Formal Rayleigh-Schroedinger perturbation theory for both degenerate and non-degenerate energy states
Degenerate and nondegenerate energy states and wave functions formulated by Rayleigh- Schroedinger perturbation theory
Hirschfelder, J. O.↗
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Results for “state energy”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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Ground-state energies of the nonlinear sigma model and the Heisenberg spin chains
A theorem on the O(3) nonlinear sigma model with the topological theta term is proved, which states that the ground-state energy at theta = pi is always higher than the ground-state energy at theta = 0, for the same value of the coupling constant g. Provided that the nonlinear sigma model gives the correct description for the Heisenberg spin chains in the large-s limit, this theorem makes a definite prediction relating the ground-state energies of the half-integer and the integer spin chains. The ground-state energies obtained from the exact Bethe ansatz solution for the spin-1/2 chain and the numerical diagonalization on the spin-1, spin-3/2, and spin-2 chains support this prediction.
Zhang, Shoucheng↗
Retarded interaction energies between like atoms in different energy states.
Retarded long range interaction energies between two like atoms in different energy states, noting selection rules for resonant interactions
Meath, W. J.↗
Near-optimal energy transitions for energy-state trajectories of hypersonic aircraft
A problem of the instantaneous energy transition that occurs in energy-state approximation is considered. The transitions are modeled as a sequence of two load-factor bounded paths (either climb-dive or dive-climb). The boundary-layer equations associated with the energy-state dynamic model are analyzed to determine the precise location of the transition.
Ardema, M. D.↗
Solid State Energy Harvesting and Power Conversion in Gas Turbine Engines
Overview: Solid state energy harvesting using waste heat available in gas turbine engine offers potential for power generation to meet growing power needs of aircraft; Thermoelectric material advances offer new opportunities; Weight-optimized integrated turbine engine structure incorporating energy conversion devices.
aircraft↗
Ground state energy of electrons in a static point-ion lattice
The ground state energy of a neutral collection of protons and electrons was investigated under the assumption that in the ground state configuration, static protons occupy the sites of a rigid Bravais lattice. The Wigner-Seitz method was used in conjunction with three postulated potentials: bare Coulomb, Thomas-Fermi screening, and screening by a uniform bare background charge. Within these approximations, the exact band-minimum energy and wave functions are derived. For each of the three potentials, the approximate minimum ground state energy per proton (relative to isolated electrons and protons) is, respectively, -1.078 Ry, -1.038 Ry, and -1.052 Ry. These three minima all fall at a density of about 0.60 gm/cu cm, which is thus an approximate lower bound on the density of metallic hydrogen at its transition pressure.
Styer, D. F.↗
The Ground State Energy of a Molecule in the Adiabatic Approximation
Ground state energy of molecule in adiabatic approximation
GROUND STATE↗
Energy-state formulation of lumped volume dynamic equations with application to a simplified free piston Stirling engine
Lumped volume dynamic equations are derived using an energy state formulation. This technique requires that kinetic and potential energy state functions be written for the physical system being investigated. To account for losses in the system, a Rayleigh dissipation function is formed. Using these functions, a Lagrangian is formed and using Lagrange's equation, the equations of motion for the system are derived. The results of the application of this technique to a lumped volume are used to derive a model for the free piston Stirling engine. The model was simplified and programmed on an analog computer. Results are given comparing the model response with experimental data.
Daniele, C. J.↗
Energy-state formulation of lumped volume dynamic equations with application to a simplified free piston Stirling engine
Lumped volume dynamic equations are derived using an energy-state formulation. This technique requires that kinetic and potential energy state functions be written for the physical system being investigated. To account for losses in the system, a Rayleigh dissipation function is also formed. Using these functions, a Lagrangian is formed and using Lagrange's equation, the equations of motion for the system are derived. The results of the application of this technique to a lumped volume are used to derive a model for the free-piston Stirling engine. The model was simplified and programmed on an analog computer. Results are given comparing the model response with experimental data.
Daniele, C. J.↗
The energy-state approximation in performance optimization of supersonic aircraft.
Energy state approximation for supersonic aircraft performance optimization with extension to maximum range problems, noting comparison with complex dynamic models
Bryson, A. E., Jr.↗
Energy-state approximation in performance optimization of supersonic aircraft
Energy state approximation for supersonic aircraft performance optimization with extension to maximum range problems, noting comparison with complex dynamic models
Bryson, A. E., Jr.↗
Determination of surface state energy positions by surface photovoltage spectrometry- CdS
Surface state energy positions determination in high-energy gap semiconductors by photovoltage spectral distribution
Balestra, C. L.↗
Bounded energy states in homogeneous turbulent shear flow: An alternative view
The equilibrium structure of homogeneous turbulent shear flow is investigated from a theoretical standpoint. Existing turbulence models, in apparent agreement with physical and numerical experiments, predict an unbounded exponential time growth of the turbulent kinetic energy and dissipation rate; only the anisotropy tensor and turbulent time scale reach a structural equilibrium. It is shown that if vortex stretching is accounted for in the dissipation rate transport equation, then there can exist equilibrium solutions, with bounded energy states, where the turbulence production is balanced by its dissipation. Illustrative calculations are present for a k-epsilon model modified to account for vortex stretching. The calculations indicate an initial exponential time growth of the turbulent kinetic energy and dissipation rate for elapsed times that are as large as those considered in any of the previously conducted physical or numerical experiments on homogeneous shear flow. However, vortex stretching eventually takes over and forces a production-equals-dissipation equilibrium with bounded energy states. The validity of this result is further supported by an independent theoretical argument. It is concluded that the generally accepted structural equilibrium for homogeneous shear flow with unbounded component energies is in need of re-examination.
Bernard, Peter S.↗
CASPEr: an Approach to Characterize the Performance of Onboard Airplane Energy State and Automation Mode Prediction Functions
The Commercial Aviation Safety Team (CAST) has identified a set of safety enhancements to mitigate the risks of loss of control in-flight (LOCI) accidents and incidents involving commercial transport airplanes. In support of this, NASA has been developing technologies intended to enhance flight crew awareness of airplane systems, attitude, and energy state. This report describes preliminary ideas for a methodology to assess the goodness of onboard airplane energy state and automation mode prediction functions. The methodology is intended to contribute to the goal of moving these prediction technologies to the readiness level required for transition to industry and reduce the technology certification risks. In addition, this report describes a simulation-based approach named CASPEr (Characterization of Airplane State Prediction Error) to characterize the performance of these predictive functions over a wide range of operational conditions. The first exploratory version of this approach is described. The bulk of the report documents the initial results of tests to characterize the performance of an airplane trajectory prediction function. Future reports will give additional performance characterization results for this function and a complete description of the proposed methodology to assess such functions.
Torres-Pomales, Wilfredo↗
Ground-state energy of the Anderson model by the cluster variation method.
Ground state energy of Anderson Hamiltonian calculated by cluster variation for cases of infinite d-d correlation energy
Bose, S. M.↗
Structural expansions for the ground state energy of a simple metal
A structural expansion for the static ground state energy of a simple metal is derived. An approach based on single particle band structure which treats the electron gas as a non-linear dielectric is presented, along with a more general many particle analysis using finite temperature perturbation theory. The two methods are compared, and it is shown in detail how band-structure effects, Fermi surface distortions, and chemical potential shifts affect the total energy. These are of special interest in corrections to the total energy beyond third order in the electron ion interaction, and hence to systems where differences in energies for various crystal structures are exceptionally small. Preliminary calculations using these methods for the zero temperature thermodynamic functions of atomic hydrogen are reported.
Hammerberg, J.↗
Ground-state energies of simple metals
A structural expansion for the static ground-state energy of a simple metal is derived. Two methods are presented, one an approach based on single-particle band structure which treats the electron gas as a nonlinear dielectric, the other a more general many-particle analysis using finite-temperature perturbation theory. The two methods are compared, and it is shown in detail how band-structure effects, Fermi-surface distortions, and chemical-potential shifts affect the total energy. These are of special interest in corrections to the total energy beyond third order in the electron-ion interaction and hence to systems where differences in energies for various crystal structures are exceptionally small. Preliminary calculations using these methods for the zero-temperature thermodynamic functions of atomic hydrogen are reported.
Hammerberg, J.↗
Long-range energy-state maneuvers for minimum time to specified terminal conditions
The calculus of variations and energy-state approximation are used to determine the optimum maneuvers in three-dimensional minimum-time aircraft flight paths to a specified final point or line. Constraints on thrust, Mach number, angle of attack, dynamic pressure, and load factor are included. It is shown that when the initial range is sufficiently large that the maximum velocity constraint is encountered en route, the calculation of minimum-time maneuvers can be greatly simplified by a separation of arcs into two two-parameter problems. Suboptimal paths along which the bank angle is restricted to three discrete values (negative maximum angle, 0, positive maximum angle) compare favorably with the optimum, continuous bank angle solutions for transonic speeds and below.
Parsons, M. G.↗