Showing papers on "Nonlinear system published in 1984"

Analysis and simulation of semiconductor devices

Abstract: 1. Introduction.- 1.1 The Goal of Modeling.- 1.2 The History of Numerical Device Modeling.- 1.3 References.- 2. Some Fundamental Properties.- 2.1 Poisson's Equation.- 2.2 Continuity Equations.- 2.3 Carrier Transport Equations.- 2.4 Carrier Concentrations.- 2.5 Heat Flow Equation.- 2.6 The Basic Semiconductor Equations.- 2.7 References.- 3. Proeess Modeling.- 3.1 Ion Implantation.- 3.2 Diffusion.- 3.3 Oxidation.- 3.4 References.- 4. The Physical Parameters.- 4.1 Carrier Mobility Modeling.- 4.2 Carrier Generation-Recombination Modeling.- 4.3 Thermal Conductivity Modeling.- 4.4 Thermal Generation Modeling.- 4.5 References.- 5. Analytical Investigations About the Basic Semiconductor Equations.- 5.1 Domain and Boundary Conditions.- 5.2 Dependent Variables.- 5.3 The Existence of Solutions.- 5.4 Uniqueness or Non-Uniqueness of Solutions.- 5.5 Sealing.- 5.6 The Singular Perturbation Approach.- 5.7 Referenees.- 6. The Diseretization of the Basic Semiconductor Equations.- 6.1 Finite Differences.- 6.2 Finite Boxes.- 6.3 Finite Elements.- 6.4 The Transient Problem.- 6.5 Designing a Mesh.- 6.6 Referenees.- 7. The Solution of Systems of Nonlinear Algebraic Equations.- 7.1 Newton's Method and Extensions.- 7.2 Iterative Methods.- 7.3 Referenees.- 8. The Solution of Sparse Systems of Linear Equations.- 8.1 Direct Methods.- 8.2 Ordering Methods.- 8.3 Relaxation Methods.- 8.4 Alternating Direction Methods.- 8.5 Strongly Implicit Methods.- 8.6 Convergence Acceleration of Iterative Methods.- 8.7 Referenees.- 9. A Glimpse on Results.- 9.1 Breakdown Phenomena in MOSFET's.- 9.2 The Rate Effect in Thyristors.- 9.3 Referenees.- Author Index.- Table Index.

Galerkin Finite Element Methods for Parabolic Problems

Abstract: The Standard Galerkin Method.- Methods Based on More General Approximations of the Elliptic Problem.- Nonsmooth Data Error Estimates.- More General Parabolic Equations.- Negative Norm Estimates and Superconvergence.- Maximum-Norm Estimates and Analytic Semigroups.- Single Step Fully Discrete Schemes for the Homogeneous Equation.- Single Step Fully Discrete Schemes for the Inhomogeneous Equation.- Single Step Methods and Rational Approximations of Semigroups.- Multistep Backward Difference Methods.- Incomplete Iterative Solution of the Algebraic Systems at the Time Levels.- The Discontinuous Galerkin Time Stepping Method.- A Nonlinear Problem.- Semilinear Parabolic Equations.- The Method of Lumped Masses.- The H1 and H?1 Methods.- A Mixed Method.- A Singular Problem.- Problems in Polygonal Domains.- Time Discretization by Laplace Transformation and Quadrature.

Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. (AM-105), Volume 105

Abstract: The description for this book, Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. (AM-105), will be forthcoming.

The concentration-compactness principle in the calculus of variations. The locally compact case, part 2

Abstract: In this paper (sequel of Part 1) we investigate further applications of the concentration-compactness principle to the solution of various minimization problems in unbounded domains. In particular we present here the solution of minimization problems associated with nonlinear field equations.

Stability in dynamical systems

Abstract: Stability in dynamical systems subject to some law of force is considered. This leads to a set of differential equations which govern the motion. (AIP)

Recursive Lagrangian Dynamics of Flexible Manipulator Arms

Abstract: Nonlinear equations of motion are developed for flexible manipulator arms consisting of rotary joints that connect pairs of flexible links. Kinematics of both the rotary-joint mo tion and the link deformation are described by 4 X 4 trans formation matrices. The link deflection is assumed small so that the link transformation can be composed of summations of assumed link shapes. The resulting equations are pre sented as scalar and 4 X 4 matrix operations ready for pro gramming. The efficiency of this formulation is compared to rigid-link cases reported in the literature.

A review of least-squares inversion and its application to geophysical problems*

Abstract: Geophysical inversion involves the estimation of the parameters of a postulated earth model from a set of observations. Since the associated model responses can be nonlinear functions of the model parameters, nonlinear least-squares techniques prove to be useful for performing the inversion. A common type of inversion applies iterative damped linear least squares through use of the Marquardt-Levenberg method. Traditionally, this method has been implemented by solving the associated normal equations in conventional ways. However, Singular Value Decomposition (SVD) produces significant improvements in computational precision when applied to the same system of normal equations. Iterative least-squares modeling finds application in a wide variety of geophysical problems. Two examples illustrate the approach: (1) seismic wavelet deconvolution, and (2) the location of a buried wedge from surface gravity data. More generally, nonlinear least-squares inversion can be used to estimate earth models for any set of geophysical observations for which an appropriate mathematical description is available.

Generalized eigenproblem algorithms and software for algebraic Riccati equations

Abstract: Numerical issues related to the computational solution of the algebraic matrix Riccati equation are discussed. The approach presented uses the generalized eigenproblem formulation for the solution of general forms of algebraic Riccati equations arising in both continuous- and discrete-time applications. These general forms result from control and filtering problems for systems in generalized (or implicit or descriptor) state space form. A Newtontype iterative refinement procedure for the generalized Riccati solution is given. The issue of numerical condition of the Riccati problem is addressed. Balancing to improve numerical condition is discussed. An overview of a software package, RICPACK, coded in portable, reliable Fortran is given. Results of numerical experiments are reported.

Fundamental properties and performance of conventional bearings-only target motion analysis

Abstract: This paper considers the problem of estimating the position and velocity of an object from noise corrupted bearing measurements obtained by a single moving observation platform. The process is inherently nonlinear and exhibits unusual observability properties that are geometry-dependent. A maximum likelihood estimate (MLE) of the target motion analysis solution is developed and its performance analyzed. A comparison is drawn between the MLE and two previously reported methods, a nonlinear modified-instrumental variable estimate (MIV) and the pseudo-linear estimate (PLE). Both the MIV and PLE are shown to derive from approximations to the nonlinear measurement equation and therefore share some common properties with the MLE. The limits on performance that can be expected from processing bearing data are detailed. Specifically, for long range-to-baseline geometries, approximate expressions for the Cramer-Rao bound are derived. Extension of the results to the practical filters approximately predicts numerically observed behavior. For less restrictive geometries, bounds are presented. Incorporation of a target speed constraint on the MLE results in a transition to a lower dimensional problem as noise level and range increases. Monte Carlo experimental results are presented and the improvements realized by the MLE techniques are evident.

Quantum measurements and stochastic processes

Abstract: A nonlinear stochastic process is presented that, for each realization and for large times, reproduces L\"uder's projection postulate. The corresponding density operator undergoes a linear evolution reproducing von Neumann's projection postulate. The violation of the Bell inequality, for instance, is described with the two apparatus acting independently on the composed system.

Propagation of nonlinear compression pulses in granular media

Abstract: The study of mechanics of a granular medium is of substantial interest, both scientifically and for the solution of applied problems. Such materials are, for example, good buffers for shock loads. Their, study is important for the development of processes of the pulse deformation of several porous materials. A review of studies of small deformations and elastic wave propagation in these media was carried out in [i] on the basis of discrete models. The structure of a stationary shock wave was analyzed in [2] as a function of its amplitude. i. Statement of the Problem. The problem of nonstationary, nonlinear perturbations in one-dimensional granular media is stated in the present paper on the basis of the wellknown interaction between neighboring granules. As an interaction law we choose the Hertz law [3]

Landau-Lifshitz and higher-order nonlinear systems gauge generated from nonlinear Schrödinger-type equations

Abstract: New Landau–Lifshitz (LL) and higher‐order nonlinear systems gauge generated from nonlinear Schrodinger (NS) type equations are presented. The consequences of gauge equivalence between different dynamical systems are discussed. The gauge connections among various LL and NS equations are found and depicted through a schematic representation.

Quadratically Convergent Optimal Power Flow

Abstract: A newly developed sparse implementation of an optimization method using exact second derivatives is applied to the optimal power flow problem. Four utility systems are studied using a variety of objective functions, including fuel costs, active and reactive losses, and new shunt capacitors. Systems solved range from 350 buses to 2000 buses. Comparisons are made with an older algorithm which uses an Augmented Lagrangian to demonstrate the advantages of run time and robustness of the new method. The algorithm and accompanying software represent a technological breakthrough, since they are suitable for solving systems on the order of 2000 buses and demonstrate solution speeds of 5 minutes on large mainframe computers. The method is particularly well suited to infeasible, or even divergent starting points. An option to add shunt capacitors in the event of hopeless infeasibility guarantees an optimal solution for many difficult to solve systems. An automatic scaling feature is added to correct numerical ill-conditioning resulting from series compensation or poor R/X ratios.

Spectral Methods for Partial Differential Equations

Abstract: Origins of spectral methods, especially their relation to the Method of Weighted Residuals, are surveyed Basic Fourier, Chebyshev, and Legendre spectral concepts are reviewed, and demonstrated through application to simple model problems Both collocation and tau methods are considered These techniques are then applied to a number of difficult, nonlinear problems of hyperbolic, parabolic, elliptic, and mixed type Fluid dynamical applications are emphasized

Nonlinear-response theory for steady planar Couette flow

Abstract: We present a simplified derivation of the Yamada-Kawasaki formula for the nonlinear adiabatic response of the stress tensor to planar Couette flow. This formally exact expression is then used to prove the validity of two nonequilibrium molecular-dynamics algorithms that have been used to study fluids undergoing planar Couette flow, very far from equilibrium.

The decoupled direct method for calculating sensitivity coefficients in chemical kinetics

Abstract: A version of the direct method for calculating first‐order sensitivity coefficients is extended to nonlinear, time‐dependent models defined by stiff differential equations. In this approach the auxiliary equations for the sensitivity coefficients are solved separately from the model equations. Accuracy and stability are maintained by using exactly the same time steps and numerical approximations in calculating the sensitivities as are used in calculating the model solution. The decoupling procedure also greatly increases the efficiency of the method by taking advantage of the fact that the auxiliary equations for different sensitivity coefficients are quite similar. The decoupled direct method is applied to stiff chemical mechanisms for the oxidation of hydrocarbons in the atmosphere, the pyrolysis of ethane, and the oxidation of formaldehyde in the presence of carbon monoxide. Sensitivity coefficients are also calculated for the three mechanisms by a method employing Green’s function and by actually vary...

Robust Adaptive Control

Abstract: The paper addresses an open problem concerned with the boundedness of signals in an adaptive loop when external perturbations are present. A complete solution is provided for the case of a first order plant with an unknown parameter by analyzing a nonlinear differential equation in R2. It is shown that if the persistent excitation of the reference input is larger than the perturbation in some sense, the solutions will be globally bounded. The same methodology appears to be applicable to the general adaptive control problem.

Large-time regularity of viscous surface waves

Abstract: Etude du mouvement d'un fluide visqueux incompressible contenu dans un ocean tridimensionnel de dimensions finies, limite en bas par un sol solide et en haut par une atmosphere a pression constante. La surface superieure se modifie en fonction du mouvement du fluide