Homogeneous row-continuous bivariate Markov chains with boundaries

Bibliography: p. 28."August 1981."U.S.A.F. OSR Grant Number AFOSR-79-0043 U. S. Air Force Geophysics Laboratory Grant Number F19628-80-C-0003 National Science Foundation Grant Number NSF/ECS 79-19880by J. Keilson, M. Zachmann

Application of the scalar and vector potentials to the aerodynamics of jets

The applicability of a method based on the Stokes potentials (vector and scalar potentials) to computations associated with the aerodynamics of jets was examined. The aerodynamic field near the nozzle could be represented and that the influence of a nonuniform velocity profile at the nozzle exit plane could be determined. Also computations were made for an axisymmetric jet exhausting into a quiescient atmosphere. The velocity at the axis of the jet, and the location of the half-velocity points along the jet yield accurate aerodynamic field computations. Inconsistencies among the different theoretical characterizations of jet flowfields are shown

Dynamic sensitivity analysis of biological systems

BACKGROUND: A mathematical model to understand, predict, control, or even design a real biological system is a central theme in systems biology. A dynamic biological system is always modeled as a nonlinear ordinary differential equation (ODE) system. How to simulate the dynamic behavior and dynamic parameter sensitivities of systems described by ODEs efficiently and accurately is a critical job. In many practical applications, e.g., the fed-batch fermentation systems, the system admissible input (corresponding to independent variables of the system) can be time-dependent. The main difficulty for investigating the dynamic log gains of these systems is the infinite dimension due to the time-dependent input. The classical dynamic sensitivity analysis does not take into account this case for the dynamic log gains. RESULTS: We present an algorithm with an adaptive step size control that can be used for computing the solution and dynamic sensitivities of an autonomous ODE system simultaneously. Although our algorithm is one of the decouple direct methods in computing dynamic sensitivities of an ODE system, the step size determined by model equations can be used on the computations of the time profile and dynamic sensitivities with moderate accuracy even when sensitivity equations are more stiff than model equations. To show this algorithm can perform the dynamic sensitivity analysis on very stiff ODE systems with moderate accuracy, it is implemented and applied to two sets of chemical reactions: pyrolysis of ethane and oxidation of formaldehyde. The accuracy of this algorithm is demonstrated by comparing the dynamic parameter sensitivities obtained from this new algorithm and from the direct method with Rosenbrock stiff integrator based on the indirect method. The same dynamic sensitivity analysis was performed on an ethanol fed-batch fermentation system with a time-varying feed rate to evaluate the applicability of the algorithm to realistic models with time-dependent admissible input. CONCLUSION: By combining the accuracy we show with the efficiency of being a decouple direct method, our algorithm is an excellent method for computing dynamic parameter sensitivities in stiff problems. We extend the scope of classical dynamic sensitivity analysis to the investigation of dynamic log gains of models with time-dependent admissible input

Optimal symmetric flight with an intermediate vehicle model

Optimal flight in the vertical plane with a vehicle model intermediate in complexity between the point-mass and energy models is studied. Flight-path angle takes on the role of a control variable. Range-open problems feature subarcs of vertical flight and singular subarcs. The class of altitude-speed-range-time optimization problems with fuel expenditure unspecified is investigated and some interesting phenomena uncovered. The maximum-lift-to-drag glide appears as part of the family, final-time-open, with appropriate initial and terminal transient exceeding level-flight drag, some members exhibiting oscillations. Oscillatory paths generally fail the Jacobi test for durations exceeding a period and furnish a minimum only for short-duration problems

Development of an integrated BEM approach for hot fluid structure interaction

The development of a boundary element formulation for the study of hot fluid-structure interaction in earth-to-orbit engine hot section components is described. The initial primary thrust of the program to date was directed quite naturally toward the examination of fluid flow, since boundary element methods for fluids are at a much less developed state. This required the development of integral formulations for both the solid and fluid, and some preliminary infrastructural enhancements to a boundary element code to permit coupling of the fluid-structure problem. Boundary element formulations are implemented in two dimensions for both the solid and the fluid. The solid is modeled as an uncoupled thermoelastic medium under plane strain conditions, while several formulations are investigated for the fluid. For example, both vorticity and primitive variable approaches are implemented for viscous, incompressible flow, and a compressible version is developed. All of the above boundary element implementations are incorporated in a general purpose two-dimensional code. Thus, problems involving intricate geometry, multiple generic modeling regions, and arbitrary boundary conditions are all supported

Analysis of the Brinkman equation as a model for flow in porous media

The fundamental solution or Green's function for flow in porous media is determined using Stokesian dynamics, a molecular-dynamics-like simulation method capable of describing the motions and forces of hydrodynamically interacting particles in Stokes flow. By evaluating the velocity disturbance caused by a source particle on field particles located throughout a monodisperse porous medium at a given value of volume fraction of solids ø, and by considering many such realizations of the (random) porous medium, the fundamental solution is determined. Comparison of this fundamental solution with the Green's function of the Brinkman equation shows that the Brinkman equation accurately describes the flow in porous media for volume fractions below 0.05. For larger volume fractions significant differences between the two exist, indicating that the Brinkman equation has lost detailed predictive value, although it still describes qualitatively the behavior in moderately concentrated porous media. At low ø where the Brinkman equation is known to be valid, the agreement between the simulation results and the Brinkman equation demonstrates that the Stokesian dynamics method correctly captures the screening characteristic of porous media. The simulation results for ø ≥ 0.05 may be useful as a basis of comparison for future theoretical work

An inverse method for obtaining the attenuation profile and small variations in the sound speed and density profiles of the ocean bottom

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution May 1985The acoustic properties of marine sediments have a direct effect on the propagation of sound in the ocean. In the frequency range of interest (50 - 500 Hz) the sediment can be modelled as a fluid. Assuming horizontal stratification of the ocean bottom, the acoustic parameters of interest are the compressional wave speed, the compressional wave attenuation and density as a function of depth. An inverse method based on a perturbation technique is presented in this thesis for the determination of these parameters. A monochromatic source experiment is proposed because of the desirability of such an experiment for determining the acoustic properties of an anelastic medium. The input information is the plane wave reflection coerricent as a function of the angle of incidence at a fixed frequency. A nonlinear integral equation relating the variations of these acoustic properties from a known reference value to the plane wave reflection coefficient is derived. This is then linearised using the Born approximation. The region of validity of the Born approximation is derived and based on this the optimum angular aperture for the input data is obtained. The linearised integral equation is a Fredholm integral equation of the first kind. An acceptable stable solution of the integral equation is obtained by imposing a priori constraints on the solution. The inversion method is tested using synthetic data and inversions are carried out for various examples of the attenuation coefficient profile and the sound speed profile. The results obtained with noise free data show good agreement between the true profiles and the reconstructed profiles. The resolution obtainable with the data set is studied using the resolving power theory of Backus and Gilbert and the inversion method is shown to provide adequate resolution. The effect of additive noise in data is examined and inversions performed with noisy data yielded stable acceptable results.I acknowledge the financial support provided by the education office in the Woods Hole Oceanographic Institution and the Office of Naval Research