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Noniterative method of obtaining rational forms as approximations to functions for power series expressions using Tchebycheff polynomial properties for improving accuracy
The extended interior penalty function formulation is implemented. A rational method for determining the transition between the interior and extended parts is set forth. The formulation includes a straightforward method for avoiding design points with some negative components, which are physically meaningless in structural analysis. The technique, when extended to problems involving parametric constraints, can facilitate closed form integration of the penalty terms over the most important parts of the parameter interval. The method lends itself well to the use of approximation concepts, such as design variable linking, constraint deletion and Taylor series expansions of response quantities in terms of design variables. Examples demonstrating the algorithm, in the context of planar orthogonal frames subjected to ground motion, are included.
Early versions of the assumed stress hybrid finite elements were based on the a priori satisifaction of stress equilibrium conditions. In the new version such conditions are relaxed but are introduced through additional internal displacement functions as Lagrange multipliers. A rational procedure is to choose the displacement terms such that the resulting strains are now of complete polynomials up to the same degree as that of the assumed stresses. Several example problems indicate that optimal element properties are resulted by this method.
The Earth Observing System (EOS) and Space Station (SS) attached payload instruments to be developed by JPL will have a consistent implied level of reliability confidence based on the application of product assurance requirements. An important subset of these requirements is a set of detailed environmental design and test requirements. These requirements have a sound technical defense, are unambiguous in their level of detail, provide rational risk management as a function of payload classification, and are rigorously enforced with a comprehensive waiver process imposed on planned deviations.
The first protein crystallization experiment in microgravity was launched in April, 1981 and used Germany's Technologische Experimente unter Schwerelosigkeit (TEXUS 3) sounding rocket. The protein P-galactosidase (molecular weight 465Kda) was chosen as the sample with a liquid-liquid diffusion growth method. A sliding device brought the protein, buffer and salt solution into contact when microgravity was reached. The sounding rocket gave six minutes of microgravity time with a cine camera and schlieren optics used to monitor the experiment, a single growth cell. In microgravity a strictly laminar diffusion process was observed in contrast to the turbulent convection seen on the ground. Several single crystals, approx 100micron in length, were formed in the flight which were of inferior but of comparable visual quality to those grown on the ground over several days. A second experiment using the same protocol but with solutions cooled to -8C (kept liquid with glycerol antifreeze) again showed laminar diffusion. The science of macromolecular structural crystallography involves crystallization of the macromolecule followed by use of the crystal for X-ray diffraction experiments to determine the three dimensional structure of the macromolecule. Neutron protein crystallography is employed for elucidation of H/D exchange and for improved definition of the bound solvent (D20). The structural information enables an understanding of how the molecule functions with important potential for rational drug design, improved efficiency of industrial enzymes and agricultural chemical development. The removal of turbulent convection and sedimentation in microgravity, and the assumption that higher quality crystals will be produced, has given rise to the growing number of crystallization experiments now flown. Many experiments can be flown in a small volume with simple, largely automated, equipment - an ideal combination for a microgravity experiment. The term "protein crystal growth" is often historically used to describe these microgravity experiments. This is somewhat inaccurate as the field involves the study of many varied biological molecules including viruses, proteins, DNA, RNA and complexes of those structures. For this reason we use the term macromolecular crystal growth. In this chapter we review a series of diagnostic microgravity crystal growth experiments carried out principally using the European Space Agency (ESA) Advanced Protein Crystallization Facility (APCF). We also review related research, both experimental and theoretical, on the aspects of microgravity fluid physics that affect microgravity protein crystal growth. Our experiments have revealed some surprises that were not initially expected. We discuss them here in the context of practical lessons learnt and how to maximize the limited microgravity opportunities available.
Considering the range of functions proteins perform, it is surprising they fold into a relatively small set of structures or "folds" that facilitate such function. One explanation is that only a minority were fit enough to emerge from Darwinian selection during the early evolution of life. Alternatively, perhaps only a fraction of all possible folds were trialed. Understanding proto-catalyst selection will aid understanding of the origins and early evolution of life. To investigate which explanation is correct, we study a protein evolved in vitro to bind ATP by Jack Szostak (Fig. 1). This protein adopts a fold which is absent from nature. We are testing whether this fold would have possessed the capability to evolve that would have been essential to survive natural selection on early Earth. Folds that couldn't improve their fitness and evolve to perform new functions would have been replaced by rivals that could. To determine whether the fold is evolvable, we are attempting to change the function of the protein by rationally redesigning to bind GTP. Two design strategies in the region of the nucleobase have been implemented to provide hydrogen bonding partners for the ligand i) an insertion ii) a MET to ASN mutation. Redesigns are being studied computationally at Ames Research Center including free energy of binding calculations. Binding affinities of promising redesigns are to be validated by experimental collaborators at ForteBio using Super Streptavidin Biosensors. If the fold is found to be non-evolvable, this may suggest that many structures were trialed, but the majority were pruned on the basis of their evolvability. Alternatively, if the fold is demonstrated to be evolvable, it would be difficult to explain its absence from nature without considering the possibility that the fold simply wasn't sampled on early Earth. This would not only further our understanding of the origins of life on Earth but also suggest a common phe-nomenon of proto-catalyst evolution.
A computer program called "Rational Sequence" generates Universal Modeling Language (UML) sequence diagrams of a target Java program running on a Java virtual machine (JVM). Rational Sequence thereby performs a reverse engineering function that aids in the design documentation of the target Java program. Whereas previously, the construction of sequence diagrams was a tedious manual process, Rational Sequence generates UML sequence diagrams automatically from the running Java code.
Two cubic spline formulations are presented for representing the quantile function (inverse cumulative distribution function) of a random sample of data. Both B-spline and rational spline approximations are compared with analytic representations of the quantile function. It is also shown how these representations can be used to generate random samples for use in simulation studies. Comparisons are made on samples generated from known distributions and a sample of experimental data. The spline representations are more accurate for multimodal and skewed samples and to require much less time to generate samples than the analytic representation.
Transfer-function approximations made optimal in special least-squares sense. Algorithm computes reduced-order rational-fraction approximates to single-input/single-output transfer functions. Reduces amount of computation needed for such purposes as numerical simulation of dynamics and design of control subsystems.
Features and sample applications of the transonic rational optimization (TRO-2D) code are outlined. TRO-2D includes the airfoil analysis code FLO-36, the CONMIN optimization code and a rational approach to defining aero-function shapes for geometry modification. The program is part of an effort to develop an aerodynamically smart optimizer that will simplify and shorten the design process. The user has a selection of drag minimization and associated minimum lift, moment, and the pressure distribution, a choice among 14 resident aero-function shapes, and options on aerodynamic and geometric constraints. Design variables such as the angle of attack, leading edge radius and camber, shock strength and movement, supersonic pressure plateau control, etc., are discussed. The results of calculations of a reduced leading edge camber transonic airfoil and an airfoil with a natural laminar flow are provided, showing that only four design variables need be specified to obtain satisfactory results.
The problem of synthesizing transfer functions from frequency response measurements is considered. Given a complex vector representing the measured frequency response of a physical system, a transfer function of specified order is determined that minimizes the sum of the magnitude-squared of the frequency response errors. This nonlinear least squares minimization problem is solved by an iterative global descent algorithm of the Newton type which converges quadratically near the minimum. The unknown transfer function is expressed as a sum of second order rational polynomials, a parameterization that facilitates a numerically robust computer implementation. The algorithm is developed for single-input, single-output, causal, stable transfer functions.
Product Distribution (PD) theory is the information-theoretic extension of conventional full- rationality game theory to bounded rational games. Here PD theory is used to investigate games in which the players use bounded rational best-response strategies. This investigation illuminates how to determine the optimal organization chart for a corporation, or more generally how to order the sequence of moves of the players / employees so as to optimize an overall objective function. It is then shown that in the continuum-time limit, bounded rational best response games result in a variant of the replicator dynamics of evolutionary game theory. This variant is then investigated for team games, in which the players share the same utility function, by showing that such continuum- limit bounded rational best response is identical to Newton-Raphson iterative optimization of the shared utility function. Next PD theory is used to investigate changing the coordinate system of the game, i.e., changing the mapping from the joint move of the players to the arguments in the utility functions. Such a change couples those arguments, essentially by making each players move be an offered binding contract.
The bounds for the normalized associated Legendre functions P sub nm were studied to provide a rational basis for the truncation of the geopotential series in spherical harmonics in various orbital analyses. The conjecture is made that the largest maximum of the normalized associated Legendre function lies in the interval which indicates the greatest integer function. A procedure is developed for verifying this conjecture. An on-line algebraic manipulator, IAM, is used to implement the procedure and the verification is carried out for all n equal to or less than 2m, for m = 1 through 6. A rigorous proof of the conjecture is not available.
Two distinct parameterization procedures are developed for investigating the grid sensitivity with respect to design parameters of a wing-section example. The first procedure is based on traditional (physical) relations defining NACA four-digit wing-sections. The second is advocating a novel (geometrical) parameterization using spline functions such as NURBS (Non-Uniform Rational B-Splines) for defining the wing-section geometry. An interactive algebraic grid generation technique, known as Hermite Cubic Interpolation, is employed to generate C-type grids around wing-sections. The grid sensitivity of the domain with respect to design and grid parameters has been obtained by direct differentiation of the grid equations. A hybrid approach is proposed for more geometrically complex configurations. A comparison of the sensitivity coefficients with those obtained using a finite-difference approach has been made to verify the feasibility of the approach. The aerodynamic sensitivity coefficients are obtained using the compressible two-dimensional thin-layer Navier-Stokes equations.
An algorithm is developed to obtain the grid sensitivity with respect to design parameters for aerodynamic optimization. The procedure is advocating a novel (geometrical) parameterization using spline functions such as NURBS (Non-Uniform Rational B-Splines) for defining the wing-section geometry. An interactive algebraic grid generation technique, known as Two-Boundary Grid Generation (TBGG) is employed to generate C-type grids around wing-sections. The grid sensitivity of the domain with respect to geometric design parameters has been obtained by direct differentiation of the grid equations. A hybrid approach is proposed for more geometrically complex configurations such as a wing or fuselage. The aerodynamic sensitivity coefficients are obtained by direct differentiation of the compressible two-dimensional thin-layer Navier-Stokes equations. An optimization package has been introduced into the algorithm in order to optimize the wing-section surface. Results demonstrate a substantially improved design due to maximized lift/drag ratio of the wing-section.
An algorithm is developed to obtain the grid sensitivity with respect to design parameters for aerodynamic optimization. The procedure is advocating a novel (geometrical) parameterization using spline functions such as NURBS (Non-Uniform Rational B- Splines) for defining the airfoil geometry. An interactive algebraic grid generation technique is employed to generate C-type grids around airfoils. The grid sensitivity of the domain with respect to geometric design parameters has been obtained by direct differentiation of the grid equations. A hybrid approach is proposed for more geometrically complex configurations such as a wing or fuselage. The aerodynamic sensitivity coefficients are obtained by direct differentiation of the compressible two-dimensional thin-layer Navier-Stokes equations. An optimization package has been introduced into the algorithm in order to optimize the airfoil surface. Results demonstrate a substantially improved design due to maximized lift/drag ratio of the airfoil.
A new method of calculating the root-mean-square (rms) pointing jitter of a scientific instrument (e.g., a camera, radar antenna, or telescope) is introduced based on a state-space concept. In comparison with the prior method of calculating the rms pointing jitter, the present method involves significantly less computation. The rms pointing jitter of an instrument (the square root of the jitter variance shown in the figure) is an important physical quantity which impacts the design of the instrument, its actuators, controls, sensory components, and sensor- output-sampling circuitry. Using the Sirlin, San Martin, and Lucke definition of pointing jitter, the prior method of computing the rms pointing jitter involves a frequency-domain integral of a rational polynomial multiplied by a transcendental weighting function, necessitating the use of numerical-integration techniques. In practice, numerical integration complicates the problem of calculating the rms pointing error. In contrast, the state-space method provides exact analytic expressions that can be evaluated without numerical integration.
In this paper the problem of synthesizing transfer functions from frequency response measurements is considered. Given a complex vector representing the measured frequency response of a physical system, a transfer function of specified order is determined that minimizes the sum of the magnitude-squared of the frequency response errors. This nonlinear least squares minimization problem is solved by an iterative global descent algorithm of the Newton type that converges quadratically near the minimum. The unknown transfer function is expressed as a sum of second-order rational polynomials, a parameterization that facilitates a numerically robust computer implementation. The algorithm is developed for single-input, single-output, causal, stable transfer functions. Two numerical examples demonstrate the effectiveness of the algorithm.