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Subsonic and supersonic indicial aerodynamics and aerodynamic transfer function for complex configurations

A general theory for indicial-potential-compressible aerodynamics around complex configurations is presented. The motion is assumed to consist of constant subsonic or supersonic speed (steady state) and small perturbations around the steady state. Using the finite-element method to discretize the space problem, a set of differential-difference equations in time relating the potential to its normal derivative on the surface of the body was obtained. The aerodynamics transfer function was derived by using standard method of operational calculus.

Morino, L.↗

Determining Concentration of Nanoparticles from Ellipsometry

A method of using ellipsometry or polarization analysis of light in total internal reflection of a surface to determine the number density of gold nanoparticles on a smooth substrate has been developed. The method can be modified to enable determination of densities of sparse distributions of nanoparticles in general, and is expected to be especially useful for measuring gold-nanoparticle-labeled biomolecules on microarrays. The method is based on theoretical calculations of the ellipsometric responses of gold nanoparticles. Elements of the calculations include the following: For simplicity, the gold nanoparticles are assumed to be spherical and to have the same radius. The distribution of gold nanoparticles is assumed to be a sub-monolayer (that is, sparser than a monolayer). The optical response of the sub-monolayer is modeled by use of a thin-island-film theory, according to which the polarizabilities parallel and perpendicular to the substrate are functions of the wavelength of light, the dielectric functions (permittivities expressed as complex functions of frequency or wavelength) of the gold and the suspending medium (in this case, the suspending medium is air), the fraction of the substrate area covered by the nanoparticles, and the radius of the nanoparticles. For the purpose of the thin-island-film theory, the dielectric function of the gold nanoparticles is modeled as the known dielectric function of bulk gold plus a correction term that is necessitated by the fact that the mean free path length for electrons in gold decreases with decreasing radius, in such a manner as to cause the imaginary part of the dielectric function to increase with decreasing radius (see figure). The correction term is a function of the nanoparticle radius, the wavelength of light, the mean free path and the Fermi speed of electrons in bulk gold, the plasma frequency of gold, and the speed of light in a vacuum. These models are used to calculate ellipsometric responses for various concentrations of gold nanoparticles having an assumed radius. The modeled data indicates distinct spectral features for both the real and the imaginary part of the dielectric function. An ellipsometric measurement would determine this distinct feature and thus can be used to measure nanoparticle concentration. By "ellipsometric responses" is meant the intensities of light measured in various polarization states as functions of the angle of incidence and the polarization states of the incident light. These calculated ellipsometric responses are used as calibration curves: Data from subsequent ellipsometric measurements on real specimens are compared with the calibration curves. The concentration of the nanoparticles on a specimen is assumed to be that of the calibration curve that most closely matches the data pertaining to that specimen.

Venkatasubbarao, Srivatsa↗

On the mapping associated with the complex representation of functions and processes.

The mapping between function spaces that is implied by the representation of a real 'bandpass' function by a complex 'low-pass' function is explicitly accepted. The discussion is extended to the representation of stationary random processes where the mapping is between spaces of random processes. This approach clarifies the nature of the complex representation, especially in the case of random processes and, in addition, derives the properties of the complex representation.-

Harger, R. O.↗

Enabling Assurance in the MBSE Environment

A number of specific benefits that fit within the hallmarks of effective development are realized with implementation of model-based approaches to systems and assurance. Model Based Systems Engineering (MBSE) enabled by standardized modeling languages (e.g., SysML®) is at the core. These benefits in the context of spaceflight system challenges can include [1]: • Improved management of complex development • Reduced risk in the development process • Improved cost management • Improved design decisions With appropriate modeling techniques the assurance community also can improve early oversight and insight into project development. NASA has shown the basic constructs of SysML in an MBSE environment offer several key advantages, within a Model Based Mission Assurance (MBMA) initiative [2, 3]. These include the following: • Model viewpoints that promote rapid and systematic assessment of requirements coverage, hazard tagging and risk management • Embedded safety assessments for launch vehicles • Deployment of model assisted development of reliability products - Failure Modes and Effects Analyses (FMEAs) and Fault Trees • Test Planning • Validation and Verification of complex functions • Support of Assurance Case development for complex systems In addition, while there are benefits to be harvested, there is a realization that these do not come without effort and cost. Enabling model-based approaches requires structure, not only in an organizational context, but in a modeling context as well. There can be a steep learning curve and costs associated to train skilled modelers. But, on the other hand, not all of the assurance community need to be modelers. Models themselves must conform to ontologies that enable assurance. This places constraints upon the models and modelers. Optimums have yet to be developed where resources and constraints on modeling must be traded off in the organization and modeling efforts for projects. A number of barriers need to be overcome, as well, which pose challenges to the developers of the software that supports MBSE/MBMA. Information and data must be made to flow seamlessly through the life cycle. Because there is a wide variety of tools used in the community, to avoid the problems of the past of silos, delays, and diverging interests, information should flow among these tools to support the “single source of truth” paradigm of MBSE. This will greatly facilitate MBMA and advancement of assurance functions.

Evans, John W.↗

Algorithm For Optimal Control Of Large Structures

Cost of computation appears competitive with other methods. Problem to compute optimal control of forced response of structure with n degrees of freedom identified in terms of smaller number, r, of vibrational modes. Article begins with Hamilton-Jacobi formulation of mechanics and use of quadratic cost functional. Complexity reduced by alternative approach in which quadratic cost functional expressed in terms of control variables only. Leads to iterative solution of second-order time-integral matrix Volterra equation of second kind containing optimal control vector. Cost of algorithm, measured in terms of number of computations required, is of order of, or less than, cost of prior algoritms applied to similar problems.

Salama, Moktar A.↗