On the closure and convexity of attainable sets in finite and infinite dimensions.
Closure and convexity of attainable control sets in finite and infinite dimensions, noting Liapunov theorem
OPTIMAL CONTROL↗
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Axial jet mixing of ethanol in cylindrical containers during weightlessness
An experimental program was conducted to examine the liquid flow patterns that result from the axial jet mixing of ethanol in 10-centimeter-diameter cylindrical tanks in weightlessness. A convex hemispherically ended tank and two Centaur liquid-hydrogen-tank models were used for the study. Four distinct liquid flow patterns were observed to be a function of the tank geometry, the liquid-jet velocity, the volume of liquid in the tank, and the location of the tube from which the liquid jet exited.
Aydelott, J. C.↗
Low-leakage and low-instability labyrinth seal
Improved labyrinth seal designs are disclosed. The present invention relates to labyrinth seal systems with selected sealing surfaces and seal geometry to optimize flow deflection and produce maximum turbulent action. Optimum seal performance is generally accomplished by providing sealing surfaces and fluid cavities formed to dissipate fluid energy as a function of the geometry of the sealing surfaces along with the position and size of the fluid cavities formed between members of the labyrinth seal system. Improved convex surfaces, annular flow reversal grooves, flow deflection blocks and rough, machined surfaces cooperate to enhance the performance of the labyrinth seal systems. For some labyrinth seal systems a mid-cavity throttle and either rigid teeth or flexible spring teeth may be included.
Rhode, David L.↗
Computerized Generation and Simulation of Meshing and Contact of New Type of Novikov-Wildhaber Helical Gears
In this report, we propose a new geometry for low-noise, increased-strength helical gears of the Novikov-Wildhaber type. Contact stresses are reduced as a result of their convex-concave gear tooth surfaces. The gear tooth surfaces are crowned in the profile direction to localize bearing contact and in the longitudinal direction to obtain a parabolic function of transmission errors. Such a function results in the reduction of noise and vibrations. Methods for the generation of the proposed gear tooth surfaces by grinding and hobbing are considered, and a tooth contact analysis (TCA) computer program to simulate meshing and contact is applied. The report also investigates the influence of misalignment on transmission errors and shift of bearing contact. Numerical examples to illustrate the developed approaches are proposed. The proposed geometry was patented by Ford/UIC (Serial Number 09-340-824, pending) on June 28, 1999.
Litvin, Faydor L.↗
Higher order sensitivity of solutions to convex programming problems without strict complementarity
Consideration is given to a family of convex programming problems which depend on a vector parameter. It is shown that the solutions of the problems and the associated Lagrange multipliers are arbitrarily many times directionally differentiable functions of the parameter, provided that the data of the problems are sufficiently regular. The characterizations of the respective derivatives are given.
Malanowski, Kazimierz↗
The shape of Eros
Monte Carlo simulations are presently used to optimize estimation, ascertain associated errors, and guide bias-correction procedures, for the Eros polar silhouette convex hull that has been estimated from radar echo spectra. This hull is trapezoidal; this nonaxisymmetric shape may account for odd harmonics in Eros' echo spectral signature as a function of rotation phase. Additional constraints have been obtained for the figure of Eros through the inversion of the optical lightcurve to estimate the asteroid's two-dimensional average of the three-dimensional shape. This 'mean cross-section' and the polar silhouette exhibit similar elongations.
Ostro, S. J.↗
Transferable Output ASCII Data (TOAD) editor version 1.0 user's guide
The Transferable Output ASCII Data (TOAD) editor is an interactive software tool for manipulating the contents of TOAD files. The TOAD editor is specifically designed to work with tabular data. Selected subsets of data may be displayed to the user's screen, sorted, exchanged, duplicated, removed, replaced, inserted, or transferred to and from external files. It also offers a number of useful features including on-line help, macros, a command history, an 'undo' option, variables, and a full compliment of mathematical functions and conversion factors. Written in ANSI FORTRAN 77 and completely self-contained, the TOAD editor is very portable and has already been installed on SUN, SGI/IRIS, and CONVEX hosts.
Bingel, Bradford D.↗
On the spectral energy distributions of blazars
The multifrequency spectral properties of complete samples of three kinds of blazars observed with the Rosat position sensitive proportional counter (PSPC) in pointed mode are investigated: radio selected BL Lacs (RBLs); X-ray selected BL Lacs (XBLs); and flat spectrum radio quasars (FSRQs). Their spectral energy distributions are compared. The bolometric luminosities and peak emission frequencies of each source are estimated by fitting parabolic functions to the individual rest frame spectra of the power per decade. The shape of the optical to X-ray continua is described, and it is found that the continua of XBLs are convex while those of FSRQs are concave.
Maraschi, L.↗
Optimal control and convex programming.
Optimal control and convex programming, discussing problem of admissible investiment program control for production constraints
OPTIMAL CONTROL↗
The Singularity Mystery Associated with a Radially Continuous Maxwell Viscoelastic Structure
The singularity problem associated with a radially continuous Maxwell viscoclastic structure is investigated. A special tool called the isolation function is developed. Results calculated using the isolation function show that the discrete model assumption is no longer valid when the viscoelastic parameter becomes a continuous function of radius. Continuous variations in the upper mantle viscoelastic parameter are especially powerful in destroying the mode-like structures. The contribution to the load Love numbers of the singularities is sensitive to the convexity of the viscoelastic parameter models. The difference between the vertical response and the horizontal response found in layered viscoelastic parameter models remains with continuous models.
Fang, Ming↗
Flexible tactile sensing arrays for robotics: Architectural robustness and yield considerations
No tactile sensor array developed to date fills all, nor even most, of the requirements of: (1) many sensor elements to minimize tactile imaging time, (2) close spacing of small sensing elements for fine spatial discrimination, (3) ability to be molded to a convex fingertip surface for taction on concave surfaces, (4) ability to sense both force and temperature in order to fully mimic biological touch, (5) tolerance to overscale forces without damage, and (6) graceful failure in use, i.e., functional survival of most of the array when part of it is damaged, well. Several investigators have recently developed tactile sensing arrays suitable for imaging shapes on hard flat surfaces, but not well suited for taction on curved surfaces. Others have developed single tactile sensors suitable for incorporation into arrays, which will probably prove uneconomical when large numbers of sensors are needed. Still others have developed flexible capacitive arrays suitable for use on curved surfaces but incapable of obtaining temperature or proximity data. A technology is being developed herein suitable to the achievement of all of the above goals, and to incrementally demonstrate useful steps toward those goals.
Barth, Phillip W.↗
Deblurring
In most instances, traditional EEG methodology provides insufficient spatial detail to identify relationships between brain electrical events and structures and functions visualized by magnetic resonance imaging or positron emission tomography. This article describes a method called Deblurring for increasing the spatial detail of the EEG and for fusing neurophysiologic and neuroanatomic data. Deblurring estimates potentials near the outer convexity of the cortex using a realistic finite element model of the structure of a subject's head determined from their magnetic resonance images. Deblurring is not a source localization technique and thus makes no assumptions about the number or type of generator sources. The validity of Deblurring has been initially tested by comparing deblurred data with potentials measured with subdural grid recordings. Results suggest that deblurred topographic maps, registered with a subject's magnetic resonance imaging and rendered in three dimensions, provide better spatial detail than has heretofore been obtained with scalp EEG recordings. Example results are presented from research studies of somatosensory stimulation, movement, language, attention and working memory. Deblurred ictal EEG data are also presented, indicating that this technique may have future clinical application as an aid to seizure localization and surgical planning.
Non-NASA Center↗
Multiple-Effector Control Allocation: Theory and Practice
Redundant controls are ubiquitous in many aerospace domains, including aircraft, spacecraft, and launch vehicles. Multiple control effectors having different capabilities (e.g., reaction controls, aerosurfaces, and vectored engines) must be optimally allocated to achieve high-performance and robust vehicle control, while considering different constraints, cost, or performance metrics associated with various control mixing schemes. These can include force or deflection limits, rate limits, propellant usage or drag penalties, cross-axis coupling, uncertainties, or even servoelastic interactions. This presentation introduces the fundamentals of control allocation theory, based on linear algebra and convex sets, using a handful of examples taken from the air and space vehicle domains. It is shown that even simple methods can provide verifiable and quantifiable performance benefits over ad-hoc approaches, and can support enhanced functions like fault tolerance and control reconfiguration.
Bill Benson↗
Efficient approximation concepts using second order information
The application of second derivative information for solving structural optimization problems is considered. In the present method, rather than building approximate nonlinear forms for the objective function and constraints, only linear approximations are used. A separable quadratic approximation of the Lagrangian function is included in the subproblem statement. The method has been successfully used for simple problems that can be solved in closed form, in addition to the sizing optimization of trusses, and it is shown to converge faster than the convex linearization method or the method of moving asymptotes.
Fleury, Claude↗
Critical examination of two-equation turbulence closure models
Comparison of the Jones-Launder, Ng-Spalding, Saffman-Wilcox, and Wilcox-Traci two-equation turbulence models has been conducted. It was shown that the Saffman-Wilcox and Wilcox-Traci dissipation-rate formulations admit straightforward integration through the viscous sublayer, whereas integration through the viscous sublayer is a more difficult issue with the Jones-Launder dissipation-function and the Ng-Spalding length-scale formulations. Numerical computations were conducted in which the models were applied to four equilibrium boundary layer flows including adverse, zero, and favorable pressure gradients. Computations of zero pressure gradient flow over a convex wall composed the final part of the comparison.
Chambers, T. L.↗
Asteroid lightcurve inversion
One of the most fundamental physical properties of any asteroid is its shape. Lightcurves provide the only source of shape information for most asteroids. Unfortunately, the functional form of a lightcurve is determined by the viewing/illumination geometry and the asteroid's light scattering characteristics as well as its shape, and in general it is impossible to determine an asteroid's shape from lightcurves. A technique called convex-profile inversion (CPI) that obtains a convex profile, P, from any lightcurve is introduced. If certain ideal conditions are satisfied, then P is an estimator for the asteroid's mean cross section, C, a convex set defined as the average of all cross sections C(z) cut by planes a distance z above the asteroids's equatorial plane. C is therefore a 2-D average of the asteroid's 3-D shape.
Ostro, Steven J.↗
Isolating Curvature Effects in Computing Wall-Bounded Turbulent Flows
The flow over the zero-pressure-gradient So-Mellor convex curved wall is simulated using the Navier-Stokes equations. An inviscid effective outer wall shape, undocumented in the experiment, is obtained by using an adjoint optimization method with the desired pressure distribution on the inner wall as the cost function. Using this wall shape with a Navier-Stokes method, the abilities of various turbulence models to simulate the effects of curvature without the complicating factor of streamwise pressure gradient can be evaluated. The one-equation Spalart-Allmaras turbulence model overpredicts eddy viscosity, and its boundary layer profiles are too full. A curvature-corrected version of this model improves results, which are sensitive to the choice of a particular constant. An explicit algebraic stress model does a reasonable job predicting this flow field. However, results can be slightly improved by modifying the assumption on anisotropy equilibrium in the model's derivation. The resulting curvature-corrected explicit algebraic stress model possesses no heuristic functions or additional constants. It lowers slightly the computed skin friction coefficient and the turbulent stress levels for this case (in better agreement with experiment), but the effect on computed velocity profiles is very small.
Rumsey, Christopher L.↗
Boundary-layer linear stability theory
Most fluid flows are turbulent rather than laminar and the reason for this was studied. One of the earliest explanations was that laminar flow is unstable, and the linear instability theory was first developed to explore this possibility. A series of early papers by Rayleigh produced many notable results concerning the instability of inviscid flows, such as the discovery of inflectional instability. Viscosity was commonly thought to act only to stabilize the flow, and flows with convex velocity profiles appeared to be stable. The investigations that led to a viscous theory of boundary layer instability was reported. The earliest application of linear stability theory to transition prediction calculated the amplitude ratio of the most amplified frequency as a function of Reynolds number for a Blasius boundary layer, and found that this quantity had values between five and nine at the observed Ret. The experiment of Schubauer and Skramstad (1947) completely reversed the prevailing option and fully vindicated the Gottingen proponents of the theory. This experiment demonstrated the existence of instability waves in a boundary layer, their connection with transition, and the quantitative description of their behavior by the theory of Tollmien and Schlichting. It is generally accepted that flow parameters such as pressure gradient, suction and heat transfer qualitatively affect transition in the manner predicted by the linear theory, and in particular that a flow predicted to be stable by the theory should remain laminar. The linear theory, in the form of the e9, or N-factor is today in routine use in engineering studies of laminar flow. The stability theory to boundary layers with pressure gradients and suction was applied. The only large body of numerical results for exact boundary layer solutions before the advent of the computer age by calculating the stability characteristics of the Falkner-Skan family of velocity profiles are given. When the digital computer reached a stage of development which permit the direct solution of the primary differential equations, numerical results were obtained from the linear theory during the next 10 years for many different boundary layer flows: three dimensional boundary layers; free convention boundary layers; compressible boundary layers; boundary layers on compliant walls; a recomputation of Falkner-Skan flows; unsteady boundary layers; and heated wall boundary layers.
Leslie M Mack↗