Ensemble non-interacting kinetic energy functional is constructed for spherically symmetric systems. The differential virial theorem is derived for the ensemble. A first-order differential equation for the functional derivative of the ensemble non-interacting kinetic energy functional and the ensemble Pauli potential is presented. This equation can be solved and a special case of the solution p...

A method is described for investigating the ionization produced in helium by collisions between quasi-stationary atoms—that is, atoms possessing only thermal velocities—and a beam of neutral helium atoms with kinetic energy less than 100 eV. Ionization is shown to begin when the kinetic energy of the bombarding atoms is twice as great as the minimum kinetic energy which electrons must possess i...

NASA/TM—2013-217850 1 ∆t∗ nondimensional time step, ∆t/(L/V0) kinetic energy dissipation rate 1 kinetic energy dissipation rate computed from deviatoric strain rate 3 kinetic energy dissipation rate computed from pressure dilatation κ angular wave number μ kinematic viscosity ν spectroscopic wave number ωi vorticity vector Ω volume ρ density σ filter damping coefficient τij stress tensor ζ enst...

The behavior of an atom in a nonuniform magnetic field is analyzed, as well as the motion of a classical magnetic dipole (a spinning charged ball) and a rotating charged ring. For the atom it is shown that, while the magnetic field does no work on the electron-orbital contribution to the magnetic moment (the source of translational kinetic energy being the internal energy of the atom), whether ...

This paper investigates the asymptotical stabilization of the time-invariant and the time-varying Port-Hamiltonian (PH) systems via a new kinetic energy-shaping (KES) method. Firstly, a desired kinetic energy function is designed for the non-trivial points. Secondly, applying the KES method to the Hamiltonian function with the desired kinetic energy function builds some matching equations. Thir...

We introduce a notion of generalized Navier-Stokes flows on mani-folds, that extends to the viscous case the one defined by Brenier. Their kinetic energy extends the kinetic energy for classical Brownian flows, defined as the L 2 norm of their drift. We prove that there exists a generalized flow which realizes the infimum of kinetic energies among all generalized flows with prescribed initial a...

We have measured the M(2,3)VV Auger spectra of Cu(110) and studied the final state interaction following the Cu 3p core electron excitation. We have observed that the kinetic energy of the M(2,3)VV Auger electron shifts to an energy higher than that of the normal Auger electrons near the Cu 3p threshold, and it converges to the constant kinetic energy of the normal Auger electrons as the excita...

Observations of turbulent kinetic energy (TKE) dynamics in the ocean surface boundary layer are presented here and compared with results from previous observational, numerical, and analytic studies. As in previous studies, the dissipation rate of TKE is found to be higher in the wavy ocean surface boundary layer than it would be in a flow past a rigid boundary with similar stress and buoyancy f...

Throughfall kinetic energy (TKE) plays an important role in soil erosion in forests. We studied TKE as a function of biodiversity, functional diversity as well as structural stand variables in a secondary subtropical broad-leaved forest in the Gutianshan National Nature Reserve (GNNR) in south-east China, a biodiversity hotspot in the northern hemisphere with more than 250 woody species present...

we prove the existence of steady 2-dimensional flows, containing a bounded vortex, and approaching a uniform flow at infinity. the data prescribed is the rearrangement class of the vorticity field. the corresponding stream function satisfies a semilinear elliptic partial differential equation. the result is proved by maximizing the kinetic energy over all flows whose vorticity fields are rearra...