scholarly journals Nonempirical generalized gradient approximation free-energy functional for orbital-free simulations

2013 ◽  
Vol 88 (16) ◽  
Author(s):  
Valentin V. Karasiev ◽  
Debajit Chakraborty ◽  
Olga A. Shukruto ◽  
S. B. Trickey
Keyword(s):  
Free Energy ◽  
Energy Functional ◽  
Generalized Gradient ◽  
Free Energy Functional ◽  
Generalized Gradient Approximation ◽  
Orbital Free

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

scholarly journals Droplet minimizers for the Cahn-Hilliard free energy functional

2006 ◽  
Vol 16 (2) ◽  
pp. 233-264 ◽  
Author(s):  
E. A. Carlen ◽  
M. C. Carvalho ◽  
R. Esposito ◽  
J. L. Lebowitz ◽  
R. Marra
Keyword(s):  
Free Energy ◽  
Energy Functional ◽  
Free Energy Functional

scholarly journals Homogenization of composite ferromagnetic materials

2015 ◽  
Vol 471 (2182) ◽  
pp. 20150365 ◽  
Author(s):  
François Alouges ◽  
Giovanni Di Fratta
Keyword(s):  
Free Energy ◽  
Ferromagnetic Material ◽  
Energy Functional ◽  
Ferromagnetic Materials ◽  
Rigorous Derivation ◽  
Free Energy Functional ◽  
Landau Free Energy ◽  
Ferromagnetic Body ◽  
The Media

The objective of this paper is to perform, by means of Γ - convergence and two-scale convergence , a rigorous derivation of the homogenized Gibbs–Landau free energy functional associated with a composite periodic ferromagnetic material, i.e. a ferromagnetic material in which the heterogeneities are periodically distributed inside the media. We thus describe the Γ -limit of the Gibbs–Landau free energy functional, as the period over which the heterogeneities are distributed inside the ferromagnetic body shrinks to zero.

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