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NASA NTRS1992

Boundary formulations for sensitivities of three-dimensional stress invariants

The direct, singular, boundary element analysis (BEA) formulation has been shown to provide a basis for a computationally efficient and accurate shape structural design sensitivity analysis (DSA) approach for three-dimensional solid objects. Within the boundary element analysis context, the theoretical formulation for sensitivities of important stress-related quantities including principal and deviatoric stresses, von Mises, maximum shear, and other stress invariants are presented, both for the surface as well as the interior of a continuum structure. Numerical results are given to demonstrate the accuracy of this approach.

Guru Prasad, K.↗
NASA NTRS1992

The application of the principles of invariance to the radiative transfer equation in plant canopies

Solutions of the radiative transfer equation describing photon interactions with vegetation canopies are important in remote sensing since they provide the canopy reflectance distribution required in the interpretation of satellite acquired information. The general one-dimensional two-angle transport problem for a finite copy of arbitrary leaf angle distribution is considered. Analytical solutions are obtained in terms of generalized Chandrasekhar's X- and Y-functions by invoking the principles of invariance. A critical step in the formulation involves the decomposition of the integral of the scattering phase function into a product of known functions of the incident and scattered photon directions. Several simplified cases previously considered in the literature are derived from the generalized solution. Various symmetries obeyed by the scattering operator and reciprocity relations are formally proved.

Ganapol, B. D.↗
NASA NTRS1992

Non-iterative computation of the infimum in H-infinity-optimization for plants with invariant zeros on the j-omega axis

A simple and noniterative procedure for the computation of the exact value of the infimum in the singular H-infinity optimization problem is presented. The problem formulation is general, and no restrictions are placed on the finite and infinite zero structures of the system and on the direct feedthrough terms between the control input and the controlled output variables and between the disturbance input and the measurement output variables. The method is applicable to a class of singular H-infinity optimization problems for which the transfer functions from the control input to the controlled output and from the disturbance input to the measurement output satisfy certain geometric conditions. In particular, the authors extend the result of B. M. Chen et al. (1991) by allowing these two transfer functions to have invariant zeros on the j-omega axis.

Chen, Ben M.↗
NASA NTRS1992

Invariant two-dimensional structures of vorticity field in nonviscous fluid

It is shown that a fluid flow which are invariant under translations along their vorticity field directions can be described in terms of a formally 2D system. Its nonviscous behavior of the scalar vorticity is governed by Hamiltonian dynamics, similar to the 2D line vortex case. Applying a statistical mechanical method, the equilibrium distribution of the vorticity field for such a general 2D system is shown to obey a nonlinear partial differential equation that is a generalization of the sinh-Poisson equation derived by Montgomery and Joyce (1973, 1974). Thus, if the domain containing the fluid is finite, similar negative temperature states may occur and the distribution of the vorticity intensity may become localized in space. The results are believed to have applications in studying large-scale partial and temporal properties of flows having small but nonzero viscosity. The analysis can probably be extended to other fluid systems with curved magnetic field lines.

Chen, Hudong↗
NASA NTRS1993

A Galilean and tensorial invariant k-epsilon model for near wall turbulence

A k-epsilon model is proposed for wall bounded turbulent flows. In this model, the eddy viscosity is characterized by a turbulent velocity scale and a turbulent time scale. The time scale is bounded from below by the Kolmogorov time scale. The dissipation rate equation is reformulated using this time scale and no singularity exists at the wall. A new parameter R = k/S(nu) is introduced to characterize the damping function in the eddy viscosity. This parameter is determined by local properties of both the mean and the turbulent flow fields and is free from any geometry parameter. The proposed model is then Galilean and tensorial invariant. The model constants used are the same as in the high Reynolds number Standard k-epsilon Model. Thus, the proposed model will also be suitable for flows far from the wall. Turbulent channel flows and turbulent boundary layer flows with and without pressure gradients are calculated. Comparisons with the data from direct numerical simulations and experiments show that the model predictions are excellent for turbulent channel flows and turbulent boundary layers with favorable pressure gradients, good for turbulent boundary layers with zero pressure gradients, and fair for turbulent boundary layer with adverse pressure gradients.

Yang, Z.↗
NASA NTRS1991

Fault tolerant sequential circuits using sequence invariant state machines

The idea of introducing redundancy to improve the reliability of digital systems originates from papers published in the 1950's. Since then, redundancy has been recognized as a realistic means for constructing reliable systems. A method using redundancy to reconfigure the Sequency Invariant State Machine (SISM) to achieve fault tolerance is introduced. This new architecture is most useful in space applications, where recovery rather than replacement of faulty modules is the only means of maintenance.

Alahmad, M.↗
NASA NTRS1992

On the decomposition of synchronous state mechines using sequence invariant state machines

This paper presents a few techniques for the decomposition of Synchronous State Machines of medium to large sizes into smaller component machines. The methods are based on the nature of the transitions and sequences of states in the machine and on the number and variety of inputs to the machine. The results of the decomposition, and of using the Sequence Invariant State Machine (SISM) Design Technique for generating the component machines, include great ease and quickness in the design and implementation processes. Furthermore, there is increased flexibility in making modifications to the original design leading to negligible re-design time.

Hebbalalu, K.↗
NASA NTRS1993

Noniterative computation of infimum in H(infinity) optimisation for plants with invariant zeros on the j(omega)-axis

A simple and noniterative procedure for the computation of the exact value of the infimum in the singular H(infinity)-optimization problem is presented, as a continuation of our earlier work. Our problem formulation is general and we do not place any restrictions in the finite and infinite zero structures of the system, and the direct feedthrough terms between the control input and the controlled output variables and between the disturbance input and the measurement output variables. Our method is applicable to a class of singular H(infinity)-optimization problems for which the transfer functions from the control input to the controlled output and from the disturbance input to the measurement output satisfy certain geometric conditions. In particular, the paper extends the result of earlier work by allowing these two transfer functions to have invariant zeros on the j(omega) axis.

Chen, B. M.↗
NASA NTRS1994

Adiabatic invariants in stellar dynamics. 1: Basic concepts

The adiabatic criterion, widely used in astronomical dynamics, is based on the harmonic oscillator. It asserts that the change in action under a slowly varying perturbation is exponentially small. Recent mathematical results that precisely define the conditions for invariance show that this model does not apply in general. In particular, a slowly varying perturbation may cause significant evolution stellar dynamical systems even if its time scale is longer than any internal orbital time scale. This additional 'heating' may have serious implications for the evolution of star clusters and dwarf galaxies which are subject to long-term environmental forces. The mathematical developments leading to these results are reviewed, and the conditions for applicability to and further implications for stellar systems are discussed. Companion papers present a computational method for a general time-dependent disturbance and detailed example.

Weinberg, Martin D.↗
NASA NTRS1996

A Galilean Invariant Explicit Algebraic Reynolds Stress Model for Curved Flows

A Galilean invariant weak-equilbrium hypothesis that is sensitive to streamline curvature is proposed. The hypothesis leads to an algebraic Reynolds stress model for curved flows that is fully explicit and self-consistent. The model is tested in curved homogeneous shear flow: the agreement is excellent with Reynolds stress closure model and adequate with available experimental data.

Girimaji, Sharath↗
NASA NTRS1998

Average Cosmological Invariant Parameters of Cosmic Gamma Ray Bursts

Average cosmological invariant parameters (ACIPs) are calculated for six groups of BATSE cosmic gamma-ray bursts selected by their peak fluxes on the 1.024s timescale. The ACIPs represent the average temporal and spectral properties of these events equally in the observer frame of reference and in the co-moving frames of outbursting emitters. The parameters are determined separately for rise fronts and for back slopes of bursts, defined as the time profiles before and after the main peaks, respectively. The ACIPs for the rise fronts are found to be different for different intensity groups, while the ACIPs for the back slopes show no significant dependence on intensity. We conclude that emitters of bursts manifest standard average properties only during the back slopes of bursts.

Mitrofanov, Igor G.↗
NASA NTRS2000

Theory of the lattice Boltzmann Method: Dispersion, Dissipation, Isotropy, Galilean Invariance, and Stability

The generalized hydrodynamics (the wave vector dependence of the transport coefficients) of a generalized lattice Boltzmann equation (LBE) is studied in detail. The generalized lattice Boltzmann equation is constructed in moment space rather than in discrete velocity space. The generalized hydrodynamics of the model is obtained by solving the dispersion equation of the linearized LBE either analytically by using perturbation technique or numerically. The proposed LBE model has a maximum number of adjustable parameters for the given set of discrete velocities. Generalized hydrodynamics characterizes dispersion, dissipation (hyper-viscosities), anisotropy, and lack of Galilean invariance of the model, and can be applied to select the values of the adjustable parameters which optimize the properties of the model. The proposed generalized hydrodynamic analysis also provides some insights into stability and proper initial conditions for LBE simulations. The stability properties of some 2D LBE models are analyzed and compared with each other in the parameter space of the mean streaming velocity and the viscous relaxation time. The procedure described in this work can be applied to analyze other LBE models. As examples, LBE models with various interpolation schemes are analyzed. Numerical results on shear flow with an initially discontinuous velocity profile (shock) with or without a constant streaming velocity are shown to demonstrate the dispersion effects in the LBE model; the results compare favorably with our theoretical analysis. We also show that whereas linear analysis of the LBE evolution operator is equivalent to Chapman-Enskog analysis in the long wave-length limit (wave vector k = 0), it can also provide results for large values of k. Such results are important for the stability and other hydrodynamic properties of the LBE method and cannot be obtained through Chapman-Enskog analysis.

Lallemand, Pierre↗
NASA NTRS1999

Average Cosmological Invariant Parameters of Cosmic Gamma-Ray Bursts

Average cosmological invariant parameters (ACIPs) are calculated for six groups of BATSE cosmic gamma-ray bursts selected by their peak fluxes on the 1.024 S timescale. The ACIPs represent the average temporal and spectral properties of these events equally in the observer frame of reference and in the comoving frames of outbursting emitters. The parameters are determined separately for rise fronts and for back slopes of bursts, defined as the time profiles before and after the main peaks, respectively. The ACIPs for the rise fronts are found to be different for different intensity groups, while the ACIPs for the back slopes show no significant dependence on intensity. We conclude that emitters of bursts manifest standard average properties only during the back slopes of bursts.

Mitrofanov, Igor G.↗
NASA NTRS2003

Use of Invariant Manifolds for Transfers Between Three-Body Systems

The Lunar L1 and L2 libration points have been proposed as gateways granting inexpensive access to interplanetary space. To date, only individual solutions to the transfer between three-body systems have been found. The methodology to solve the problem for arbitrary three-body systems and entire families of orbits does not exist. This paper presents the initial approaches to solve the general problem for single and multiple impulse transfers. Two different methods of representing and storing 7-dimensional invariant manifold data are presented. Some particular solutions are presented for the transfer problem, though the emphasis is on developing methodology for solving the general problem.

Beckman, Mark↗
NASA NTRS2004

Representations of Invariant Manifolds for Applications in Three-Body Systems

The Lunar L1 and L2 libration points have been proposed as gateways granting inexpensive access to interplanetary space. To date, only individual solutions to the transfer between three-body systems have been found. The methodology to solve the problem for arbitrary three-body systems and entire families of orbits is currently being studied. This paper presents an initial approach to solve the general problem for single and multiple impulse transfers. Two different methods of representing and storing the invariant manifold data are presented. Some particular solutions are presented for two types of transfer problems, though the emphasis is on developing the methodology for solving the general problem.

Howell, K.↗
NASA NTRS2002

Training invariant support vector machines

Practical experience has shown that in order to obtain the best possible performance, prior knowledge about invariances of a classification problem at hand ought to be incorporated into the training procedure.

Support vector machines invarianceimage classifica↗
NASA NTRS2006

A High-Order, Linear Time-Invariant Model for Application to Higher Harmonic Control and Flight Control System Interaction

This research describes a new methodology for the extraction of a high-order, linear time invariant model, which allows the periodicity of the helicopter response to be accurately captured. This model provides the needed level of dynamic fidelity to permit an analysis and optimization of the AFCS and HHC algorithms. The key results of this study indicate that the closed-loop HHC system has little influence on the AFCS or on the vehicle handling qualities, which indicates that the AFCS does not need modification to work with the HHC system. However, the results show that the vibration response to maneuvers must be considered during the HHC design process, and this leads to much higher required HHC loop crossover frequencies. This research also demonstrates that the transient vibration responses during maneuvers can be reduced by optimizing the closed-loop higher harmonic control algorithm using conventional control system analyses.

Cheng, Rendy P.↗