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Higher order derivatives of energy with respect to internuclear separation for diatomic molecules derived from ordinary and integral Hellmann- Feynman theorems
Efforts are described to extend the averaged Lagrangian method of describing small signal wave propagation and nonlinear wave interaction, developed by earlier workers for cold plasmas, to the more general conditions of warm collisionless plasmas, and to demonstrate particularly the effectiveness of the method in analyzing wave-wave interactions. The theory is developed for both the microscopic description and the hydrodynamic approximation to plasma behavior. First, a microscopic Lagrangian is formulated rigorously, and expanded in terms of perturbations about equilibrium. Two methods are then described for deriving a hydrodynamic Lagrangian. In the first of these, the Lagrangian is obtained by velocity integration of the exact microscopic Lagrangian. In the second, the expanded hydrodynamic Lagrangian is obtained directly from the ex...
Predictions of the backscatter spectrum are compared, including effects of ionospheric inhomogeneity with experimental observations of incoherent backscatter from an artificially heated region. Calculations show that the strongest backscatter echo received is not, in fact, from the reflection level, but from a region some distance below (about 0.5 km for an experiment carried out at Arecibo), where the pump wave from a HF transmitter approximately 100 kW) is below the threshold for parametric amplification. By taking the standing wave pattern of the pump into account, asymmetry is explained of the up-shifted and down-shifted plasma lines in the backscatter spectrum, and the several peaks typically observed in the region of the spectrum near the HF transmitter frequency.
An orbit perturbation procedure is applied to the description of monochromatic, large-amplitude, electrostatic plasma wave propagation. In the lowest-order approximation, untrapped electrons are assumed to follow constant-velocity orbits and trapped electrons are assumed to execute simple harmonic motion. The deviations of these orbits from the actual orbits are regarded as perturbations. The nonlinear damping rate and frequency shift are then obtained in terms of simple functions. The results are in good agreement with previous less approximate analyses. A significant feature of the analysis is that it treats a single wave by techniques previously applied to turbulent spectra. The analysis can consequently be extended to the case of a large-amplitude wave interacting with a lower-amplitude spectrum of waves.
This thesis is a work on a contact line instability at a finite Reynolds number, 0 < Re < O(100). This problem corresponds to an immersion droplet applied in a liquid- immersion lithography machine. We perform extensive works to understand this instability problem by means of experimental, numerical, and theoretical ways. First, in order to measure the 3D internal flow pattern, we perform 3D-3C velocimetry techniques, i.e. tomographic particle image velocimetry and 3D particle tracking velocimetry. Furthermore, we observe droplet shape changes by shadowgraphy. Second, based on these experimental results, we develop a modified three-dimensional lubrication model including inertial effects. In this model, the pressure is described as a combination of dynamic pressure effects and capillary pressure effects. By this extended model, we obta...
An orbit perturbation procedure was applied to the description of monochromatic, large-amplitude, electrostatic plasma wave propagation. In the lowest order approximation, untrapped electrons were assumed to follow constant-velocity orbits and trapped electrons were assumed to execute simple harmonic motion. The deviations of these orbits from the actual orbits were regarded as perturbations. The nonlinear damping rate and frequency shift were then obtained in terms of simple functions. The results are in good agreement with previous less approximate analyses.
This paper examined persistence of energy savings from the application of the Monitoring andVerification (M&V) for the Fort Hood EnergyServices Performance Contract (ESPC). The first and second ESPC Delivery Orders (DO) wereimplemented for 58 buildings in 2004-2005 and for 47 building in 2006-2008, respectively. To evaluate the long-term energy savings from the first and second ESPCs, ten sites where the hourly data in 2008-2010 were available were selected, and weather-dependent and weather-independent linear and change-point linear models were calculated with the ASHRAE's Inverse Modeling Toolkit (IMT). The results show there was a considerable difference in persistence of energy savings site-by-site: varying from -352% to 677% of the audit-estimated electricity savings for the six DO#1 and four DO#2 buildings. For all ten buildings,...
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