scholarly journals A solvation-free-energy functional: A reference-modified density functional formulation

2015 ◽  
Vol 36 (18) ◽  
pp. 1359-1369 ◽  
Author(s):  
Tomonari Sumi ◽  
Ayori Mitsutake ◽  
Yutaka Maruyama
Keyword(s):  
Free Energy ◽  
Density Functional ◽  
Solvation Free Energy ◽  
Energy Functional ◽  
Free Energy Functional ◽  
Functional Formulation

Density profiles of fluids in some special symmetries

1995 ◽  
Vol 73 (7-8) ◽  
pp. 432-439 ◽  
Author(s):  
Seong-Chan Lee ◽  
Zi-Hong Yoon ◽  
Soon-Chul Kim
Keyword(s):  
Free Energy ◽  
Computer Simulations ◽  
Hard Sphere ◽  
Density Functional ◽  
Energy Functional ◽  
Empirical Method ◽  
Density Profiles ◽  
Functional Approximation ◽  
Free Energy Functional ◽  
Lennard Jones

A free-energy-functional approximation based on a semi-empirical method is proposed. The main advantage of the free-energy-functional approximation is its accuracy compared with other models and its relative simplicity compared with other well-known weighted-density approximations. The free-energy-functional approximation is applied to predict the density profiles of the hard-sphere fluids and the Lennard–Jones fluids in some special symmetries. For the density profiles near a hard flat wall, the results reproduced the hard-sphere oscillatory structures qualitatively and quantitatively. For the density profiles of hard-sphere fluids confined in a spherical cage, the results are also in a fair agreement with the computer simulations. For Lennard–Jones fluids, two kinds of density-functional perturbation theories, the density-functional mean-field theory (DFMFT) and the density-functional perturbation theory (DFPT), examined. The results show that at higher temperature the DFPT compares well with computer simulations. However, the agreement deteriorates slightly as the temperature of the Lennard–Jones fluids is reduced. These results demonstrate that both the free-energy-functional approximation and the DFPT succesfully describe the inhomogeneous properties of classical fluids.

scholarly journals On the Kirchhoff-Love Hypothesis (Revised and Vindicated)

2021 ◽  
Author(s):  
Olivier Ozenda ◽  
Epifanio G. Virga
Keyword(s):  
Free Energy ◽  
Dimension Reduction ◽  
Three Dimensional ◽  
Energy Functional ◽  
The Other ◽  
Variational Model ◽  
Two Dimensional ◽  
Elastic Plates ◽  
Kinematic Constraint ◽  
Free Energy Functional

AbstractThe Kirchhoff-Love hypothesis expresses a kinematic constraint that is assumed to be valid for the deformations of a three-dimensional body when one of its dimensions is much smaller than the other two, as is the case for plates. This hypothesis has a long history checkered with the vicissitudes of life: even its paternity has been questioned, and recent rigorous dimension-reduction tools (based on standard $\varGamma $ Γ -convergence) have proven to be incompatible with it. We find that an appropriately revised version of the Kirchhoff-Love hypothesis is a valuable means to derive a two-dimensional variational model for elastic plates from a three-dimensional nonlinear free-energy functional. The bending energies thus obtained for a number of materials also show to contain measures of stretching of the plate’s mid surface (alongside the expected measures of bending). The incompatibility with standard $\varGamma $ Γ -convergence also appears to be removed in the cases where contact with that method and ours can be made.

scholarly journals Droplet minimizers for the Gates–Lebowitz–Penrose free energy functional

Nonlinearity ◽  
2009 ◽  
Vol 22 (12) ◽  
pp. 2919-2952 ◽  
Author(s):  
E A Carlen ◽  
M C Carvalho ◽  
R Esposito ◽  
J L Lebowitz ◽  
R Marra
Keyword(s):  
Free Energy ◽  
Energy Functional ◽  
Free Energy Functional
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