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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 73 records · Page 4

Analysis of the electromagnetic scattering from an inlet geometry with lossy walls

One of the primary goals is to develop an approximate but sufficiently accurate analysis for the problem of electromagnetic (EM) plane wave scattering by an open ended, perfectly-conducting, semi-infinite hollow circular waveguide (or duct) with a thin, uniform layer of lossy or absorbing material on its inner wall, and with a simple termination inside. The less difficult but useful problem of the EM scattering by a two-dimensional (2-D), semi-infinite parallel plate waveguide with an impedance boundary condition on the inner walls was chosen initially for analysis. The impedance boundary condition in this problem serves to model a thin layer of lossy dielectric/ferrite coating on the otherwise perfectly-conducting interior waveguide walls. An approximate but efficient and accurate ray solution was obtained recently. That solution is presently being extended to the case of a moderately thick dielectric/ferrite coating on the walls so as to be valid for situations where the impedance boundary condition may not remain sufficiently accurate.

Myung, N. H.↗

Thoughts Without Content are Empty, Intuitions Without Concepts are Blind - Determinism and Contingency Revisited

Was the emergence of life a predictable outcome of chemical evolution on earth? Could evolution produce life very different from ours? These are one of the oldest questions in the field of the origin of life that not only have broad philosophical implications but also impact how we approach the problem from the methodological standpoint. Framing the issue in terms of the dichotomy between contingency and determinism is not a fortunate because these two terms in their conventional meaning are neither mutually exclusive nor jointly exhaustive. Determinism, represented in natural sciences by Newtonian physics, relies on the assumption that every event is causally determined by a chain of previous events. In the context of the origin of life it means that once the initial conditions on the early earth have been specified further evolution follows inevitably. Considering uncertainties about conditions on the prebiotic earth, many plausible sets of initial conditions can be defined, each followed by a separate deterministic trajectory. This conventional understanding of determinism does not admit contingency. Further, it has no implications for evaluating how many sets of initial conditions lead to the emergence of life. It appears that a better framing of the problem is as follows: given plausible sets of initial conditions on the early earth how probable and broadly spread are evolutionary trajectories that lead to life? Instead of undertaking an impossible task of specifying microscopic initial conditions for all components of the system one uses a reduced representation of this system and specify only a small set of essential macroscopic parameters, values (or ranges of values) of which can be identified, inferred or estimated from experiment, theory or historical record. The following evolutionary trajectories are still governed by laws of physics and chemistry but become probabilistic and "contingency" is admitted as variations in other variables in the system. A similar reasoning is common in other fields of science, for example in statistical mechanics. Some trajectories lead to life, perhaps in different forms, whereas others do not. Of our true interest is the ratio of these two outcomes. The issue of determinism does not directly enter the picture. The debate about the likelihood of the emergence of life is quite old. One view holds that the origin of life is an event governed by chance, and the result of so many random events (contingencies) is unpredictable. This view was eloquently expressed by Monod. In his book "Chance or Necessity" he argued that life was a product of "nature's roulette." In an alternative view, expressed in particular by deDuve and Morowitz, the origin of life is considered a highly probable or even inevitable event (although its details need not be determined in every respect). Only in this sense the origin of life can be considered a "deterministic event".

Pohorille, Andrew↗

The choice of numerical boundary conditions for hyperbolic systems

Two fundamental problems for mixed initial boundary value problems with applications in fluid mechanics are discussed. First, different stability properties are discussed which are of importance for long time integrations and steady state calculations. Secondly, a new numerical technique for problems with an artificial boundary is introduced.

Gustafson, B.↗

Hill Problem Analytical Theory to the Order Four. Application to the Computation of Frozen Orbits around Planetary Satellites

Frozen orbits of the Hill problem are determined in the double averaged problem, where short and long period terms are removed by means of Lie transforms. The computation of initial conditions of corresponding quasi periodic solutions in the non-averaged problem is straightforward for the perturbation method used provides the explicit equations of the transformation that connects the averaged and non-averaged models. A fourth order analytical theory reveals necessary for the accurate computation of quasi periodic, frozen orbits.

Lara, Martin↗

On the stability of the solutions of the general problem of three bodies

The extent through which the initial conditions of a given three-body system may be varied without completely changing the qualitative nature of the subsequent system evolution is investigated. It is assumed that the three masses are equal, all initial velocities are zero, the first two bodies initially lie on the x-axis, and the position of the third body is confined to a specific region of space. Analysis of the system evolution for different initial positions of the third body shows that there is a whole area or 'island' in the x-y plane throughout which the initial position of the third body may be moved in a continuous fashion to produce an evolution which also changes in a continuous manner. A Monte Carlo approach is adopted to determine the full extent of this island in the general problem. It is concluded that the stability of a full solution may be directly related to the size of its island in phase space.

Standish, E. M., Jr.↗

Least squares adjustment with relatively large observation errors, inaccurate initial approximations, or both

Least squares adjustment problems are considered in which the condition equations are nonlinear in both the observations and the adjustment parameters ('unknowns'). A solution algorithm is presented which takes into account the second (as well as the first) order derivatives in the adjustment residuals (observation errors) and the corrections to the initially available approximations to the adjustment parameters. The inclusion of second-order terms in the adjustment residuals is necessary whenever the adjustment residuals themselves cannot be regarded as negligible as compared to the adjustment parameters, i.e., whenever the linearized condition equations would no longer be practically equivalent to the rigorous ones. The consideration of second-order terms in the parameter corrections is completely independent of the second-order terms in the adjustment residuals.

Eichhorn, H.↗

Spherical means of solutions of partial differential equations in a conical region

The spherical means of the solutions of a linear partial differential equation Lu = f in a conical region are studied. The conical region is bounded by a surface generated by curvilinear ti surfaces. The spherical mean is the average of u over a constant ti surface. The conditions on the linear differential operator, L, and on the orthogonal coordinates (ti, eta, zeta) are established so that the spherical mean of the solution subjected to the appropriate boundary and initial conditions can be determined directly as a problem with only space variable. Conditions are then established so that the spherical mean of the solution in one concial region will be proportional to that of a known solution in another conical region. Applications to various problems of mathematical physics and their physical interpretations are presented.

Ting, L.↗

Program for the solution of multipoint boundary value problems of quasilinear differential equations

Linear equations are solved by a method of superposition of solutions of a sequence of initial value problems. For nonlinear equations and/or boundary conditions, the solution is iterative and in each iteration a problem like the linear case is solved. A simple Taylor series expansion is used for the linearization of both nonlinear equations and nonlinear boundary conditions. The perturbation method of solution is used in preference to quasilinearization because of programming ease, and smaller storage requirements; and experiments indicate that the desired convergence properties exist although no proof or convergence is given.

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On the advantages of the vorticity-velocity formulation of the equations of fluid dynamics

The mathematical properties of the pressure-velocity and vorticity-velocity formulations of the equations of viscous flow are compared. It is shown that a vorticity-velocity formulation exists which has the interesting property that non-inertial effects only enter the problem through the implementation of initial and boundary conditions. This valuable characteristic, along with other advantages of the vorticity-velocity approach, are discussed in detail.

Speziale, C. G.↗

On the advantages of the vorticity-velocity formulation of the equations of fluid dynamics

The mathematical properties of the pressure-velocity and vorticity-velocity formulations of the equations of viscous flow are compared. It is shown that a vorticity-velocity formulation exists which has the interesting property that noninertial effects only enter into the problem through the implementation of initial and boundary conditions. This valuable characteristic, along with other advantages of the vorticity-velocity approach, are discussed in detail.

Speziale, Charles G.↗

Dynamical approach study of spurious steady-state numerical solutions of nonlinear differential equations. Part 1: The ODE connection and its implications for algorithm development in computational fluid dynamics

Spurious stable as well as unstable steady state numerical solutions, spurious asymptotic numerical solutions of higher period, and even stable chaotic behavior can occur when finite difference methods are used to solve nonlinear differential equations (DE) numerically. The occurrence of spurious asymptotes is independent of whether the DE possesses a unique steady state or has additional periodic solutions and/or exhibits chaotic phenomena. The form of the nonlinear DEs and the type of numerical schemes are the determining factor. In addition, the occurrence of spurious steady states is not restricted to the time steps that are beyond the linearized stability limit of the scheme. In many instances, it can occur below the linearized stability limit. Therefore, it is essential for practitioners in computational sciences to be knowledgeable about the dynamical behavior of finite difference methods for nonlinear scalar DEs before the actual application of these methods to practical computations. It is also important to change the traditional way of thinking and practices when dealing with genuinely nonlinear problems. In the past, spurious asymptotes were observed in numerical computations but tended to be ignored because they all were assumed to lie beyond the linearized stability limits of the time step parameter delta t. As can be seen from the study, bifurcations to and from spurious asymptotic solutions and transitions to computational instability not only are highly scheme dependent and problem dependent, but also initial data and boundary condition dependent, and not limited to time steps that are beyond the linearized stability limit.

Yee, H. C.↗

Dynamical approach study of spurious steady-state numerical solutions of nonlinear differential equations. I - The dynamics of time discretization and its implications for algorithm development in computational fluid dynamics

Spurious stable as well as unstable steady state numerical solutions, spurious asymptotic numerical solutions of higher period, and even stable chaotic behavior can occur when finite difference methods are used to solve nonlinear differential equations (DE) numerically. The occurrence of spurious asymptotes is independent of whether the DE possesses a unique steady state or has additional periodic solutions and/or exhibits chaotic phenomena. The form of the nonlinear DEs and the type of numerical schemes are the determining factor. In addition, the occurrence of spurious steady states is not restricted to the time steps that are beyond the linearized stability limit of the scheme. In many instances, it can occur below the linearized stability limit. Therefore, it is essential for practitioners in computational sciences to be knowledgeable about the dynamical behavior of finite difference methods for nonlinear scalar DEs before the actual application of these methods to practical computations. It is also important to change the traditional way of thinking and practices when dealing with genuinely nonlinear problems. In the past, spurious asymptotes were observed in numerical computations but tended to be ignored because they all were assumed to lie beyond the linearized stability limits of the time step parameter delta t. As can be seen from the study, bifurcations to and from spurious asymptotic solutions and transitions to computational instability not only are highly scheme dependent and problem dependent, but also initial data and boundary condition dependent, and not limited to time steps that are beyond the linearized stability limit.

Yee, H. C.↗

Application of the Hughes-LIU algorithm to the 2-dimensional heat equation

An implicit explicit algorithm for the solution of transient problems in structural dynamics is described. The method involved dividing the finite elements into implicit and explicit groups while automatically satisfying the conditions. This algorithm is applied to the solution of the linear, transient, two dimensional heat equation subject to an initial condition derived from the soluton of a steady state problem over an L-shaped region made up of a good conductor and an insulating material. Using the IIT/PRIME computer with virtual memory, a FORTRAN computer program code was developed to make accuracy, stability, and cost comparisons among the fully explicit Euler, the Hughes-Liu, and the fully implicit Crank-Nicholson algorithms. The Hughes-Liu claim that the explicit group governs the stability of the entire region while maintaining the unconditional stability of the implicit group is illustrated.

Malkus, D. S.↗

Plasma oscillations and Landau damping

The Fourier-Hermite expansion is used to follow the time development of a non-analytic initial perturbation of the linearized Vlasov-Poisson system. The calculations differ from some previous applications of the Fourier-Hermite expansion in that they relax certain symmetry conditions on the distribution functions and in that many coefficients are required to describe the initial conditions. The results confirm Weitzner's prediction of the asymptotic t to the -3rd time dependence for this problem, and exhibit the way in which this behavior develops. An appendix outlines the way in which the initial conditions are expanded in Hermite functions.

Crownfield, F. R., Jr.↗

Malfunction of Television Camera Monitor on Command Module

The command module television camera monitor exhibited loss of horizontal synchronization during the initial usage. This condition cleared and performance of the monitor was normal until the press conference telecast during the transearth coast phase. At that time, the monitor had the same horizontal synchronization problem reported during the initial usage. The horizontal hold control adjustment would not correct the condition. The monitor was turned off for approximately 5 minutes, then turned back on, after which the monitor's picture was normal. The loss of horizontal synchronization was most likely caused by either an intermittent condition in the precision voltage regulator circuit assembly in the low voltage power supply, or the shift of the stable range of the horizontal potentiometer setting when warming up after turn-on.

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Indirect learning control for nonlinear dynamical systems

In a previous paper, learning control algorithms were developed based on adaptive control ideas for linear time variant systems. The learning control methods were shown to have certain advantages over their adaptive control counterparts, such as the ability to produce zero tracking error in time varying systems, and the ability to eliminate repetitive disturbances. In recent years, certain adaptive control algorithms have been developed for multi-body dynamic systems such as robots, with global guaranteed convergence to zero tracking error for the nonlinear system euations. In this paper we study the relationship between such adaptive control methods designed for this specific class of nonlinear systems, and the learning control problem for such systems, seeking to converge to zero tracking error in following a specific command repeatedly, starting from the same initial conditions each time. The extension of these methods from the adaptive control problem to the learning control problem is seen to be trivial. The advantages and disadvantages of using learning control based on such adaptive control concepts for nonlinear systems, and the use of other currently available learning control algorithms are discussed.

Ryu, Yeong Soon↗