Showing papers on "Nonlinear system published in 1982"

Generalized Nonlinear Inverse Problems Solved Using the Least Squares Criterion

Abstract: We attempt to give a general definition of the nonlinear least squares inverse problem. First, we examine the discrete problem (finite number of data and unknowns), setting the problem in its fully nonlinear form. Second, we examine the general case where some data and/or unknowns may be functions of a continuous variable and where the form of the theoretical relationship between data and unknowns may be general (in particular, nonlinear integrodierentia l equations). As particular cases of our nonlinear algorithm we find linear solutions well known in geophysics, like Jackson’s (1979) solution for discrete problems or Backus and Gilbert’s (1970) a solution for continuous problems.

Orbital stability of standing waves for some nonlinear Schrödinger equations

Abstract: We present a general method which enables us to prove the orbital stability of some standing waves in nonlinear Schrodinger equations. For example, we treat the cases of nonlinear Schrodinger equations arising in laser beams, of time-dependent Hartree equations ....

The Waveform Relaxation Method for Time-Domain Analysis of Large Scale Integrated Circuits

Abstract: The Waveform Relaxation (WR) method is an iterative method for analyzing nonlinear dynamical systems in the time domain. The method, at each iteration, decomposes the system into several dynamical subsystems each of which is analyzed for the entire given time interval. Sufficient conditions for convergence of the WR method are proposed and examples in MOS digital integrated circuits are given to show that these conditions are very mild in practice. Theoretical and computational studies show the method to be efficient and reliable.

Upwind difference schemes for hyperbolic systems of conservation laws

Abstract: We derive a new upwind finite difference approximation to systems of nonlinear hyperbolic conservation laws. The scheme has desirable properties for shock calculations. Under fairly general hypotheses we prove that limit solutions satisfy the entropy condition and that discrete steady shocks exist which are unique and sharp. Numerical examples involving the Euler and Lagrange equations of compressible gas dynamics in one and two space dimensions are given.

Nonlinear gyrokinetic equations for low-frequency electromagnetic waves in general plasma equilibria

Abstract: A nonlinear gyrokinetic formalism for low‐frequency (less than the cyclotron frequency) microscopic electromagnetic perturbations in general magnetic field configurations is developed The nonlinear equations thus derived are valid in the strong‐turbulence regime and contain effects due to finite Larmor radius, plasma inhomogeneities, and magnetic field geometries The specific case of axisymmetric tokamaks is then considered and a model nonlinear equation is derived for electrostatic drift waves Also, applying the formalism to the shear Alfven wave heating scheme, it is found that nonlinear ion Landau damping of kinetic shear‐Alfven waves is modified, both qualitatively and quantitatively, by the diamagnetic drift effects In particular, wave energy is found to cascade in wavenumber instead of frequency

Fast Nonlinear Control with Arbitrary Pole-Placement for Industrial Robots and Manipulators

Abstract: Models of industrial robots are characterized by highly nonlinear equations with nonlinear couplings between the variables of motion. In this paper, three nonlinear methods are presented, two of which are direct design procedures for industrial robots. These direct nonlinear methods are based on a suitable partition of the dynamic equation of the industrial robot and provide directly applicable, explicit control laws for each drive. The design procedures presented greatly simplify the derivation of the algorithm for computer-controlled industrial robots. The methods are applied to two different types of industrial robots.

A Survey of Full Length Nonlinear Shift Register Cycle Algorithms

Abstract: Shift registers have been used to generate sequences of 0’s and 1’s for over thirty years. A wide variety of applications has been made of these sequences. Principally, communications have made use of the sequences generated.One particular class of shift register sequences for which applications exist is the full length nonlinear shift register sequences. These sequences are periodic and of length $2^n $ and all $2^n $ different binary n-tuples appear exactly one time in a periodic portion of the sequence. In this paper we discuss various algorithms which have been suggested for generating these sequences.

A neural model for category learning

Abstract: We present a general neural model for supervised learning of pattern categories which can resolve pattern classes separated by nonlinear, essentially arbitrary boundaries. The concept of a pattern class develops from storing in memory a limited number of class elements (prototypes). Associated with each prototype is a modifiable scalar weighting factor (?) which effectively defines the threshold for categorization of an input with the class of the given prototype. Learning involves (1) commitment of prototypes to memory and (2) adjustment of the various ? factors to eliminate classification errors. In tests, the model ably defined classification boundaries that largely separated complicated pattern regions. We discuss the role which divisive inhibition might play in a possible implementation of the model by a network of neurons.

Nonlinear theory of film rupture

Abstract: The present work aims at examining nonlinear effects on film rupture by investigating the stability of thin films to finite amplitude disturbances. The dynamics of the liquid film is formulated using the Navier-Stokes equations augmented by a body force describing the London/van der Waals attractions. The liquid film is assumed to be charge neutralized, nondraining, and laterally unbounded. A nonlinear evolution equation is derived for h ( x , t ), the film thickness. This strongly nonlinear partial differential equation is solved by numerical methods as part of an initial-value problem for periodic boundary conditions in x , the lateral space dimension. Given this model, one obtains true rupture in the sense that the film thickness becomes zero in a finite time. The results reveal rupture characteristics and effects of nonlinearities on the rupture properties.

Nonlinear Dynamics of Deep-Water Gravity Waves

Abstract: Publisher Summary This chapter reviews some recent progress in the nonlinear dynamics of deep-water gravity waves. It attempts to highlight the major developments in theory and experiment commencing with the finding by Lighthill (1965) that a nonlinear, deep-water gravity wave train is unstable to modulational perturbation, up to the present investigations of various aspects of nonlinear phenomena, including three-dimensional instabilities, bifurcations into new steady solutions, statistical properties of random wave fields, and chaotic behavior in time evolution. The governing equations for inviscid, irrotational, incompressible, free surface flows are given in Section II of the chapter, together with some basic steady solutions of the system. The concept of a wave train is introduced in Section III. The stability and evolutionary properties of a weakly nonlinear wave train in two dimensions are considered in Section IV, based on the nonlinear Schrodinger equation, which is an equation describing the wave envelope. Some interesting phenomena, such as the existence of envelope solitons, and the Fermi-Pasta-Ulam recurrence in time of an unstable wave train, are examined. Section V extends these results to three dimensions, using the three-dimensional nonlinear Schrodinger equation. The results indicate that whereas the nonlinear Schrodinger equation is remarkably successful in describing the two-dimensional dynamics, it is inadequate for treatment of the three-dimensional case.

A projected Lagrangian algorithm and its implementation for sparse nonlinear constraints

Abstract: An algorithm is described for solving large-scale nonlinear programs whose objective and constraint functions are smooth and continuously differentiable The algorithm is of the projected Lagrangian type, involving a sequence of sparse, linearly constrained subproblems whose objective functions include a modified Lagrangian term and a modified quadratic penalty function

Memoryless nonlinearities with Gaussian inputs: Elementary results

Abstract: The distortion-to-signal power ratio at the output of a memoryless nonlinearity is determined by simple calculations. This is done by application of Bussgang's theorem, which may also be obtained as a special case of Price's theorem. Specific results are given for hard and soft instantaneous and envelope limiters.

Quantitative feedback theory

Abstract: In quantitative feedback theory, plant parameter and disturbance uncertainty are the reasons for using feedback. They are defined by means of a set Q = {P} of plant operators and a set D = {D} of disturbances. The desired system performance is defined by sets of acceptable outputs A u in response to an input u, to be achieved for all Pϵ Q. If any design freedom remains in the achievement of the design specifications, it is used to minimise the effect of sensor noise at the plant input. Rigorous, exact quantitative synthesis theories have been established to a fair extent for highly uncertain linear, nonlinear and time-varying single-input single-output, single-loop and some multiple-loop structures; also for multiple-input multiple-output plants with output feedback and with internal variable feedback, both linear and nonlinear. There have been many design examples vindicating the theory. Frequency-response methods have been found to be especially useful and transparent, enabling the designer to see the trade-off between conflicting design factors. The key tool in dealing with uncertain nonlinear and multiple-input multiple-output plants is their conversion into equivalent uncertain linear time-invariant single-input single-output plants. Schauder's fixed-point theorem justifies the equivalence. Modern control theory, in particular singular-value theory, is examined and judged to be comparatively inadequate for dealing with plant parameter uncertainties.

Nonlinear Optical Phase Conjugation

Abstract: The real-time information processing and manipulation of electromagnetic waves using nonlinear Qptical techniques has resulted in a myriad of new applications in diverse fields such as quantum electronics, image processing, optical computing, adaptive optics, and nonlinear spectroscopy. In this paper, we review and explore the field, provide a historical perspective, analyze several of the nonlinear interactions useful for the generation of phase-conjugate replicas, and conclude with a brief survey of potential applications and suitable nonlinear media.

The instability and breaking of deep-water waves

Abstract: An experimental study of the evolution to breaking of a nonlinear deep-water wave train is reported. Two distinct regimes are found. For ak 6 0-29 the evolution is sensibly two-dimensional with the Ben jamin-Feir instability leading directly to breaking as found by Longuet-Higgins & Cokelet (1978). The measured side-band frequencies agree very well with those predicted by Longuet-Higgins (1978b). It is found that the evolution of the spectrum is not restricted to a few discrete frequencies but also involves a growing continuous spectrum, and the description of the evolution as a recurrence phenomenon is incomplete. It is found that the onset of breaking corresponds to the onset of the asymmetric development of the side bands about the fundamental frequency and its higher harmonics. This asymmetric evolution, which ultimately leads to the shift to lower frequency first reported by Lake et al. (1977), is interpreted in termsof Longuct-Higgins’ (19786) breaking instability. For ak 2 0.31 a full three-dimensional instability dominates the Benjamin-Feir instability and leads rapidly to breaking. Preliminary measurements of this instability agree very well with the recent results of McLean et al. (1981).

Evidence for universal chaotic behavior of a driven nonlinear oscillator

Abstract: A bifurcation diagram for a driven nonlinear semiconductor oscillator is measured directly, showing successive subharmonic bifurcations to f/32, onset of chaos, noise band merging, and extensive noise-free windows. The overall diagram closely resembles that computed for the logistic model. Measured values of universal numbers are reported, including effects of added noise.

Glimm's Method for Gas Dynamics

Abstract: We investigate Glimm's method, a method for constructing approximate solutions to systems of hyperbolic conservation laws in one space variable by sampling explicit wave solutions It is extended to several space variables by operator splitting We consider two problems 1) We propose a highly accurate form of the sampling procedure, in one space variable, based on the van der Corput sampling sequence We test the improved sampling procedure numerically in the case of inviscid compressible flow in one space dimension and find that it gives high resolution results both in the smooth parts of the solution, as well as at discontinuities 2) We investigate the operator splitting procedure by means of which the multidimensional method is constructed An $O(1)$ error stemming from the use of this procedure near shocks oblique to the spatial grid is analyzed numerically in the case of the equations for inviscid compressible flow in two space dimensions We present a hybrid method which eliminates this error, consisting of Glimm's method, used in continuous parts of the flow, and the nonlinear Godunov method, used in regions where large pressure jumps are generated The resulting method is seen to be a substantial improvement over either of the component methods for multidimensional calculations

Prediction of Subsonic Aerodynamic Characteristics: A Case for Low-Order Panel Methods

Abstract: A low-order panel method is presented for the calculation of subsonic aerodynamic characteristics of general configurations. The method is based on piecewise constant doublet and source singularities. Two forms of the internal Dirichlet boundary condition are discussed and the source distribution is determined by the external Neumann boundary condition. Calculations are compared with higher-order solutions for a number of cases. It is demonstrated that for comparable density of control points where the boundary conditions are satisfied, the low-order method gives comparable accuracy to the higher-order solutions. It is also shown that problems associated with some earlier low-order panel methods, e.g., leakage in internal flows and junctions and also poor trailing-edge solutions, do not appear for the present method. Further, the application of the Kutta condition is extremely simple; no extra equation or trailing-edge velocity point is required. The method has very low computing costs and this has made it practical for application to nonlinear problems requiring iterative solutions and to three-dimensional unsteady problems using a time-stepping approach. In addition, the method has been extended to model separated flows in three dimensions, using free vortex sheets to enclose the separated zone.

Cosmology without singularity and nonlinear gravitational Lagrangians

Abstract: We investigate the generalized Einstein equations derived from the Lagrangian which is an arbitrary function ofR. The importance of the saturation phenomenon is underlined, which may replace the role of a cosmological constant. The spherically symmetric homogeneous model is analyzed in more detail, and an approximate solution without singularity is constructed using the method of matched asymptotic expansions.

Large-amplitude free and driven drop-shape oscillations - Experimental observations

Abstract: A quantitative study of some nonlinear aspects of drop-shape oscillations in a liquid-liquid system has been completed. The results suggest a soft nonlinearity in the fundamental resonant mode frequency as the oscillation amplitude is increased. Indications of an increase in the rate of decay have also been obtained. A study of the internal flow fields has revealed patterns of circulation not present at low amplitude.