scholarly journals Incompressible limit for a magnetostrictive energy functional

2013 ◽  
Vol 61 (4) ◽  
pp. 1025-1030
Author(s):  
B. Gambin ◽  
W. Bielski
Keyword(s):  
Free Energy ◽  
Energy Functional ◽  
Elastic Behaviour ◽  
Incompressible Limit ◽  
Elastic Deformations ◽  
Energy Functionals ◽  
Second Gradient ◽  
Non Local ◽  
Γ Convergence ◽  
Non Locality

Abstract The modern materials undergoing large elastic deformations and exhibiting strong magnetostrictive effect are modelled here by free energy functionals for nonlinear and non-local magnetoelastic behaviour. The aim of this work is to prove a new theorem which claims that a sequence of free energy functionals of slightly compressible magnetostrictive materials with a non-local elastic behaviour, converges to an energy functional of a nearly incompressible magnetostrictive material. This convergence is referred to as a Γ -convergence. The non-locality is limited to non-local elastic behaviour which is modelled by a term containing the second gradient of deformation in the energy functional.

scholarly journals Existence of ground states for aggregation-diffusion equations

2019 ◽  
Vol 17 (03) ◽  
pp. 393-423 ◽  
Author(s):  
J. A. Carrillo ◽  
M. G. Delgadino ◽  
F. S. Patacchini
Keyword(s):  
Free Energy ◽  
Ground States ◽  
Energy Functional ◽  
Multi Agent Systems ◽  
Linear Diffusion ◽  
Sharp Condition ◽  
Macroscopic Models ◽  
Energy Functionals ◽  
Continuous Description ◽  
Degenerate Diffusions

We analyze free energy functionals for macroscopic models of multi-agent systems interacting via pairwise attractive forces and localized repulsion. The repulsion at the level of the continuous description is modeled by pressure-related terms in the functional making it energetically favorable to spread, while the attraction is modeled through nonlocal forces. We give conditions on general entropies and interaction potentials for which neither ground states nor local minimizers exist. We show that these results are sharp for homogeneous functionals with entropies leading to degenerate diffusions while they are not sharp for fast diffusions. The particular relevant case of linear diffusion is totally clarified giving a sharp condition on the interaction potential under which the corresponding free energy functional has ground states or not.

scholarly journals Free energy functionals for polarization fluctuations: Pekar factor revisited

2017 ◽  
Vol 146 (6) ◽  
pp. 064504 ◽  
Author(s):  
Mohammadhasan Dinpajooh ◽  
Marshall D. Newton ◽  
Dmitry V. Matyushov
Keyword(s):  
Free Energy ◽  
Energy Functionals
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