Generalized Fermi sea for plane-wave Hartree-Fock theory: One dimensional model calculation

1979 ◽  
Vol 19 (3) ◽  
pp. 1083-1088 ◽  
Author(s):  
M. de Llano ◽  
J. P. Vary
Keyword(s):  
Plane Wave ◽  
Model Calculation ◽  
Dimensional Model ◽  
One Dimensional ◽  
Hartree Fock

EFFECT OF ELECTRON CORRELATION ON THE TWO-PARTICLE DYNAMICS OF A HELIUM ATOM IN A STRONG LASER PULSE

2002 ◽  
Vol 16 (03) ◽  
pp. 415-452 ◽  
Author(s):  
NILS ERIK DAHLEN
Keyword(s):  
Laser Pulse ◽  
Helium Atom ◽  
Electron Correlation ◽  
Density Functional ◽  
Femtosecond Laser Pulses ◽  
Time Dependent ◽  
Electron Dynamics ◽  
Dimensional Model ◽  
One Dimensional ◽  
Hartree Fock

This review discusses the complicated two-electron dynamics of a helium atom in an intense, short laser pulse. A helium gas in femtosecond laser pulses at long wave lengths (λ~700 nm) and high intensities (I~1015 W /cm2) produces surprisingly high numbers of He2+ ions. These laser fields cause large and fast electron oscillations, which makes a solution of the time-dependent Schrödinger equation numerically demanding. The system can be studied using a one-dimensional model atom, which has many of the same properties as the He atom. Using the one-dimensional model, the importance of including electron correlation in a simplified description of the two-electron dynamics is demonstrated. It is shown that electron correlation becomes much less important if the laser field has a short wave length, in which case the electron oscillations are smaller and slower. The problem of including electron correlation in the calculations is discussed in terms of approaches such as time-dependent Hartree–Fock, time-dependent density functional theory and time-dependent extended Hartree–Fock. Some of the commonly used semi-classical models for describing the double-ionization process are presented.

Modelling Techniques in Applied Glaciology: Numerical Modelling of Avalanches

1983 ◽  
Vol 4 ◽  
pp. 297-297
Author(s):  
G. Brugnot
Keyword(s):  
Finite Difference Method ◽  
Transverse Velocity ◽  
Longitudinal Velocity ◽  
Momentum Conservation ◽  
Dimensional Model ◽  
One Dimensional ◽  
Modelling Techniques ◽  
Reference Grid ◽  
The One ◽  
Near Future

We consider the paper by Brugnot and Pochat (1981), which describes a one-dimensional model applied to a snow avalanche. The main advance made here is the introduction of the second dimension in the runout zone. Indeed, in the channelled course, we still use the one-dimensional model, but, when the avalanche spreads before stopping, we apply a (x, y) grid on the ground and six equations have to be solved: (1) for the avalanche body, one equation for continuity and two equations for momentum conservation, and (2) at the front, one equation for continuity and two equations for momentum conservation. We suppose the front to be a mobile jump, with longitudinal velocity varying more rapidly than transverse velocity.We solve these equations by a finite difference method. This involves many topological problems, due to the actual position of the front, which is defined by its intersection with the reference grid (SI, YJ). In the near future our two directions of research will be testing the code on actual avalanches and improving it by trying to make it cheaper without impairing its accuracy.

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