Spherical Boundary Conditions: A Finite and System Size Independent Geometry for Simulations of Electrolytic Liquids

2003 ◽  
Vol 29 (9) ◽  
pp. 527-533 ◽  
Author(s):  
Shabnam Hanassab ◽  
T.J. VanderNoot
Keyword(s):  
Boundary Conditions ◽  
System Size ◽  
Spherical Boundary ◽  
Spherical Boundary Conditions

Thomas-Fermi equation with non-spherical boundary conditions

1987 ◽  
Vol 70 (2) ◽  
pp. 284-294 ◽  
Author(s):  
M Friedman ◽  
A Rabinovitch ◽  
Y Rosenfeld ◽  
R Thieberger
Keyword(s):  
Boundary Conditions ◽  
Thomas Fermi ◽  
Spherical Boundary ◽  
Spherical Boundary Conditions

scholarly journals Boundary conditions and linear analysis of finite-cell Rayleigh–Bénard convection

1992 ◽  
Vol 241 ◽  
pp. 549-585 ◽  
Author(s):  
Yih-Yuh Chen
Keyword(s):  
Boundary Conditions ◽  
Critical Rayleigh Number ◽  
System Size ◽  
Perturbative Approach ◽  
Bénard Convection ◽  
Reaction Diffusion Model ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard ◽  
Finite Cell

The linear stability of finite-cell pure-fluid Rayleigh–Bénard convection subject to any homogeneous viscous and/or thermal boundary conditions is investigated via a variational formalism and a perturbative approach. Some general properties of the critical Rayleigh number with respect to change of boundary conditions or system size are derived. It is shown that the chemical reaction–diffusion model of spatial-pattern-forming systems in developmental biology can be thought of as a special case of the convection problem. We also prove that, as a result of the imposed realistic boundary conditions, the nodal surfaces of the temperature of a nonlinear stationary state have a tendency to be parallel or orthogonal to the sidewalls, because the full fluid equations become linear close to the boundary, thus suggesting similar trend for the experimentally observed convective rolls.

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