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At least 73 records · Page 4

On the stability of numerical integration routines for ordinary differential equations.

Numerical integration methods for the solution of initial value problems for ordinary vector differential equations may be modelled as discrete time feedback systems. The stability criteria discovered in modern control theory are applied to these systems and criteria involving the routine, the step size and the differential equation are derived. Linear multistep, Runge-Kutta, and predictor-corrector methods are all investigated.

Glover, K.↗

Numerical solutions of differential equations

Various numerical methods for solving differential equations were analyzed and refined in an effort to develop a method which was adaptable to a large class of problems. The prime capabilities of the method included accuracy, numerical stability, and economic use of computer time. In multistep processes the corrector was changed at each step.

Wesson, J. R.↗

Improving the numerical integration solution of satellite orbits in the presence of solar radiation pressure using modified back differences

The method of modified back differences, a technique that significantly reduces the numerical integration errors associated with crossing shadow boundaries using a fixed-mesh multistep integrator without a significant increase in computer run time, is presented. While Hubbard's integral approach can produce significant improvements to the trajectory solution, the interpolation method provides the best overall results. It is demonstrated that iterating on the point mass term correction is also important for achieving the best overall results. It is also shown that the method of modified back differences can be implemented with only a small increase in execution time.

Lundberg, J. B.↗

Building and Breaking Carbon Composites with REACTER

Carbon composites have become indispensable for aerospace and other high-performance applications, and a detailed picture of their morphology and failure mechanisms remains difficult to obtain through experiment. REACTER is a versatile computational modeling tool for atomistic molecular dynamics designed to model chemical reactions at the speed and length scales of classical force fields.1 In this work, several recent features of REACTER were applied to the creation and subsequent mechanical testing of two classes of carbon composites, carbon-fiber reinforced polymers (CFRP) and carbon nanotube (CNT) composites. Carbon fiber core morphologies were created by the method of Desai et al.,2 but using the advanced reaction constraints framework of REACTER, their proposed multistep procedure was reduced to a single uninterrupted molecular dynamics simulation. The carbon fiber filler was embedded into a polymer matrix by simulated in situ polymerization of several thermosetting resins, including bismaleimide and polyarylacetylene, to obtain the final CFRP model. To generate the second class of carbon composite, CNT networks were grown dynamically using the new ‘create atoms’ feature of REACTER, and similarly infiltrated with resin to obtain CNT composites. The resulting models were compared directly to experiment using simulated high resolution transmission electron microscopy and x-ray diffraction. Failure mechanisms were elucidated by simulating mechanically induced bond breaking, as characterized by third-order DFT-based tight-binding (DFTB3) simulations, via a reaction constraint on the total potential energy of the involved atoms.

Molecular Dynamics↗

Design of multisample, multistep phase partitioning apparatus for use on Space Shuttle Spacelab, and Spacelab missions

Traditional separation techniques are inadequate for many new bioprocessing challenges. Innovative separation methods such as aqueous two phase partitioning are needed to perpetuate bioprocess commercialization. Aqueous two phase polymer partitioning systems provide a process for separating biological materials when combined with microgravity. An innovative space qualified apparatus developed for carrying out separations by partitioning in immiscible polymer systems under mirogravity conditions is described. The apparatus offers an innovative approach to low gravity bioseparations in general and phase partitioning in particular. These capabilities support NASA's interest in serving the biotechnology research community and providing quantitative data in the gravity dependent components of separation processes.

Deuser, Mark S.↗

A study of numerical methods of solution of the equations of motion of a controlled satellite under the influence of gravity gradient torque

Numerical methods of integration of the equations of motion of a controlled satellite under the influence of gravity-gradient torque are considered. The results of computer experimentation using a number of Runge-Kutta, multi-step, and extrapolation methods for the numerical integration of this differential system are presented, and particularly efficient methods are noted. A large bibliography of numerical methods for initial value problems for ordinary differential equations is presented, and a compilation of Runge-Kutta and multistep formulas is given. Less common numerical integration techniques from the literature are noted for further consideration.

Thompson, J. F.↗

The long-term prediction of artificial satellite orbits

Survey of averaging and multirevolution methods for long-term orbit prediction. A technical approach with the following features is recommended: (1) averaged variation-of-parameter equations, (2) analytical expressions for oblateness and third-body effects, (3) definite integrals for atmospheric drag and lunar effects (for long-period orbits), (4) nonsingular equinoctial element formulation, (5) multistep numerical integration processes, and (6) precise osculating-to-mean element transformation. Several orbital predictions illustrate the contribution of this technical approach to overall accuracy and efficiency. Future development of the analytical averaging method in nonsingular coordinates by automated manipulation of literal series is discussed.

Cefola, P. J.↗

Multistep integration formulas for the numerical integration of the satellite problem

The use of two Class 2/fixed mesh/fixed order/multistep integration packages of the PECE type for the numerical integration of the second order, nonlinear, ordinary differential equation of the satellite orbit problem. These two methods are referred to as the general and the second sum formulations. The derivation of the basic equations which characterize each formulation and the role of the basic equations in the PECE algorithm are discussed. Possible starting procedures are examined which may be used to supply the initial set of values required by the fixed mesh/multistep integrators. The results of the general and second sum integrators are compared to the results of various fixed step and variable step integrators.

Lundberg, J. B.↗

Adaptive quadrilateral and triangular finite-element scheme for compressible flows

The development of an adaptive mesh refinement procedure for analyzing high-speed compressible flows using the finite-element method is described. This new adaptation procedure, which uses both quadrilateral and triangular elements, was implemented with two explicit finite-element algorithms - the two-step Taylor-Galerkin and the multistep Galerkin-Runge-Kutta schemes. A von Neumann stability analysis and a rotating 'cosine hill'problem demonstrate the instability of the Taylor-Galerkin scheme when coupled with the adaptation procedure. For the same adaptive refinement scheme, the Galerkin-Runge-Kutta procedure yields stable solutions within its explicit stability limit. The utility of this new adaptation procedure for the prediction of compressible flow features is illustrated for inviscid problems involving strong shock interactions at hypersonic speeds.

Ramakrishnan, R.↗

Chromosomal changes in cultured human epithelial cells transformed by low- and high-LET radiation

For a better assessment of radiation risk in space, an understanding of the responses of human cells, especially the epithelial cells, to low- and high-LET radiation is essential. In our laboratory, we have successfully developed techniques to study the neoplastic transformation of two human epithelial cell systems by ionizing radiation. These cell systems are human mammary epithelial cells (H184B5) and human epidermal keratinocytes (HEK). Both cell lines are immortal, anchorage dependent for growth, and nontumorigenic in athymic nude mice. Neoplastic transformation was achieved by irradiating cells successively. Our results showed that radiogenic cell transformation is a multistep process and that a single exposure of ionizing radiation can cause only one step of transformation. It requires, therefore, multihits to make human epithelial cells fully tumorigenic. Using a simple karyotyping method, we did chromosome analysis with cells cloned at various stages of transformation. We found no consistent large terminal deletion of chromosomes in radiation-induced transformants. Some changes of total number of chromosomes, however, were observed in the transformed cells. These transformants provide an unique opportunity for further genetic studies at a molecular level.

NASA Discipline Number 04-10↗

A computational design tool for scramjet combustor film cooling and fuel mixing predictions

A methodology for the analysis of a film cooled combustor of a hydrogen-fueled, supersonic combustion ramjet (scramjet) is presented. The SHIP3D parabolic flow code, based on an extension of the pressure-correction method of Patankar and Spalding for compressible flow is used to compute the flow field in the combustor. The effect of film cooling on the overall vehicle performance is then calculated using the one-dimensional, multistep cycle code, CPIPE. Results are presented for a conceptual combustor at Mach 16 flight conditions. It is seen that film cooling can have a significant effect on the engine performance.

Kamath, Pradeep S.↗

Ultrahigh molecular weight aromatic siloxane polymers

The condensation of a diol with a silane in toluene yields a silphenylene-siloxane polymer. The reaction of stiochiometric amounts of the diol and silane produced products with molecular weights in the range 2.0 - 6.0 x 10 to the 5th power. The molecular weight of the product was greatly increased by a multistep technique. The methodology for synthesis of high molecular weight polymers using a two step procedure was refined. Polymers with weight average molecular weights in excess of 1.0 x 10 to the 6th power produced by this method. Two more reactive silanes, bis(pyrrolidinyl)dimethylsilane and bis(gamma butyrolactam)dimethylsilane, are compared with the dimethyleminodimethylsilane in ability to advance the molecular weight of the prepolymer. The polymers produced are characterized by intrinsic viscosity in tetrahydrofuran. Weight and number average molecular weights and polydispersity are determined by gel permeation chromatography.

Ludwick, L. M.↗

Cell separation and electrofusion in space

In microgravity, free-fluid electrophoretic methods for separating living cells and proteins are improved significantly by the absence of gravity-driven phenomena. Cell fusion, culture, and other bioprocessing steps are being investigated to understand the limits of earth-based processing. A multistep space bioprocess is described that includes electrophoretic separation of human target cells, single-cell manipulations using receptor-specific antibodies, electrofusion to produce immortal hybridomas, gentle suspension culture, and monoclonal antibody recovery using continuous-flow electrophoresis or recirculating isoelectric focusing. Improvements in several key steps already have been demonstrated by space experiments, and others will be studied on Space Station Freedom.

Morrison, D. R.↗

Complex Decision-Making Applications for the NASA Space Launch System

The Space Shuttle program is ending and elements of the Constellation Program are either being cancelled or transitioned to new NASA exploration endeavors. NASA is working diligently to select an optimum configuration for the Space Launch System (SLS), a heavy lift vehicle that will provide the foundation for future beyond LEO large ]scale missions for the next several decades. Thus, multiple questions must be addressed: Which heavy lift vehicle will best allow the agency to achieve mission objectives in the most affordable and reliable manner? Which heavy lift vehicle will allow for a sufficiently flexible exploration campaign of the solar system? Which heavy lift vehicle configuration will allow for minimizing risk in design, test, build and operations? Which heavy lift vehicle configuration will be sustainable in changing political environments? Seeking to address these questions drove the development of an SLS decisionmaking framework. From Fall 2010 until Spring 2011, this framework was formulated, tested, fully documented, and applied to multiple SLS vehicle concepts at NASA from previous exploration architecture studies. This was a multistep process that involved performing FOM-based assessments, creating Pass/Fail gates based on draft threshold requirements, performing a margin-based assessment with supporting statistical analyses, and performing sensitivity analysis on each. This paper discusses the various methods of this process that allowed for competing concepts to be compared across a variety of launch vehicle metrics. The end result was the identification of SLS launch vehicle candidates that could successfully meet the threshold requirements in support of the SLS Mission Concept Review (MCR) milestone.

Lyles, Garry↗

Performance comparison of five frequency domain system identification techniques for helicopter higher harmonic control

This paper presents the results of a computer simulation comparing the performance of five system identification techniques currently proposed for use with helicopter, frequency domain, higher harmonic vibration control algorithms. The system identification techniques studied were: (1) the weighted least squares method in moving block format, (2) the classical Kalman filter, (3) a generalized Kalman filter, (4) the classical least mean square (LMS) filter, and (5) a generalized LMS filter. The generalized Kalman and LMS filters were derived by allowing for multistep operation, rather than the single-step update approach used by their classical versions. Both open-loop and closed-loop (vibration control mode) identification results are presented in the paper. The algorithms are evaluated in terms of their accuracy, stability, convergence properties, computation speeds, and the relative ease with which these techniques may be directly applied to the helicopter vibration control problem.

Jacklin, Stephen A.↗

Complex Decision-Making Applications for the NASA Space Launch System

The Space Shuttle program is ending and elements of the Constellation Program are either being cancelled or transitioned to new NASA exploration endeavors. The National Aeronautics and Space Administration (NASA) has worked diligently to select an optimum configuration for the Space Launch System (SLS), a heavy lift vehicle that will provide the foundation for future beyond low earth orbit (LEO) large-scale missions for the next several decades. Thus, multiple questions must be addressed: Which heavy lift vehicle will best allow the agency to achieve mission objectives in the most affordable and reliable manner? Which heavy lift vehicle will allow for a sufficiently flexible exploration campaign of the solar system? Which heavy lift vehicle configuration will allow for minimizing risk in design, test, build and operations? Which heavy lift vehicle configuration will be sustainable in changing political environments? Seeking to address these questions drove the development of an SLS decision-making framework. From Fall 2010 until Spring 2011, this framework was formulated, tested, fully documented, and applied to multiple SLS vehicle concepts at NASA from previous exploration architecture studies. This was a multistep process that involved performing figure of merit (FOM)-based assessments, creating Pass/Fail gates based on draft threshold requirements, performing a margin-based assessment with supporting statistical analyses, and performing sensitivity analysis on each. This paper discusses the various methods of this process that allowed for competing concepts to be compared across a variety of launch vehicle metrics. The end result was the identification of SLS launch vehicle candidates that could successfully meet the threshold requirements in support of the SLS Mission Concept Review (MCR) milestone.

Lyles, Garry↗

Hot-Dipped Metal Films as Epitaxial Substrates

Multistep process forms semiconductor devices on macrocrystalline films of cadmium or zinc. Solar-cell fabrication processes use hot-dipped macrocrystalline films on low-cost sheet-metal base as substrates for epitaxy. Epitaxial layers formed by variety of methods of alternative sequence paths. Solar cells made economically by forming desired surface substance directly on metal film by chemical reactions.

Shlichta, P. J.↗

Multistep matrix integrators for real-time simulation

An explicit linear multistep matrix-integration technique is presented for vector systems of ODEs which employs the stability region placement approach to permit the time-step to be chosen independently of system eigenvalues. Closed-form solutions for the general p-step method and the case where the system matrix has zero eigenvalues are given. It is shown that system mode shapes are preserved over the integration process, and that the technique remains applicable to systems with eigenvalues at their origin without need for computing a matrix inversion.

De Abreu-Garcia, J. A.↗