scholarly journals Free-Energy Functional Approach to Inverse Problems for Self-Assembly of Three-Dimensional Crystals

2021 ◽  
Vol 90 (2) ◽  
pp. 024603
Author(s):  
Masashi Torikai
Keyword(s):  
Free Energy ◽  
Inverse Problems ◽  
Self Assembly ◽  
Three Dimensional ◽  
Energy Functional ◽  
Functional Approach ◽  
Free Energy Functional

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.

Generalized van der Waals theory. I. Basic formulation and application to uniform fluids

1980 ◽  
Vol 33 (9) ◽  
pp. 2013 ◽  
Author(s):  
S Nordholm ◽  
ADJ Haymet
Keyword(s):  
Free Energy ◽  
Equation Of State ◽  
Particle Density ◽  
Van Der Waals ◽  
Three Dimensional ◽  
Energy Functional ◽  
Coarse Grained ◽  
Uniform Structure ◽  
Free Energy Functional ◽  
Van Der Waals Theory

A generalized van der Waals theory is derived on the basis of simple physical and mathematical arguments. The derivation results in a free- energy functional wherein the independent variable is a coarse-grained particle density. It is assumed that a well defined particle density dominates the free energy and this density is to be obtained by minimizing the free energy functional. The variational theory so obtained can be applied to non-uniform fluids. In the present work the possibility of stable non-uniform structure is neglected and the theory is applied to uniform fluids. It then produces an equation of state identical in form to that proposed originally by van der Waals but the excluded volume is only about half as large in the three-dimensional case. Applications to several two- and three-dimensional systems indicate that the new equation of state is a distinct improvement over the traditional van der Waals theory when the full range of fluid densities is considered. The quantitative accuracy in the case of simple uniform fluids is sufficient to warrant further development and exploitation of the theory.

3D WAVELET TREATMENT OF SOLVATED BIPOLARON AND POLARON

2005 ◽  
Vol 04 (03) ◽  
pp. 751-767 ◽  
Author(s):  
G. N. CHUEV ◽  
M. V. FEDOROV ◽  
H. J. LUO ◽  
D. KOLB ◽  
E. G. TIMOSHENKO
Keyword(s):  
Free Energy ◽  
Three Dimensional ◽  
Energy Functional ◽  
Wave Functions ◽  
Basis Set ◽  
Electron Wave ◽  
Solvated Electron ◽  
Hartree Fock ◽  
Free Energy Functional ◽  
Excess Electrons

Three-dimensional discrete tensor wavelets are applied to calculate wave functions of excess electrons solvated in polar liquids. Starting from the Hartree–Fock approximation for the electron wave functions and from the linear response to the solute charge for the solvent, we have derived the approximate free energy functional for the excess electrons. The orthogonal Coifman basis set is used to minimize the free energy functional and to approximate the electron wave functions. The scheme is applied to the calculation of the properties of the solvated electron and the singlet bipolaron formation. The obtained results indicate that the proposed algorithm is fast and rather efficient for calculating the electronic structure of the solvated molecular solutes.

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.

Sign in / Sign up

Export Citation Format

Share Document