Applications of symbolic computing methods to the dynamic analysis of large systems

Since the symbolic computing language is very well suited to the operations with algebraic equations, techniques use the transfer function concept as a tool for the analysis of large linear dynamic systems. Techniques were coded in the experimental symbolic computer language FORMAC. The first of these approaches, REDUCE 1, establishes the techniques and a computer program to symbolically reduce arbitrary block diagrams associated with large systems for desired transfer functions. Symbolic closed form solutions are determined in several forms including an expanded form in terms of the driving frequencies and system constants. Programs are also written to numerically evaluate the symbolic solutions. A second computer program, REDUCE 2, is also based on the use of symbolic computing methods and was written to accommodate large engineering systems

Studies on interaction between synoptic and mesoscale weather elements in the tropics: report no. 1

June 1968.Includes bibliographical references.Pt. 1. Some aspects of cumulus-scale downdrafts / by R. Riehl -- Pt. 2. Vorticity budgets derived from Caribbean data / by R. P. Pearce

OTIS 3.2 Software Released

Trajectory, mission, and vehicle engineers concern themselves with finding the best way for an object to get from one place to another. These engineers rely upon special software to assist them in this. For a number of years, many engineers have used the OTIS program for this assistance. With OTIS, an engineer can fully optimize trajectories for airplanes, launch vehicles like the space shuttle, interplanetary spacecraft, and orbital transfer vehicles. OTIS provides four modes of operation, with each mode providing successively stronger optimization capability. The most powerful mode uses a mathematical method called implicit integration to solve what engineers and mathematicians call the optimal control problem. OTIS 3.2, which was developed at the NASA Glenn Research Center, is the latest release of this industry workhorse and features new capabilities for parameter optimization and mission design. OTIS stands for Optimal Control by Implicit Simulation, and it is implicit integration that makes OTIS so powerful at solving trajectory optimization problems. Why is this so important? The optimization process not only determines how to get from point A to point B, but it can also determine how to do this with the least amount of propellant, with the lightest starting weight, or in the fastest time possible while avoiding certain obstacles along the way. There are numerous conditions that engineers can use to define optimal, or best. OTIS provides a framework for defining the starting and ending points of the trajectory (point A and point B), the constraints on the trajectory (requirements like "avoid these regions where obstacles occur"), and what is being optimized (e.g., minimize propellant). The implicit integration method can find solutions to very complicated problems when there is not a lot of information available about what the optimal trajectory might be. The method was first developed for solving two-point boundary value problems and was adapted for use in OTIS. Implicit integration usually allows OTIS to find solutions to problems much faster than programs that use explicit integration and parametric methods. Consequently, OTIS is best suited to solving very complicated and highly constrained problems

An (∞,2)(\infty,2)-categorical pasting theorem

We show that any pasting diagram in any $(\infty,2)$-category has ahomotopically unique composite. This is achieved by showing that the free 2-category generated by a pasting scheme is the homotopy colimit of its cells as an $(\infty,2)$-category. We prove this explicitly in the simplicial categories model and then explain how to deduce the model-independent statement from that calculation

NEXT Ion Propulsion System Configurations and Performance for Saturn System Exploration

The successes of the Cassini/Huygens mission have heightened interest to return to the Saturn system with focused robotic missions. The desire for a sustained presence at Titan, through a dedicated orbiter and in-situ vehicle, either a lander or aerobot, has resulted in definition of a Titan Explorer flagship mission as a high priority in the Solar System Exploration Roadmap. The discovery of active water vapor plumes erupting from the tiger stripes on the moon Enceladus has drawn the attention of the space science community. The NASA's Evolutionary Xenon Thruster (NEXT) ion propulsion system is well suited to future missions to the Saturn system. NEXT is used within the inner solar system, in combination with a Venus or Earth gravity assist, to establish a fast transfer to the Saturn system. The NEXT system elements are accommodated in a separable Solar Electric Propulsion (SEP) module, or are integrated into the main spacecraft bus, depending on the mission architecture and performance requirements. This paper defines a range of NEXT system configurations, from two to four thrusters, and the Saturn system performance capability provided. Delivered mass is assessed parametrically over total trip time to Saturn. Launch vehicle options, gravity assist options, and input power level are addressed to determine performance sensitivities. A simple two-thruster NEXT system, launched on an Atlas 551, can deliver a spacecraft mass of over 2400 kg on a transfer to Saturn. Similarly, a four-thruster system, launched on a Delta 4050 Heavy, delivers more than 4000 kg spacecraft mass. A SEP module conceptual design, for a two thruster string, 17 kW solar array, configuration is characterized

Influence of structure on the optical limiting properties of nanotubes

We investigate the role of carbon nanotubes structure on their optical limiting properties. Samples of different and well-characterized structural features are studied by optical limiting and pump-probe experiments. The influence of the diameter's size on the nano-object is demonstrated. Indeed, both nucleation and growth of gas bubbles are expected to be sensitive to diameter

Characterization of the Electronic Excited-State Energetics and Solution Structure of Lanthanide(III) Complexes with the Polypyridine Ligand 6,6\u27-Bis[bis(2-pyridylmethyl)aminomethyl]-2,2\u27-bipyridine

Absorption, emission, and excitation spectra for solid-state and solution of Tb(III), Dy(III), and Gd(III) complexes with the polypyridine ligand 6,6‘-bis[bis(2-pyridylmethyl)-aminomethyl]-2,2‘-bipyridine (C36H34N8) are presented. Measurements of excited-state lifetimes and quantum yields in various solvents at room temperature and 77 K are also reported and used to characterize the excited-state energetics of this system. Special attention is given to the characterization of metal-to-ligand energy transfer efficiency and mechanisms. The measurement of circularly polarized luminescence (CPL) from the solution of the Dy(III) complex following circularly polarized excitation confirms the chiral structure of the complexes under study. No CPL is present in the luminescence from the Eu(III) or Tb(III) complex because of efficient racemization. The variation of the magnitude of the CPL as a function of temperature from an aqueous solution of DyL is used for the first time to characterize the solution equilibria between different chiral species

Lanthanide Spectroscopic Studies of the Dinuclear and Mg(II)-Dependent PvuII Restriction Endonuclease

Type II restriction enzymes are homodimeric systems that bind four to eight base pair palindromic recognition sequences of DNA and catalyze metal ion-dependent phosphodiester cleavage. While Mg(II) is required for cleavage in these enzymes, in some systems Ca(II) promotes avid substrate binding and sequence discrimination. These properties make them useful model systems for understanding the roles of alkaline earth metal ions in nucleic acid processing. We have previously shown that two Ca(II) ions stimulate DNA binding by PvuII endonuclease and that the trivalent lanthanide ions Tb(III) and Eu(III) support subnanomolar DNA binding in this system. Here we capitalize on this behavior, employing a unique combination of luminescence spectroscopy and DNA binding assays to characterize Ln(III) binding behavior by this enzyme. Upon excitation of tyrosine residues, the emissions of both Tb(III) and Eu(III) are enhanced severalfold. This enhancement is reduced by the addition of a large excess of Ca(II), indicating that these ions bind in the active site. Poor enhancements and affinities in the presence of the active site variant E68A indicate that Glu68 is an important Ln(III) ligand, similar to that observed with Ca(II), Mg(II), and Mn(II). At low micromolar Eu(III) concentrations in the presence of enzyme (10−20 μM), Eu(III) excitation 7F0 → 5D0 spectra yield one dominant peak at 579.2 nm. A second, smaller peak at 579.4 nm is apparent at high Eu(III) concentrations (150 μM). Titration data for both Tb(III) and Eu(III) fit well to a two-site model featuring a strong site (Kd = 1−3 μM) and a much weaker site (Kd ≈ 100−200 μM). Experiments with the E68A variant indicate that the Glu68 side chain is not required for the binding of this second Ln(III) equivalent; however, the dramatic increase in DNA binding affinity around 100 μM Ln(III) for the wild-type enzyme and metal-enhanced substrate affinity for E68A are consistent with functional relevance for this weaker site. This discrimination of sites should make it possible to use lanthanide substitution and lanthanide spectroscopy to probe individual metal ion binding sites, thus adding an important tool to the study of restriction enzyme structure and function

Trajectory Optimization: OTIS 4

The latest release of the Optimal Trajectories by Implicit Simulation (OTIS4) allows users to simulate and optimize aerospace vehicle trajectories. With OTIS4, one can seamlessly generate optimal trajectories and parametric vehicle designs simultaneously. New features also allow OTIS4 to solve non-aerospace continuous time optimal control problems. The inputs and outputs of OTIS4 have been updated extensively from previous versions. Inputs now make use of objectoriented constructs, including one called a metastring. Metastrings use a greatly improved calculator and common nomenclature to reduce the user s workload. They allow for more flexibility in specifying vehicle physical models, boundary conditions, and path constraints. The OTIS4 calculator supports common mathematical functions, Boolean operations, and conditional statements. This allows users to define their own variables for use as outputs, constraints, or objective functions. The user-defined outputs can directly interface with other programs, such as spreadsheets, plotting packages, and visualization programs. Internally, OTIS4 has more explicit and implicit integration procedures, including high-order collocation methods, the pseudo-spectral method, and several variations of multiple shooting. Users may switch easily between the various methods. Several unique numerical techniques such as automated variable scaling and implicit integration grid refinement, support the integration methods. OTIS4 is also significantly more user friendly than previous versions. The installation process is nearly identical on various platforms, including Microsoft Windows, Apple OS X, and Linux operating systems. Cross-platform scripts also help make the execution of OTIS and post-processing of data easier. OTIS4 is supplied free by NASA and is subject to ITAR (International Traffic in Arms Regulations) restrictions. Users must have a Fortran compiler, and a Python interpreter is highly recommended