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At least 829 records · Page 46

Estimation in nonlinear systems with transport delay.

The problem of estimation of state in nonlinear dynamical systems containing time delays is studied. The plant is specified by a set of nonlinear differential-difference equations. Observations are a nonlinear function of current and/or delayed states. Both contain additive disturbances. The criterion used for the optimal estimates is the integral of the weighted squared error. Using the theory of the calculus of variations, equations are developed for the estimation. They are first expressed in the form of a split boundary value problem, which is then converted to an initial value problem for on-line estimation. The result yields a sequential estimation scheme in which filtered and smoothed estimates are computed in a sequential manner. The applicability of the procedure is demonstrated by a practical example.

Stoller, R. L.↗

A Stable and Conservative Interface Treatment of Arbitrary Spatial Accuracy

Stable and accurate interface conditions are derived for the linear advection-diffusion equation. The conditions are functionally independent of the spatial order of accuracy and rely only on the form of the discrete operator. We focus on high-order finite-difference operators that satisfy the summation-by-parts (SBP) property. We prove that stability is a natural consequence of the SBP operators used in conjunction with the new boundary conditions. In addition, we show that the interface treatments are conservative. New finite-difference operators of spatial accuracy up to sixth order are constructed: these operators satisfy the SBP property. Finite-difference operators are shown to admit design accuracy (p(sup th)-order global accuracy) when (p - 1)(sup th)-order stencil closures are used near the boundaries if the physical boundary conditions are implemented to at least p(sup th)-order accuracy. Stability and accuracy are demonstrated on the nonlinear Burgers' equation for an twelve-subdomain problem with randomly distributed interfaces.

Carpenter, Mark H.↗

Large-amplitude hydromagnetic waves

Several aspects of the theory of large-amplitude hydromagnetic waves and their behavior in the interplanetary medium are examined. The characteristic modes of the full (i.e., nonlinearized) MHD equations and their modification by collisionless and finite-frequency effects are considered. Special attention is paid to the transverse Alfven mode, which is undamped and characterized by strictly constant pressure, density, and B; this seems to be the predominant propagating fluctuation at 1 AU. It is shown that its propagation in the small-wavelength (WKB) approximation is essentially identical to that of the small-amplitude Alfven wave of linearized theory. It is also suggested that its presence at 1 AU may provide a natural explanation of the observed power anisotropy of the fluctuations. A second-order analysis is used to study fluctuations that are not characteristic modes. It is found that for a small range of propagation directions, and subject to third-order effects, a finite-amplitude wave can exist that is linearly polarized with delta B perpendicular to both B sub zero and k; such a wave can damp nonlinearly.

Barnes, A.↗

Nonlinear Dynamics of Cantilever-Sample Interactions in Atomic Force Microscopy

The interaction of the cantilever tip of an atomic force microscope (AFM) with the sample surface is obtained by treating the cantilever and sample as independent systems coupled by a nonlinear force acting between the cantilever tip and a volume element of the sample surface. The volume element is subjected to a restoring force from the remainder of the sample that provides dynamical equilibrium for the combined systems. The model accounts for the positions on the cantilever of the cantilever tip, laser probe, and excitation force (if any) via a basis set of set of orthogonal functions that may be generalized to account for arbitrary cantilever shapes. The basis set is extended to include nonlinear cantilever modes. The model leads to a pair of coupled nonlinear differential equations that are solved analytically using a matrix iteration procedure. The effects of oscillatory excitation forces applied either to the cantilever or to the sample surface (or to both) are obtained from the solution set and applied to the to the assessment of phase and amplitude signals generated by various acoustic-atomic force microscope (A-AFM) modalities. The influence of bistable cantilever modes of on AFM signal generation is discussed. The effects on the cantilever-sample surface dynamics of subsurface features embedded in the sample that are perturbed by surface-generated oscillatory excitation forces and carried to the cantilever via wave propagation are accounted by the Bolef-Miller propagating wave model. Expressions pertaining to signal generation and image contrast in A-AFM are obtained and applied to amplitude modulation (intermittent contact) atomic force microscopy and resonant difference-frequency atomic force ultrasonic microscopy (RDF-AFUM). The influence of phase accumulation in A-AFM on image contrast is discussed, as is the effect of hard contact and maximum nonlinearity regimes of A-AFM operation.

Cantrell, John H.↗

Aerodynamic simulation on massively parallel systems

This paper briefly addresses the computational requirements for the analysis of complete configurations of aircraft and spacecraft currently under design to be used for advanced transportation in commercial applications as well as in space flight. The discussion clearly shows that massively parallel systems are the only alternative which is both cost effective and on the other hand can provide the necessary TeraFlops, needed to satisfy the narrow design margins of modern vehicles. It is assumed that the solution of the governing physical equations, i.e., the Navier-Stokes equations which may be complemented by chemistry and turbulence models, is done on multiblock grids. This technique is situated between the fully structured approach of classical boundary fitted grids and the fully unstructured tetrahedra grids. A fully structured grid best represents the flow physics, while the unstructured grid gives best geometrical flexibility. The multiblock grid employed is structured within a block, but completely unstructured on the block level. While a completely unstructured grid is not straightforward to parallelize, the above mentioned multiblock grid is inherently parallel, in particular for multiple instruction multiple datastream (MIMD) machines. In this paper guidelines are provided for setting up or modifying an existing sequential code so that a direct parallelization on a massively parallel system is possible. Results are presented for three parallel systems, namely the Intel hypercube, the Ncube hypercube, and the FPS 500 system. Some preliminary results for an 8K CM2 machine will also be mentioned. The code run is the two dimensional grid generation module of Grid, which is a general two dimensional and three dimensional grid generation code for complex geometries. A system of nonlinear Poisson equations is solved. This code is also a good testcase for complex fluid dynamics codes, since the same datastructures are used. All systems provided good speedups, but message passing MIMD systems seem to be best suited for large miltiblock applications.

Haeuser, Jochem↗

Turbofan Engine Simulated in a Graphical Simulation Environment

Recently, there has been an increase in the development of intelligent engine technology with advanced active component control. The computer engine models used in these control studies are component-level models (CLM), models that link individual component models of state space and nonlinear algebraic equations, written in a computer language such as Fortran. The difficulty faced in performing control studies on Fortran-based models is that Fortran is not supported with control design and analysis tools, so there is no means for implementing real-time control. It is desirable to have a simulation environment that is straightforward, has modular graphical components, and allows easy access to health, control, and engine parameters through a graphical user interface. Such a tool should also provide the ability to convert a control design into real-time code, helping to make it an extremely powerful tool in control and diagnostic system development. Simulation time management is shown: Mach number versus time, power level angle versus time, altitude versus time, ambient temperature change versus time, afterburner fuel flow versus time, controller and actuator dynamics, collect initial conditions, CAD output, and component-level model: CLM sensor, CAD input, and model output. The Controls and Dynamics Technologies Branch at the NASA Glenn Research Center has developed and demonstrated a flexible, generic turbofan engine simulation platform that can meet these objectives, known as the Modular Aero-Propulsion System Simulation (MAPSS). MAPSS is a Simulink-based implementation of a Fortran-based, modern high pressure ratio, dual-spool, low-bypass, military-type variable-cycle engine with a digital controller. Simulink (The Mathworks, Natick, MA) is a computer-aided control design and simulation package allows the graphical representation of dynamic systems in a block diagram form. MAPSS is a nonlinear, non-real-time system composed of controller and actuator dynamics (CAD) and component-level model (CLM) modules. The controller in the CAD module emulates the functionality of a digital controller, which has a typical update rate of 50 Hz. The CLM module simulates the dynamics of the engine components and uses an update rate of 2500 Hz, which is needed to iterate to balance mass and energy among system components. The actuators in the CAD module use the same sampling rate as those in the CLM. Two graphs of normalized spool speed versus time in seconds and one graph of normalized average metal temperature versus time in seconds is shown. MAPSS was validated via open-loop and closed-loop comparisons with the Fortran simulation. The preceding plots show the normalized results of a closed-loop comparison looking at three states of the model: low-pressure spool speed, high-pressure spool speed, and the average metal temperature measured from the combustor to the high-pressure turbine. In steady state, the error between the simulations is less than 1 percent. During a transient, the difference between the simulations is due to a correction in MAPSS that prevents the gas flow in the bypass duct inlet from flowing forward instead of toward the aft end, which occurs in the Fortran simulation. A comparison between MAPSS and the Fortran model of the bypass duct inlet flow for power lever angles greater than 35 degrees is shown.

Parker, Khary I.↗

Computer program determines chemical equilibria in complex systems

Computer program numerically solves nonlinear algebraic equations for chemical equilibrium based on iteration equations independent of choice of components. This program calculates theoretical performance for frozen and equilibrium composition during expansion and Chapman-Jouguet flame properties, studies combustion, and designs hardware.

Gordon, S.↗

Numerical integration and Riemann-Stieltjes sums.

Numerical integration based on definition of Riemann integral, describing application to nonlinear integral equations of isotropic scattering of radiation in plane parallel atmosphere

RIEMANN INTEGRAL↗