Showing papers on "Nonlinear system published in 1985"
TL;DR: In this article, the authors proposed a joint probability density function (pdf) of the three components of velocity and of the composition variables (species mass fractions and enthalpy) to calculate the properties of turbulent reactive flow fields.
2,578 citations
1,792 citations
TL;DR: In this paper, it is shown that consistency between the tangent operator and the integration algorithm employed in the solution of the incremental problem plays crucial role in preserving the quadratic rate of asymptotic convergence of iterative solution schemes based upon Newton's method.
1,702 citations
TL;DR: General equations are derived that can be used to analyze tissue uptake data when the blood–plasma concentration of the test substance cannot be easily measured and for situations when trapping of theTest substance is incomplete and for a combination of these two conditions.
Abstract: The method of graphical analysis for the evaluation of sequential data (e.g., tissue and blood concentrations over time) in which the test substance is irreversibly trapped in the system has been expanded. A simpler derivation of the original analysis is presented. General equations are derived that can be used to analyze tissue uptake data when the blood–plasma concentration of the test substance cannot be easily measured. In addition, general equations are derived for situations when trapping of the test substance is incomplete and for a combination of these two conditions. These derivations are independent of the actual configuration of the compartmental system being analyzed and show what information can be obtained for the period when the reversible compartments are in effective steady state with the blood. This approach is also shown to result in equations with at least one less nonlinear term than those derived from direct compartmental analysis. Specific applications of these equations are illustr...
1,623 citations
TL;DR: Recursive input-output models for non-linear multivariate discrete-time systems are derived, and sufficient conditions for their existence are defined.
Abstract: Recursive input-output models for non-linear multivariate discrete-time systems are derived, and sufficient conditions for their existence are defined. The paper is divided into two parts. The first part introduces and defines concepts such as Nerode realization, multistructural forms and results from differential geometry which are then used to derive a recursive input-output model for multivariable deterministic non-linear systems. The second part introduces several examples, compares the derived model with other representations and extends the results to create prediction error or innovation input-output models for non-linear stochastic systems. These latter models are the generalization of the multivariable ARM AX models for linear systems and are referred to as NARMAX or Non-linear AutoRegressive Moving Average models with exogenous inputs.
1,198 citations
TL;DR: In this article, a method for designing asymptotic observers for a class of nonlinear systems is presented, where the error between the state of the systems and the observer in appropriate coordinates evolves linearly and can be made to decay aribtrarily exponentially fast.
Abstract: A new method for designing asymptotic observers for a class of nonlinear systems is presented. The error between the state of the systems and the state of the observer in appropriate coordinates evolves linearly and can be made to decay aribtrarily exponentially fast.
1,062 citations
Book•
07 Aug 1985
TL;DR: In this paper, the authors introduce the sequential probability ratio test (SPRT), a test for estimating the probability of a given event to be true, and a series of other tests with curved stopping boundary crossing problems.
Abstract: I Introduction and Examples.- II The Sequential Probability Ratio Test.- III Brownian Approximations and Truncated Tests.- IV Tests with Curved Stopping Boundaries.- V Examples of Repeated Significance Tests.- VI Allocation of Treatments.- VII Interval Estimation of Prescribed Accuracy.- VIII Random Walk and Renewal Theory.- IX Nonlinear Renewal Theory.- X Corrected Brownian Approximations.- XI Miscellaneous Boundary Crossing Problems.- Appendix 1 Brownian Motion.- Appendix 2 Queueing and Insurance Risk Theory.- Appendix 3 Martingales and Stochastic Integrals.- Appendix 4 Renewal Theory.- Bibliographical Notes.- References.
1,010 citations
Abstract: We have examined the response of an exact and an MCSCF reference state to a general time‐dependent field. The time development of both the exact and the MCSCF reference state have been parametrized in terms of explicit exponential time‐dependent transformations. The time development has been determined by requiring the Ehrenfest theorem to be satisfied through each order in the interaction between the molecular system and the field. The response of the exact and the MCSCF reference state has been used to evaluate linear, quadratic, and cubic response functions. It has been shown how a large variety of molecular properties may be expressed in terms of these response functions. It has also been demonstrated that molecular properties containing the electric dipole operator may be expressed in equivalent forms involving the momentum operator both for the exact and the MCSCF state. The MCSCF response functions have been transformed to computationally attractive expressions which do not contain summation indices over intermediate states and which allow direct techniques to be straightforwardly applied.
1,003 citations
TL;DR: In this article, it was shown that any time-invariant continuous nonlinear operator with fading memory can be approximated by a Volterra series operator, and that the approximating operator can be realized as a finite-dimensional linear dynamical system with a nonlinear readout map.
Abstract: Using the notion of fading memory we prove very strong versions of two folk theorems. The first is that any time-invariant (TI) continuous nonlinear operator can be approximated by a Volterra series operator, and the second is that the approximating operator can be realized as a finite-dimensional linear dynamical system with a nonlinear readout map. While previous approximation results are valid over finite time intervals and for signals in compact sets, the approximations presented here hold for all time and for signals in useful (noncompact) sets. The discretetime analog of the second theorem asserts that any TI operator with fading memory can be approximated (in our strong sense) by a nonlinear moving- average operator. Some further discussion of the notion of fading memory is given.
923 citations
01 Jan 1985
TL;DR: Some applications of Volterraequations LinearVolterra equations of the second kind Nonlinear equations ofthe second kind Equations of the first kind Convolution equations The numerical solution of equations ofThe second kind.
Abstract: Some applications of Volterraequations Linear Volterra equations of the second kind Nonlinear equations of the second kind Equations of the first kind Convolution equations The numerical solution of equations of the second kind Product Integration methods for equations of the second kind Equations of the first kind with differentiable kernels Equations of the Abel type Integrodifferential equations Some computer programs Case studies.
TL;DR: In this paper, the modulational stability of ground state solitary wave solutions of nonlinear Schrodinger equations relative to perturbations in the equation and initial data is studied.
Abstract: The modulational stability of ground state solitary wave solutions of nonlinear Schrodinger equations relative to perturbations in the equation and initial data is studied. In the “subcritical case” ground states are shown by variational methods to be stable modulo time-dependent adjustments (modulations) of free parameters. These parameters satisfy the modulation equations, a coupled system of nonlinear ODE’S governing the amplitude, phase, position and speed of the dominant solitary wave part of the solution.
TL;DR: In this article, a local multiplicative split of the deformation gradient into volume-preserving and dilatational parts is proposed, without relying on rate forms of the weak form of momentum balance.
TL;DR: In this paper, the general nonlinear scalar model is studied at asymptotically low temperature near two dimensions, and the low temperature expansion is renormalized and effective algorithms are derived for calculation to all orders in the renormalised expansion.
TL;DR: It is concluded that existing adaptive control algorithms, as presented in the literature referenced in this paper, cannot be used with confidence in practical designs where the plant contains unmodeled dynamics because instability is likely to result.
Abstract: This paper examines the robustness properties of existing adaptive control algorithms to unmodeled plant high-frequency dynamics and unmeasurable output disturbances. It is demonstrated thai there exist two infinite-gain operators in the nonlinear dynamic system which determines the time-evolution of output and parameter errors. The pragmatic implication of the existence of such infinite-gain operators is that 1) sinusoidal reference inputs at specific frequencies and/or 2) sinusoidal output disturbances at any frequency (including dc), can cause the loop gain to increase without bound, thereby exciting the unmodeled high-frequency dynamics, and yielding an unstable control system. Hence, it is concluded that existing adaptive control algorithms as they are presented in the literature referenced in this paper, cannot be used with confidence in practical designs where the plant contains unmodeled dynamics because instability is likely to result. Further understanding is required to ascertain how the currently implemented adaptive systems differ from the theoretical systems studied here and how further theoretical development can improve the robustness of adaptive controllers.
Book•
01 Jan 1985
TL;DR: In this article, the author's previous book ''New Generalized Functions and Multiplication of Distributions' (North-Holland, 1984) introduced ''new generalized functions'' in order to explain heuristic computations of physics and to give a meaning to any finite product of distributions.
Abstract: The author's previous book `New Generalized Functions and Multiplication of Distributions' (North-Holland, 1984) introduced `new generalized functions' in order to explain heuristic computations of Physics and to give a meaning to any finite product of distributions. The aim here is to present these functions in a more direct and elementary way. In Part I, the reader is assumed to be familiar only with the concepts of open and compact subsets of R , of C # functions of several real variables and with some rudiments of integration theory. Part II defines tempered generalized functions, i.e. generalized functions which are, in some sense, increasing at infinity no faster than a polynomial (as well as all their partial derivatives). Part III shows that, in this setting, the partial differential equations have new solutions. The results obtained show that this setting is perfectly adapted to the study of nonlinear partial differential equations, and indicate some new perspectives in this field.
TL;DR: In this article, a recent extension of sliding mode control is shown to handle nonlinearities, is highly robust to imprecise models, explicitly accounts for the presence of high-frequency unmodeled dynamics, and produces designs that are easy to understand.
Abstract: underwater vehicles present difficult control-system design problems due to their nonlinear dynamics, uncertain models, and the presence of disturbances that are difficult to measure or estimate. In this paper, a recent extension of sliding mode control is shown to handle these problems effectively. The method deals directly with nonlinearities, is highly robust to imprecise models, explicitly accounts for the presence of high-frequency unmodeled dynamics, and produces designs that are easy to understand. Using a nonlinear vehicle simulation, the relationship between model uncertainty and performance is examined. The results show that adequate controllers can be designed using simple nonlinear models, but that performance improves as model uncertainty is decreased and the improvements can be predicted quantitatively.
Book•
06 May 1985
TL;DR: In this paper, the authors introduce optical phase conjugation (OPC) and its application in four-wave mixing, and present specific features of OPC-SS and nonlinear mechanisms for FWM.
Abstract: 1. Introduction to Optical Phase Conjugation.- 2. Physics of Stimulated Scattering.- 3. Properties of Speckle-Inhomogeneous Fields.- 4. OPC by Backward Stimulated Scattering.- 5. Specific Features of OPC-SS.- 6. OPC in Four-Wave Mixing.- 7. Nonlinear Mechanisms for FWM.- 8. Other Methods of OPC.- References.
TL;DR: In this article, the effect of dissipation models on the accuracy, stability, and convergence of transonic airfoils is investigated using an implicit approximate factorization code (ARC2D).
Abstract: Various artificial dissipation models that are used with central difference algorithms for the Euler equations are analyzed for their effect on accuracy, stability, and convergence rates. In particular, linear and nonlinear models are investigated using an implicit approximate factorization code (ARC2D) for transonic airfoils. Fully implicit application of the dissipation models is shown to improve robustness and convergence rates. The treatment of dissipation models at boundaries will be examined. It will be shown that accurate, error free solutions with sharp shocks can be obtained using a central difference algorithm coupled with an appropriate nonlinear artificial dissipation model. I. Introduction T HE solution of the Euler equations using numerical techniques requires the use of either a differencing method with inherent dissipation or the addition of dissipation terms to a nondissipative scheme. This is because the Euler equations do not provide any natural dissipation mechanism (such as viscosity in the Navier-Stokes equations) that would eliminate high frequencies which are caused by nonlinearitie s and especially shocks. A variety of numerical algorithms and computer codes for the Euler equations have been developed. Methods such as MacCormack's1 explicit
TL;DR: In this paper, a time-space continuum model for transport of hydrothermal fluids in porous media is presented which provides for simultaneous, reversible and irreversible chemical reactions involving liquids, gases and minerals.
Book•
07 Aug 1985
TL;DR: Algebraic and Transcendental Equations Integrals Conservative Equations with Odd Nonlinearities Free Oscillations of Positively Damped Systems Self-Excited Oscillators Free oscillations of Systems with Quadratic Nonlinearity General Systems with Odd nonlinearities Nonlinear Systems Subject to Harmonic Excitations Multifrequency Excitations Parametric Excitations Boundary-Layer Problems Linear Equation with Variable Coefficients Differential Equations and a Large Parameter Solvability Conditions Index
Abstract: Algebraic and Transcendental Equations Integrals Conservative Equations with Odd Nonlinearities Free Oscillations of Positively Damped Systems Self-Excited Oscillators Free Oscillations of Systems with Quadratic Nonlinearities General Systems with Odd Nonlinearities Nonlinear Systems Subject to Harmonic Excitations Multifrequency Excitations Parametric Excitations Boundary-Layer Problems Linear Equations with Variable Coefficients Differential Equations with a Large Parameter Solvability Conditions Index
TL;DR: In this paper, an efficient method for sensitivity analysis of nonlinear initial value problems, which may include algebraic equations as well as ordinary differential equations, is described, which is implemented with the implicit integrator DASSL and demonstrated on a stiff industrial reaction model.
TL;DR: In this paper, the authors established a sharp instability theorem for the bound states of lowest energy of the nonlinear Klein-Gordon equation and the Schrodinger equation, where ε ≥ 0.
Abstract: We establish a sharp instability theorem for the bound states of lowest energy of the nonlinear Klein-Gordon equation,u
tt−◃u+f(u)=0, and the nonlinear Schrodinger equation, −iu
t−◃u+f(u)=0.
TL;DR: In this paper, a new implicit unconditionally stable high resolution total variation diminishing (TVD) scheme was proposed for steady state calculations, which is a member of a one parameter family of explicit and implicit second order accurate schemes developed by Harten for the computation of weak solutions of hyperbolic conservation laws.
TL;DR: In this article, a multiphase approach to the modeling of aquifer contamination by organic compounds is developed, which makes it possible to describe the simultaneous transport of a chemical contaminant in three physical forms: as a nonaqueous phase, as a soluble component of an aqueous phase and as a mobile fraction of a gas phase.
Abstract: A multiphase approach to the modeling of aquifer contamination by organic compounds is developed. This approach makes it possible to describe the simultaneous transport of a chemical contaminant in three physical forms: as a nonaqueous phase, as a soluble component of an aqueous phase, and as a mobile fraction of a gas phase. The contaminant may be composed of, at most, two distinct components, one of which may be volatile and slightly water soluble and the other of which is both nonvolatile and insoluble in water. Equations which describe this complex system are derived from basic conservation of mass principles by the application of volume averaging techniques and the incorporation of various constitutive relations and approximations. Effects of matrix and fluid compressibilities, gravity, phase composition, interphase mass exchange, capillarity, diffusion, and dispersion are all considered. The resulting mathematical model consists of a system of three nonlinear partial differential equations subject to two equilibrium constraints. These equations relate five unknowns: two capillary pressures and three mass fractions.
TL;DR: In this article, a more efficient method of computing the nonlinear transfer in a surface wave spectrum is developed which is symmetrical with respect to all wavenumbers of the resonant interaction quadruplets.
Abstract: A more efficient method of computing the nonlinear transfer in a surface wave spectrum is developed which is symmetrical with respect to all wavenumbers of the resonant interaction quadruplets. This enables a large number of computations to be carried out, as required for investigations of the spectral energy balance or the development of parameterizations. New results are presented for finite-depth surface waves. By filtering out regions in interaction phase space, the assumptions involved in the narrow-peak and local-interaction approx-imations are investigated. Both approximations are found to be useful but are generally not sufficiently accurate to replace exact computations or provide adequate parameterizations for wave models.
TL;DR: On considere le probleme de Dirichlet pour des equations elliptiques non lineaires d'ordre 2 pour une fonction reelle dans un domaine borne Ω de R n a frontiere lisse ∂ Ω as discussed by the authors.
Abstract: On considere le probleme de Dirichlet pour des equations elliptiques non lineaires d'ordre 2 pour une fonction reelle dans un domaine borne Ω de R n a frontiere lisse ∂Ω