Dual Functions and Heat Expansions
Radial heat polynomial transformations in series expansions of heat equation
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Radial heat polynomial transformations in series expansions of heat equation
Asymptotic expansion method for solving certain classes of singular perturbation problems with application in viscous flow
Propagation of elastic expansion wave from circular hole in cylindrical, anisotropic, inhomogeneous plate
Matched asymptotic expansion method applied to ordinary and optimal trajectory problems in hypervelocity flight dynamics
Application of matched asymptotic expansions to hypervelocity flight mechanics
Algorithm and recursion formulas for series expansion of three-body problem
Spectrophotometric measurements of vibrational relaxation of CO in shock wave and nozzle expansion-flow environments
Impact expansions and interference patterns in atomic scattering theory for cases of forward scattering, backscatter, inversion problem and screened Coulomb potential approximation
Length-temperature measurements for several polymers and mixtures for detection of transitions and determination of location and magnitude of expansion coefficient changes
Power series expansion of electron velocity distribution function, computing harmonic electric current densities in plasma
A non contact measurement technique for the density and the thermal expansion coefficient of.
The Mode-Expansion Method (MEM) is introduced to calculate the electromagnetic (EM) waves scattered by 2-D rough water surfaces at low-grazing angles. The Electric Field Integral Equation (EFIE) is used in defining the problem and is simplified by using the Impedance Boundary Condition (IBC). The surface currents are expressed as the sum of modes expanded as the Fourier series with incident wave as the dominant mode. It is shown that, by the MEM and for the geometry with transmitting and receiving waves at low-grazing angles, very few modes are needed in solving the forward scattering field with reasonable accuracy.
The dark colors of Jupiter's North Equatorial Belt (NEB, 7-17degN) appeared to expand northward into the neighboring one in 2015, consistent with a 35 year cycle. Inversions of thermal-IR imaging from the Very Large Telescope revealed a moderate warming and reduction of aerosol opacity at the cloud tops at 17-20degN, suggesting subsidence and drying in the expanded sector. Two new thermal waves were identified during this period: (i) an upper tropospheric thermal wave (wave number 16-17, amplitude 2.5 K at 170 mbar) in the mid-NEB that was anticorrelated with haze reflectivity; and (ii) a stratospheric wave (wave number 13-14, amplitude 7.3 K at 5 mbar) at 20-30degN. Both were quasi-stationary, confined to regions of eastward zonal flow, and are morphologically similar to waves observed during previous expansion events.
High temperature X-ray diffraction (XRD) scans of Y2Si2O7 and Yb2Si2O7 reactions with calcium-magnesium-aluminosilicates (CMAS) were utilized to determine thermal expansion coefficients (CTEs) of Ca2Y8(SiO4)6O2 and Ca2Yb8(SiO4)6O2 apatite materials. In order to validate these measurements, the CTEs of Y2Si2O7, Yb2Si2O7 and SiO2 were also determined from the same scans. The directional CTEs for γ-Y2Si2O7 were determined to be αa=5.84×10-6/K, αb=6.81×10-6/K and αc=0.81×10-6/K, and β-Yb2Si2O7 was determined to have values of αa=6.89×10-6/K, αb=4.81×10-6/K and αc=2.78×10-6/K. The average CTEs of γ-Y2Si2O7 and β-Yb2Si2O7 were determined to be 4.5×10-6/K and 4.7×10-6/K, respectively, which agreed with previous analyses. Ca2Y8(SiO4)6O2 exhibited directional CTEs of αa=9.36×10-6/K and αc=7.95×10-6/K (averaged between two sets of data), whereas Ca2Yb8(SiO4)6O2 had values that were very similar (αa=9.63×10-6/K, αc=7.45×10-6/K). Both results for the Ca2RE8(SiO4)6O2 apatites correlated well with the limited data on apatite-type silicates available in literature.
Environmental barrier coatings (EBCs) are an enabling technology for silicon carbide (SiC)-based ceramic matrix composites (CMCs) in extreme environments such as gas turbine engines. However, development of new coating systems is hindered by the large design space and difficulty in predicting properties for these materials. Density Functional Theory (DFT) has successfully been used to model and predict some thermodynamic and thermo-mechanical properties of high-temperature ceramics for EBCs, although these calculations are challenging due to their high computational costs. In this work, we use machine learning to train a deep neural network potential (DNP) for Y 2 Si 2 O 7 , which is then applied to calculate thermodynamic and thermo-mechanical properties at near-DFT accuracy much faster and using less computational resources than DFT. We use this DNP to predict phonon-based thermodynamic properties of Y 2 Si 2 O 7 with good agreement to DFT and experiments. We also utilize the DNP to calculate the anisotropic, lattice direction-dependent coefficients of thermal expansion (CTEs) for Y 2 Si 2 O 7 . Molecular dynamics trajectories using the DNP correctly demonstrate accurate prediction of the anisotropy of the CTE in good agreement with diffraction experiments. In the future, this DNP could be applied to accelerate additional property calculations for Y 2 Si 2 O 7 compared to DFT or experiments.
The intermittent nature of renewable energy poses new challenges for power grids due to its variable and un- certain power output. These features of renewable generation are becoming more relevant to transmission planning as grids reach higher penetration levels of renewable energy. In this paper we present an approach for transmission planning based on scalable computational approaches which enable the explicit consideration of operational uncertainties in the planning process. Using three-stage stochastic programming and the progressive hedging algorithm, we compute transmission expansion decisions on a modified RTS-GMLC test system. We augment the grid with large amounts of wind generation and consider many operational scenarios subject to wind uncertainty. This is an example of a possible use of the ExaSGD security constrained AC optimal power flow solver.
This fact sheet focuses specifically on one element of the long-term planning process, the capacity expansion model. It highlights the key advances in these models to enable planning for systems with growing shared of renewable energy and storage.
The intermittent nature of power from renewable energy sources poses new challenges for electrical grids. This is due to the variable and uncertain nature of the power output from these resources. These features of renewable generation are becoming more relevant to energy system planning as grids reach higher penetration levels of renewable energy. In this presentation we present approaches for energy system planning based on scalable computational approaches which enable the explicit consideration of operational uncertainties in the planning process. Using multi-stage stochastic programming and the progressive hedging algorithm, we compute energy system expansion decisions on modified versions of the RTS-GMLC test system augmented with large amounts of renewable generation.