A simple analytical form of the Thomas-Fermi screening function and of Firsov's atomic interaction potential

1968 ◽  
Vol 1 (2) ◽  
pp. 307-314 ◽  
Author(s):  
P T Wedepohl
Keyword(s):  
Interaction Potential ◽  
Analytical Form ◽  
Atomic Interaction ◽  
Thomas Fermi ◽  
Simple Analytical Form

scholarly journals A Simple Free Energy for the Isotropic-Nematic Phase Transition of Rods

2016 ◽  
Vol 2016 ◽  
pp. 1-6 ◽  
Author(s):  
Remco Tuinier
Keyword(s):  
Free Energy ◽  
Nematic Phase ◽  
Analytical Form ◽  
Orientation Distribution ◽  
Scaled Particle Theory ◽  
Particle Theory ◽  
Aspect Ratios ◽  
Wide Range ◽  
Hard Rods ◽  
Simple Analytical Form

A free energy expression is proposed that describes the isotropic-nematic binodal concentrations of hard rods. A simple analytical form for this free energy was yet only available using a Gaussian trial function for the orientation distribution function (ODF), leading, however, to a significant deviation of the predicted binodals. The new free energy proposed here is based upon a rationalized correction to the orientational and packing entropies when using the Gaussian ODF. In combination with Parsons-Lee theory or scaled particle theory, it enables describing the isotropic-nematic phase coexistence concentrations of rods accurately using the simple Gaussian ODF for a wide range of aspect ratios.

Theory of Shock-Wave Ionization upon High-Velocity Impact of Micrometeorites

1974 ◽  
Vol 29 (6) ◽  
pp. 870-879 ◽  
Author(s):  
S. Drapatz ◽  
K. W. Michel
Keyword(s):  
Shock Wave ◽  
Particle Density ◽  
Analytical Form ◽  
High Impact ◽  
Surface Ionization ◽  
High Velocity Impact ◽  
Laboratory Measurements ◽  
Isentropic Expansion ◽  
Rate Processes ◽  
Simple Analytical Form

The relevant processes in shock wave ionization of a solid Fe micrometeorite impinging on a W target are analyzed. The internal energy behind the shock wave in shown to depend on impact velocity w, target and meteorite density in a simple analytical form. For low impact velocities (w<7 km sec-1) the ions generated by the shock are mostly due to surface ionization. For high impact velocities [w>20 km sec-1) the number of ions can satisfactorily be explained by isentropic expansion of the shocked material to a particle density of n ≈ 1020 cm-3 whereupon the rate processes in the expanding ion cloudlet govern the residual ionization. In velocity regions where laboratory measurements can be carried out, the agreement between theory and experiment confirms the assumptions made.

Neutral eigensolutions of the stability equation for stratified shear flow

1969 ◽  
Vol 36 (4) ◽  
pp. 673-683 ◽  
Author(s):  
S. A. Thorpe
Keyword(s):  
Differential Equation ◽  
Shear Flow ◽  
Analytical Form ◽  
Analytic Solutions ◽  
Stability Equation ◽  
Hypergeometric Differential Equation ◽  
Stratified Shear Flow ◽  
Parallel Shear Flow ◽  
The Stability ◽  
Simple Analytical Form

Many of the known analytic solutions of the equation for neutral disturbances to a stably stratified, inviscid, parallel shear flow are shown to belong to a wider family of solutions when a transformation to the hypergeometric differential equation is possible. Two particular cases in which the transformation can be made are examined in some detail and the solutions are expressed in a simple analytical form. A number of novel solutions are presented as examples.

On the transient Leveque's problem with an application in electrochemistry

1981 ◽  
Vol 46 (13) ◽  
pp. 3209-3220 ◽  
Author(s):  
Ondřej Wein
Keyword(s):  
Mass Transfer ◽  
Shear Flow ◽  
Analytical Form ◽  
Step Change ◽  
Electrochemical Potential ◽  
Uniform Shear ◽  
Uniform Shear Flow ◽  
Efficient Data ◽  
Current Densities ◽  
Simple Analytical Form

The electrochemically induced unsteady mass transfer to a uniform shear flow from a local wall electrode subjected to a step change in electrochemical potential is studied. Due to neglecting the streamwise diffusion, the problem has two solutions which however differ only insignificantly. The resulting transient characteristics of current densities have a simple analytical form suitable for an efficient data treatment.

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