Classical Scaling Relations Research Articles

A Lagrangian stochastic model for turbulent dispersion

A Lagrangian stochastic model is adopted for the calculations of turbulent dispersion in turbulent channel flows. Dispersion of a fluid particle and relative dispersion between two particles released at the same location are investigated and compared with the classical scaling relations for homogeneous turbulence. The viscous effect is realized by adding a Browinian random walk to the calculation of the position of a particle. The near-wall accumulation of particles is examined.

Numerical Study of Shear-Enhanced Turbulent Diffusion

The purpose of this study is to investigate the effect of shear on turbulent diffusion. Turbulent Couette flows at low Reynolds number are numerically simulated using a Lagrangian PDF method. Flow field and particle trajectories are computed and analyzed in detail. Statistics for particle dispersion obtained from numerical simulations is compared with the classical scaling relations for dispersion in a shear flow.

Percolation models for gate oxide breakdown

Computer calculations of the formation of a percolation path across a finite lattice are used to model dielectric breakdown. The classical scaling relations for percolation are expected to be valid only for large (finite) systems near pc. We investigate the opposite limit of very small samples, comparable to the lattice spacing. It is shown that relatively simple numerical calculations can quantitatively describe the statistics and thickness dependence of oxide breakdown in thin samples. The critical defect density for breakdown shows a strong decrease with thickness below about 5 nm, then becomes constant below 3 nm. Both of these features can be quantitatively explained by percolation on a finite lattice. The effective defect “size” of about 3 nm is obtained from the thickness dependence of the breakdown distributions. The model predicts a singular behavior when the oxide thickness becomes less than the defect size, because in this limit a single defect near the center of the oxide is sufficient to create a continuous path across the sample. It is found that a given percolation path has a probability of about 10−3 for initiating destructive breakdown. We investigate both homogeneous percolation and percolation in a nonuniform density of sites.

Ionization and charge transfer in collisions of protons with Ba+ and Sr+ ions

A fast intersecting beam technique previously developed in this laboratory has been used to study collisions of protons with the alkali-like ions Ba+ and Sr+ at CM energies within the range 50-500 keV. Absolute cross sections for Ba2+ and Sr2+ production from the combined processes of charge transfer and ionization have been measured. Separate measurements of the cross sections for charge transfer also allowed cross sections for ionization to be determined. Measured cross sections for charge transfer are shown to be in poor agreement with available theoretical predictions. Cross sections for ionization (believed to be dominated by excitation-autoionization) are compared with those for equivelocity electron impact and Born predictions. The applicability of a simple classical scaling relation is also considered.

Charge transfer and ionisation of H+-C+and H+-N+collisions

An intersecting beam technique has been used to determine cross sections for C2+ and N2+ production from the combined processes of charge transfer and ionisation in H+-C+ and H+-N+ collisions at CM energies ranging from 65 keV to 470 keV. Ionisation is believed to provide the main contribution to the measured cross sections. Results are compared with other relevant data and considered in terms of a simple classical scaling relation.