A Computer Program for 3D Simulation of a Li-ion Half-Cell during Charging

This code provides computational facilities to simulate current versus time during the charging of Li-ion cells at desire constant voltage by considering multiscale physical phenomena. This code only considers a powder of active materials (at microscale or nanoscale) and a small part of electrolyte around it as a half cell. Then it is extended to a complete cell by applying correct boundary conditions. This code is very useful by modifying code parameters to understand the effect of the complex shape of active materials powder (surface area and powder size), kind of electrolyte, and the applied voltages on the charging response of Li-ion cell. As a summary, a microscale approach to the design of Li-ion cells has been provided via this code.

One-electron capture from K shell of atomic targets by proton impact

A first-order four-body perturbation theory is developed to calculate both the differential and integral cross-sections for [Formula: see text]-shell charge exchange from multi-electron atomic targets to the [Formula: see text] bound state of the fast proton projectiles. The correct boundary conditions are incorporated in the formalism. The model is applied to the single electron capture process from carbon, nitrogen, oxygen, neon and argon atoms for which the experimental data are available. The results are compared with their corresponding experimental values and also with those obtained from three-body version of the theory. A comparison is also made between the present predicted cross-sections and those obtained from other theories. Comparisons show that the suggested approximation is in reasonable agreement with the experimental data and is compatible with the other theories.

On the distinguished limits of the Navier slip model of the moving contact line problem

When a droplet spreads on a solid substrate, it is unclear what the correct boundary conditions are to impose at the moving contact line. The classical no-slip condition is generally acknowledged to lead to a non-integrable singularity at the moving contact line, which a slip condition, associated with a small slip parameter, ${\it\lambda}$, serves to alleviate. In this paper, we discuss what occurs as the slip parameter, ${\it\lambda}$, tends to zero. In particular, we explain how the zero-slip limit should be discussed in consideration of two distinguished limits: one where time is held constant, $t=O(1)$, and one where time tends to infinity at the rate $t=O(|\!\log {\it\lambda}|)$. The crucial result is that in the case where time is held constant, the ${\it\lambda}\rightarrow 0$ limit converges to the slip-free equation, and contact line slippage occurs as a regular perturbative effect. However, if ${\it\lambda}\rightarrow 0$ and $t\rightarrow \infty$, then contact line slippage is a leading-order singular effect.

Four-body treatment of the K-shell positronium formation from multi-electron atoms

The four-body Coulomb-Born distorted-wave approximation with correct boundary conditions (CBDW-4B) is applied to the K-shell positronium formation from multi-electron atoms at intermediate and high impact energies. In the present approach, both K-shell electrons are treated as active electrons. For collisions of positrons with helium, carbon, and neon atoms, both the post and prior forms of the transition amplitude are calculated and the corresponding differential and integral cross sections are compared with the results of the three-body version of the formalism (CBDW-3B). In order to investigate the effects of the static electronic correlations on the process, initial bound states of the active electrons in helium atoms are described by Hylleraas and Silverman wave functions. Also for positronium formation from helium atoms the obtained cross sections are compared with the available experimental data and also with the results of the other theories.