Continuum discretization using orthogonal polynomials
A method for discretizing the continuum by using a transformed harmonic oscillator basis has recently been presented @Phys. Rev. A 63, 052111 ~2001!#. In the present paper, we propose a generalization of that formalism which does not rely on the harmonic oscillator for the inclusion of the continuum in the study of weakly bound systems. In particular, we construct wave functions that represent the continuum by making use of families of orthogonal polynomials whose weight function is the square of the ground state wave function, expressed in terms of a suitably scaled variable. As an illustration, the formalism is applied to one-dimensional ‘
Nuclear density functional theory
An understanding of atomic nuclei is crucial for a complete nuclear theory, for the nuclear astrophysics, for performing new experimental tasks, and for various other applications. Within a density functional theory, the total binding energy of the nucleus is given by a functional of the nuclear density matrices and their derivatives. The variation of the energy density functional with respect to particle and pairing densities leads to the Hartree-Fock-Bogoliubov equations. The “Universal Nuclear Energy Density Functional” (UNEDF) SciDAC project to develop and optimize the energy density functional for atomic nuclei using state-of-the-art computational infrastructure, is briefly described. The ultimate goal is to replace current phenomenological models of the nucleus with a well-founded microscopic theory with minimal uncertainties, capable of describing nuclear data and extrapolating to unknown regions.
Turbulent boundary layer wall‐pressure fluctuations downstream from an abrupt change in surface roughness
Spectra of wall‐pressure fluctuations beneath a turbulent boundary layer have been investigated immediately downstream from an abrupt change in surface roughness, from slightly rough to very rough. Over the measurable frequency band (400 Hz to 7 kHz), the spectra in the first 150 mm scale on wall variables. This indicates that the motions responsible for the pressure fluctuations measured in this region are very close to the wall. Farther downstream this scaling procedure breaks down. It is suggested that the initially thin internal layer behaves independently of the flow external to it until it has grown appreciably and only then interacts with the outer boundary layer. It was found that, for all frequencies measured, the dimensional spectral level decreases initially then rises to a maximum at 250 mm from the roughness change before decreasing once more. The position of the maximum is close to where the internal layer ceases to have a distinct edge.