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An approximation framework is presented for computation (in finite dimensional spaces) of Riccati operators that can be guaranteed to converge to the Riccati operator in feedback controls for abstract evolution systems in a Hilbert space. It is indicated how these results may be used in the linear optimal regulator problem for a large class of parabolic systems.
New convenient stability criteria are provided in this paper for a large class of finite difference approximations to initial-boundary value problems associated with the hyperbolic system u sub t = au sub x + Bu + f in the quarter plane x or = 0, t or = 0. Using the new criteria, stability is easily established for numerous combinations of well known basic schemes and boundary conditins, thus generalizing many special cases studied in recent literature.
It is pointed out that preliminary design and optimization studies for new aerospace vehicles require techniques which can calculate aerodynamic heating rates accurately and efficiently. The method employed to calculate the flow field depends to a large extent on the shape of the vehicle, Mach number, Reynolds number, and Knudsen number. In the case of the aero-assisted orbital transfer vehicle (AOTV), a substantial portion of the flight will be in the transitional regime between continuum and free molecule flow. The present paper discusses some approximate methods which have been used to calculate heating rates on high-speed vehicles. Attention is given to the stagnation point and leading edges, the downstream region, the axisymmetric analog, laminar and turbulent heating rates, transition heating rates, gas models, and three-dimensional applications.
An approximate analysis of atmospheric effects on wake vortex motion and decay is presented. The effects of density stratification, turbulence, and Reynolds number are combined in a single model so that the relative importance of different parameters can be determined. Predicted wake motion is shown to be in good agreement with limited data from both ground facility and flight test measurements taken under low turbulence conditions. Wake decay was found to depend strongly on both density stratification and turbulence. For typical levels of turbulence, wake decay was found to result from the 'Crow instability' except under strongly stratified conditions.
New convenient stability criteria are provided for a large class of finite difference approximations to initial-boundary value problems associated with the hyperbolic system u sub t = Au sub x + Bu + f in the quarter plane x greater than or equal to 0, t greater than or equal to 0. The criteria are used to easily establish stability for numerous combinations of well known basic schemes and boundary conditions, thus generalizing many special cases studied in the recent literature. A number of examples are examined, including the unitary unconditionally stable Crank-Nicholson scheme and an almost-dissipative unconditionally stable backward Euler scheme.
An automatic history matching algorithm is developed based on bi-cubic spline approximations of permeability and porosity distributions and on the theory of regularization to estimate permeability or porosity in a single-phase, two-dimensional real reservoir from well pressure data. The regularization feature of the algorithm is used to convert the ill-posed history matching problem into a well-posed problem. The algorithm employs the conjugate gradient method as its core minimization method. A number of numerical experiments are carried out to evaluate the performance of the algorithm. Comparisons with conventional (non-regularized) automatic history matching algorithms indicate the superiority of the new algorithm with respect to the parameter estimates obtained. A quasioptimal regularization parameter is determined without requiring a priori information on the statistical properties of the observations.
The problem of optimally assigning the modules of a parallel/pipelined program over the processors of a multiple computer system under certain restrictions on the interconnection structure of the program as well as the multiple computer system was considered. For a variety of such programs it is possible to find linear time if a partition of the program exists in which the load on any processor is within a certain bound. This method, when combined with a binary search over a finite range, provides an approximate solution to the partitioning problem. The specific problems considered were: a chain structured parallel program over a chain-like computer system, multiple chain-like programs over a host-satellite system, and a tree structured parallel program over a host-satellite system. For a problem with m modules and n processors, the complexity of the algorithm is no worse than O(mnlog(W sub T/epsilon)), where W sub T is the cost of assigning all modules to one processor and epsilon the desired accuracy.
For a nonlinear system with output derivative x = f(x) and y = h(x), two types of linearizations about a point x(0) in state space are considered. One is the usual Taylor series approximation, and the other is defined by linearizing the appropriate Lie derivatives of the output with respect to f about x(0). The latter is called the obvservation model and appears to be quite natural for observation. It is noted that there is a coordinate system in which these two kinds of linearizations agree. In this coordinate system, a technique to construct an observer is introduced.
The purpose of this paper is to achieve more versatile, convenient stability criteria for a wide class of finite-difference approximations to initial boundary value problems associated with the hyperbolic system u sub t = au sub x + Bu + f in the quarter-plane x greater than or equal to 0, t greater than or equal to 0. With these criteria, stability is easily established for a large number of examples, thus incorporating and generalizing many of the cases studied in recent literature.
The report provides approximations for estimating the capacitance and the ratio of electric field strength to potential for a certain class of electrode geometries. The geometry consists of an electrode near a grounded plane, with the electrode being a surface of revolution about the perpendicular to the plane. Some examples which show the accuracy of the capacitance estimate and the accuracy of the estimate of electric field over potential can be found in the appendix. When it is possible to estimate the potential of the electrode, knowing the ratio of electric field to potential will help to determine if an electrostatic discharge is likely to occur. Knowing the capacitance will help to determine the strength of the discharge (the energy released by it) if it does occur. A brief discussion of discharge mechanisms is given. The medium between the electrode and the grounded plane may be a neutral gas, a vacuum, or an unchanged homogeneous isotropic dielectric.
A new approximate LU factorization scheme is developed to solve the steady state Reynolds-averaged Navier-Stokes (NS) equations. Central differencing is used for both implicit and explicit operator and special care is taken to obtain well-conditioned factors on the implicit side. The scheme is then analyzed and optimized according to a simple linear analysis. It is unconditionally stable for the model hyperbolic equation in both two- and three-dimensions. However, the requirement for well-conditioned factors has essentially limited the effective time step the scheme can achieve. Supersonic and transonic three-dimensinal flows past a hemisphere cylinder are computed to demonstrate the convergence characteristics of the scheme. A good convergence rate is achieved for the inviscid case. Finally, an explicit eigenvector annihilation procedure is adopted successfully to remove the stiffness caused by the fine grid spacing for viscous flows.
Radiative transfer through sharp, quasi-static atmospheres containing mostly hydrogen is considered at densities low enough that scattering dominates absorption and collisional excitations are negligible. It is found that the balance between photoionization and radiative recombination which governs the atomic level populations greatly reduces the effective absorptive opacity. Approximate results for the emergent continuum spectral flux are obtained, significantly different than if local thermodynamic equilibrium level populations were assumed. The flux jumps at the photoionization thresholds are relatively small for the photospheric temperatures T sub p(v) greater than or about 6000 K considered, and T sub p increases toward the far-ultraviolet. It appears that the lack of a Balmer jump in spectra of Type II supernovae implies that the flux is diluted below that of a blackbody at the same color temperature, which increases the value of the Hubble constant obtained by the Baade (1926) method.
Large plasmaspheric electric fields at L is approximately 2 measured by the S3-3 satellite during strong geomagnetic activity are reported. Since these measurements have amplitudes comparable to those of the local corotation electric field, during such events the plasmasphere is expected to get strongly altered event at such low L-values. Furthermore, those measurements could contribute to the understanding of the physics of the convection/electric field penetration to the low latitude plasmaphere as well as the disturbed dynamo, during strong geomagnetic activity. For this purpose, critical parameters related to geomagnetic activity are also presented for the reported electric field events.
An implicit approximate factorization algorithm is employed to quantify the parametric effects of Courant number and artificial smoothing on numerical solutions of the unsteady 3-D Euler equations for a windmilling propeller (low speed) flow field. The results show that propeller global or performance chracteristics vary strongly with Courant number and artificial dissipation parameters, though the variation is such less severe at high Courant numbers. Candidate sets of Courant number and dissipation parameters could result in parameter-dependent solutions. Parameter-independent numerical solutions can be obtained if low values of the dissipation parameter-time step ratio are used in the computations. Furthermore, it is realized that too much artificial damping can degrade numerical stability. Finally, it is demonstrated that highly resolved meshes may, in some cases, delay convergence, thereby suggesting some optimum cell size for a given flow solution. It is suspected that improper boundary treatment may account for the cell size constraint.
A theoretical model employing one-dimensional (depth) transport equations to describe vertical redistribution of ocean-floor and lake-floor sediment (particulates, volcanic ash, microtektites, or radioactive tracers) by episodic and nonepisodic events including bioturbation is developed analytically and demonstrated. The principles underlying the model are explained; the model equations are derived; the inverse problem of identifying the depth-dependent bioturbation coefficient is addressed; two approximation theorems are presented; and numerical results for two sample problems are presented graphically. It is suggested that compatification, porosity effects, and depth-dependent sedimentation be taken into account when formulating future models.
A factorization approach is presented for deriving approximations to the optimal feedback gain for the linear regulator-quadratic cost problem associated with time-varying functional differential equations with control delays. The approach is based on a discretization of the state penalty which leads to a simple structure for the feedback control law. General properties of the Volterra factors of Hilbert-Schmidt operators are then used to obtain convergence results for the feedback kernels.
A system identification technique is developed for classes of distributed systems using finite element approximations. Vibrating systems represented by partial differential equations have physical parameters associated with mass, stiffness, and damping distributions which need to be known in order to properly control and design mathematical models of the system. In order to identify these parameters a weighted least-squares algorithm and modified Newton-Raphson method is used for the identification process. The theory and technique is demonstrated by estimating the system parameters of a vibrating cantilever beam made up of several different structural properties.
Report presents algorithm for calculating feedback gain for control of hereditary dynamical systems with control delay. Problem is to approximate optimal feedback gain that minimizes cost function of state and control. Theory applicable to design of controllers for mechanical systems subject to thermal deformation, electrical systems with delay, electrical systems with plasma components, and other systems that exhibit memory.