Gafiychuk V.,SGT Inc. |
Gafiychuk V.,NASA |
Datsko B.,Ukrainian Academy of Sciences
Computers and Mathematics with Applications | Year: 2010
In this article we investigate possible scenarios of pattern formations in reaction-diffusion systems with time fractional derivatives. Linear stability analysis is performed for different values of derivative orders. Results of qualitative analysis are confirmed by numerical simulations of specific partial differential equations. Most attention is paid to two models: a fractional order reaction diffusion system with Bonhoeffer-van der Pol kinetics and to the Brusselator model. © 2009 Elsevier Ltd. All rights reserved. Source
Sankararaman S.,SGT Inc.
Journal of Aerospace Information Systems | Year: 2015
This paper presents a computational framework for uncertainty characterization and propagation, as well as sensitivity analysis under the presenceofaleatory and epistemic uncertainties, and it developsarigorous methodology for efficient refinement of epistemic uncertainty by identifying important epistemic variables that significantly affect the overall performance of an engineering system. The proposed methodology is illustrated using the NASA Langley Research Center Uncertainty Quantification Challenge problem that deals with an uncertainty analysis of a generic transport model. First, Bayesian inference is used to infer subsystem-level epistemic quantities using the subsystemlevel model and corresponding data. Second, tools of variance-based global sensitivity analysis are used to identify four important epistemic variables (this limitation, specified in the NASA Langley Research Center Uncertainty Quantification Challenge, is reflective of practical engineering situations where not all epistemic variables can be refined due to time/budget constraints) that significantly affect system-level performance. The most significant contribution of this paper isthe development ofthe sequential refinement methodology, where epistemic variables for refinement are not identified all at once. Instead, only one variable isfirst identified, and then, Bayesian inference and global sensitivity calculations are repeated to identify the next important variable. This procedure is continued until all four variables are identified and the refinement in the system-level performance is computed. The advantages of the proposed sequential refinement methodology over the all-at-once uncertainty refinement approach are explained and numerically demonstrated, before being applied to the NASA Langley Research Center Uncertainty Quantification Challenge problem. Copyright © 2014 by the American Instituteof Aeronautics and Astronautics, Inc. Source
Wang Y.M.,National Oceanic and Atmospheric Administration |
Yang X.,SGT Inc.
Journal of Geodesy | Year: 2013
This paper is devoted to the spherical and spheroidal harmonic expansion of the gravitational potential of the topographic masses in the most rigorous way. Such an expansion can be used to compute gravimetric topographic effects for geodetic and geophysical applications. It can also be used to augment a global gravity model to a much higher resolution of the gravitational potential of the topography. A formulation for a spherical harmonic expansion is developed without the spherical approximation. Then, formulas for the spheroidal harmonic expansion are derived. For the latter, Legendre's functions of the first and second kinds with imaginary variable are expanded in Laurent series. They are then scaled into two real power series of the second eccentricity of the reference ellipsoid. Using these series, formulas for computing the spheroidal harmonic coefficients are reduced to surface harmonic analysis. Two numerical examples are presented. The first is a spherical harmonic expansion to degree and order 2700 by taking advantage of existing software. It demonstrates that rigorous spherical harmonic expansion is possible, but the computed potential on the geoid shows noticeable error pattern at Polar Regions due to the downward continuation from the bounding sphere to the geoid. The second numerical example is the spheroidal expansion to degree and order 180 for the exterior space. The power series of the second eccentricity of the reference ellipsoid is truncated at the eighth order leading to omission errors of 25 nm (RMS) for land areas, with extreme values around 0.5 mm to geoid height. The results show that the ellipsoidal correction is 1.65 m (RMS) over land areas, with maximum value of 13.19 m in the Andes. It shows also that the correction resembles the topography closely, implying that the ellipsoidal correction is rich in all frequencies of the gravity field and not only long wavelength as it is commonly assumed. © 2013 Springer-Verlag Berlin Heidelberg. Source
McClelland R.S.,SGT Inc.
IEEE Aerospace Conference Proceedings | Year: 2015
Lightweight and high resolution optics are needed for future space-based X-ray telescopes to achieve advances in high-energy astrophysics. The Next Generation X-ray Optics (NGXO) team at NASA GSFC is nearing mission readiness for a 10 arc-second Half Power Diameter (HPD) slumped glass mirror technology while laying the groundwork for a future 1-2 arc-second technology based on polished silicon mirrors. Technology Development Modules (TDMs) have been designed, fabricated, integrated with mirrors segments, and extensively tested to demonstrate technology readiness. Tests include X-ray performance, thermal vacuum, acoustic load, and random vibration. The thermal vacuum and acoustic load environments have proven relatively benign, while the random vibration environment has proven challenging due to large input amplification at frequencies above 500 Hz. Epoxy selection, surface preparation, and larger bond area have increased bond strength while vibration isolation has decreased vibration amplification allowing for space launch requirements to be met in the near term. The next generation of TDMs, which demonstrate a lightweight structure supporting more mirror segments, has been recently fabricated. Analysis predicts superior performance characteristics due to the use of E-60 Beryllium-Oxide Metal Matrix Composite material, with only a modest cost increase. These TDMs are larger, lighter, stiffer, and stronger than the current generation. Preliminary steps are being taken to enable mounting and testing of 1-2 arc-second mirror segments expected to be available in the future. A Vertical Beam Line (VBL) test facility will minimize mirror gravity distortion and allow for less constrained mirror mounts, such as fully kinematic mounts. Permanent kinematic mounting into a modified TDM has been demonstrated to achieve 2 arc-second level distortion free alignment. © 2015 IEEE. Source
Nishimori H.,Tokyo Institute of Technology |
Tsuda J.,Tokyo Institute of Technology |
Knysh S.,NASA |
Knysh S.,SGT Inc.
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics | Year: 2015
Relations of simulated annealing and quantum annealing are studied by a mapping from the transition matrix of classical Markovian dynamics of the Ising model to a quantum Hamiltonian and vice versa. It is shown that these two operators, the transition matrix and the Hamiltonian, share the eigenvalue spectrum. Thus, if simulated annealing with slow temperature change does not encounter a difficulty caused by an exponentially long relaxation time at a first-order phase transition, the same is true for the corresponding process of quantum annealing in the adiabatic limit. One of the important differences between the classical-to-quantum mapping and the converse quantum-to-classical mapping is that the Markovian dynamics of a short-range Ising model is mapped to a short-range quantum system, but the converse mapping from a short-range quantum system to a classical one results in long-range interactions. This leads to a difference in efficiencies that simulated annealing can be efficiently simulated by quantum annealing but the converse is not necessarily true. We conclude that quantum annealing is easier to implement and is more flexible than simulated annealing. We also point out that the present mapping can be extended to accommodate explicit time dependence of temperature, which is used to justify the quantum-mechanical analysis of simulated annealing by Somma, Batista, and Ortiz. Additionally, an alternative method to solve the nonequilibrium dynamics of the one-dimensional Ising model is provided through the classical-to-quantum mapping. © 2015 American Physical Society. Source