupling, plasma and processing uniformity and mechanism is important. This understanding is facilitated by comprehensive modeling and simulation as well as plasma diagnostics to provide the necessary data for model validation which are addressed in this presentation. We have developed a complete code for simulating an ICP reactor and the model consists of transport of electrons, ions, and neutrals, Poisson's equation, and Maxwell's equation along with gas flow and energy equations. Results will be presented for chlorine and fluorocarbon plasmas and compared with data from Langmuir probe, mass spectrometry and FTIR.

Meyyappan, M.↗
NASA NTRS1996

Electrical double layers at the oil/water interface

This review presents the historical development and current status of the theory of the electrical double layer at a liquid/liquid interface. It gives rigorous thermodynamic definitions of all basic concepts related to liquid interfaces and to the electrical double layer. The difference between the surface of a solid electrode and the interface of two immiscible electrolyte solutions (ITIES) is analyzed in connection to their electrical properties. The most important classical relationships for the electrical double layer are presented and critically discussed. The generalized adsorption isotherm is derived. After a short review of the classical Gouy-Chapman and Verwey-Niessen models, more recent developments of the double layer theory are presented. These include effects of variable dielectric permittivity, nonlocal electrostatics, hydration forces, the modified Poisson-Boltzmann equation and the ion-dipole plasma. The relative merits of different theories are estimated by comparing them with computer simulation of the ITIES and electrical double layer. Special attention is given to the structure of ITIES and its variation due to adsorption of ions and amphiphilic molecules.

Non-NASA Center↗
DOE OSTI2017

Modeling electrokinetics in ionic liquids: General

Using direct numerical simulations we provide a thorough study on the electrokinetics of ionic liquids. In particular, the modfied Poisson-Nernst-Planck (MPNP) equations are solved to capture the crowding and overscreening effects that are the characteristics of an ionic liquid. For modeling electrokinetic flows in an ionic liquid, the MPNP equations are coupled with the Navier-Stokes equations to study the coupling of ion transport, hydrodynamics, and electrostatic forces. Specifically, we consider the ion transport between two parallel plates, charging dynamics in a 2D straight-walled pore, electro-osmotic ow in a nano-channel, electroconvective instability on a plane ion-selective surface, and electroconvective ow on a curved ion-selective surface. We discuss how the crowding and overscreening effects and their interplay affect the electrokinetic behaviors of ionic liquids in these application problems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2011

Current-free double layers: A review

During the last decade, there has been an upsurge in the research on current-free DLs (CFDLs). Research includes theory, laboratory measurements, and various applications of CFDLs ranging from plasma thrusters to acceleration of charged particles in space and astrophysical plasmas. The purpose of this review is to present a unified understanding of the basic plasma processes, which lead to the formation of CFDLs. The review starts with the discussion on early research on electric fields and double layers (DLs) and ion acceleration in planar plasma expansion. The review continues with the formation of DLs and rarefaction shocks (RFS) in expanding plasma with two electron populations with different temperatures. The basic theory mitigating the formation of a CFDL by two-electron temperature population is reviewed; we refer to such CFDLs as double layers structures formation by two-temperature electron populations (TET-CFDLs). Application of TET-CFDLS to ion acceleration in laboratory and space plasmas was discussed including the formation of stationary steady-state DLs. A quite different type of CFDLs forms in a helicon plasma device (HPD), in which plasma abruptly expands from a narrow plasma source tube into a wide diffusion tube with abruptly diverging magnetic fields. The formation mechanism of the CFDL in HPD, referred here as current free double layer structure in helicon plasma device (HPD-CFDL), and its applications are reviewed. The formation of a TET-CFDL is due to the self-consistent separation of the two electron populations parallel to the ambient magnetic field. In contrast, a HPD-CFDL forms due to self-consistent separation of electrons and ion perpendicular to the abruptly diverging magnetic field in conjunction with the conducting wall of the expansion chamber in the HPD. One-dimensional theoretical models of CFDLs based on steady-state solution of Vlasov-Poisson system of equations are briefly discussed. Applications of CFDLs ranging from helicon double-layer thrusters (HDLTs) to the accelerations of ions in space and astrophysical plasmas are summarized.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

A Poisson–Nernst–Planck Model of Ion Transport and Interface Segregation in Metal–Insulator–Semiconductor Structures and Solar Cells

A numerical model that describes the transport of mobile ionic species in metal–insulator–semiconductor (MIS) and photovoltaic (PV) devices subject to temperature and voltage stress is presented. The finite element method (FEM) is used to solve the Nernst–Planck equation while imposing Poisson's equation self-consistently as a restriction for the electrostatic potential. This allows the contribution of the ionic species to the potential to be taken into account. Using a variational formulation eases the implementation of diverse boundary conditions, including the incorporation of segregation kinetics at the device interfaces. Segregation across the dielectric–semiconductor interface is relevant to modeling the electronic device degradation in systems where contamination reaches the semiconductor. The model in closed systems with no-flux boundary conditions is validated first. In the limiting case of low contamination levels with respect to the gate bias, the FEM solution matches analytically derived approximations. Then, the implementation is broadened to include an open boundary at the dielectric–semiconductor interface to account for leakage of ions. The predicted time dependence of the flatband voltage in Na-contaminated MIS test structures agrees well with measurements. This model successfully captures the role of long-range ion transport at concentrations of relevance to electronic and PV device instability and neuromorphic computing.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

A Legendre–Fourier spectral method with exact conservation laws for the Vlasov–Poisson system

In this study, we present the design and implementation of an L 2 -stable spectral method for the discretization of the Vlasov–Poisson model of a collisionless plasma in one space and velocity dimension. The velocity and space dependence of the Vlasov equation are resolved through a truncated spectral expansion based on Legendre and Fourier basis functions, respectively. The Poisson equation, which is coupled to the Vlasov equation, is also resolved through a Fourier expansion. The resulting system of ordinary differential equation is discretized by the implicit second-order accurate Crank–Nicolson time discretization. The non-linear dependence between the Vlasov and Poisson equations is iteratively solved at any time cycle by a Jacobian-Free Newton–Krylov method. In this work we analyze the structure of the main conservation laws of the resulting Legendre–Fourier model, e.g., mass, momentum, and energy, and prove that they are exactly satisfied in the semi-discrete and discrete setting. The L 2 -stability of the method is ensured by discretizing the boundary conditions of the distribution function at the boundaries of the velocity domain by a suitable penalty term. The impact of the penalty term on the conservation properties is investigated theoretically and numerically. An implementation of the penalty term that does not affect the conservation of mass, momentum and energy, is also proposed and studied. A collisional term is introduced in the discrete model to control the filamentation effect, but does not affect the conservation properties of the system. Numerical results on a set of standard test problems illustrate the performance of the method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Electrostatic surface waves on a magnetized quantum plasma half-space

A theory of electrostatic surface waves on a quantum plasma half-space is developed with the inclusion of external magnetic field effects for the geometry in which the magnetic field is parallel to the surface and the direction of propagation is perpendicular to the magnetic field. A general analytical expression for dispersion relation of surface waves is obtained by solving Poisson and quantum magnetohydrodynamic equations with appropriate quantum boundary conditions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1995

A fast Poisson solver for unsteady incompressible Navier-Stokes equations on the half-staggered grid

In this paper, a fast Poisson solver for unsteady, incompressible Navier-Stokes equations with finite difference methods on the non-uniform, half-staggered grid is presented. To achieve this, new algorithms for diagonalizing a semi-definite pair are developed. Our fast solver can also be extended to the three dimensional case. The motivation and related issues in using this second kind of staggered grid are also discussed. Numerical testing has indicated the effectiveness of this algorithm.

Golub, G. H.↗
NASA NTRS1993

Characteristics of 0.8- and 0.2-microns gate length In(x)Ga(1-x) As/In(0.52)Al(0.48)As/InP (0.53 less than or equal to x less than or equal to 0.70) modulation-doped field-effect transistors at cryogenic temperatures

The performance characteristics of InP-based In(x)Ga(1-x)As/In(0.52)Al(0.48)As (0.53 is less than or equal to x is less than or equal to 0.70) pseudomorphic modulation-doped field-effect transistors (MODFET's) as a function of strain in the channel, gate, length, and temperature were investigated analytically and experimentally. The strain in the channel was varied by varying the In composition x. The temperature was varied in the range of 40-300 K and the devices have gate lengths L(sub g) of 0.8 and 0.2 microns. Analysis of the device was done using a one-dimensional self consistent solution of the Poisson and Schroedinger equations in the channel, a two-dimensional Poisson solver to obtain the channel electric field, and a Monte Carlo simulation to estimate the carrier transit times in the channel. An increase in the value of the cutoff frequency is predicted for an increase in In composition, a decrease in temperature, and a decrease in gate length. The improvements seen with decreasing temperature, decreasing gate length, and increased In composition were smaller than those predicted by analysis. The experimental results on pseudomorphic InGaAs/InAlAs MODFET's showed that there is a 15-30 percent improvement in cutoff frequency in both the 0.8- and 0.2-micron gate length devices when the temperature is lowered from 300 to 40 K.

Lai, Richard↗
DOE OSTI2017

Convergence of Spectral Discretizations of the Vlasov--Poisson System

Here we prove the convergence of a spectral discretization of the Vlasov-Poisson system. The velocity term of the Vlasov equation is discretized using either Hermite functions on the infinite domain or Legendre polynomials on a bounded domain. The spatial term of the Vlasov and Poisson equations is discretized using periodic Fourier expansions. Boundary conditions are treated in weak form through a penalty type term that can be applied also in the Hermite case. As a matter of fact, stability properties of the approximated scheme descend from this added term. The convergence analysis is carried out in detail for the 1D-1V case, but results can be generalized to multidimensional domains, obtained as Cartesian product, in both space and velocity. The error estimates show the spectral convergence under suitable regularity assumptions on the exact solution.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Asymptotic and spectral analysis of the gyrokinetic-waterbag integro-differential operator in toroidal geometry

Achieving plasmas with good stability and confinement properties is a key research goal for magnetic fusion devices. The underlying equations are the Vlasov–Poisson and Vlasov–Maxwell (VPM) equations in three space variables, three velocity variables, and one time variable. Even in those somewhat academic cases where global equilibrium solutions are known, studying their stability requires the analysis of the spectral properties of the linearized operator, a daunting task. We have identified a model, for which not only equilibrium solutions can be constructed, but many of their stability properties are amenable to rigorous analysis. It uses a class of solution to the VPM equations (or to their gyrokinetic approximations) known as waterbag solutions which, in particular, are piecewise constant in phase-space. It also uses, not only the gyrokinetic approximation of fast cyclotronic motion around magnetic field lines, but also an asymptotic approximation regarding the magnetic-field-induced anisotropy: the spatial variation along the field lines is taken much slower than across them. Together, these assumptions result in a drastic reduction in the dimensionality of the linearized problem, which becomes a set of two nested one-dimensional problems: an integral equation in the poloidal variable, followed by a one-dimensional complex Schrödinger equation in the radial variable. We show here that the operator associated to the poloidal variable is meromorphic in the eigenparameter, the pulsation frequency. We also prove that, for all but a countable set of real pulsation frequencies, the operator is compact and thus behaves mostly as a finite-dimensional one. The numerical algorithms based on such ideas have been implemented in a companion paper [D. Coulette and N. Besse, “Numerical resolution of the global eigenvalue problem for gyrokinetic-waterbag model in toroidal geometry” (submitted)] and were found to be surprisingly close to those for the original gyrokinetic-Vlasov equations. The purpose of the present paper is to make these new ideas accessible to two readerships: applied mathematicians and plasma physicists.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗