Variational Characterization of Free Energy: Theory and Algorithms

Free and constrained equilibrium states in a variational problem on a surface

We study the equilibrium states for an energy functional with a parametric force field on a region of a surface. Consideration of free equilibrium states is based on Lyusternik - Schnirelman's and Skrypnik's variational methods. Consideration of equilibrium states under a constraint of geometrical character is based on an analog of Skrypnik's method, described in [P. Vyridis, {it Bifurcation in...

Investigation of the Size Effect on the Nano-beam Type Piezoelectric Low Power Energy Harvesting

In this paper, size dependent beam type peizoelectric energy hardvester is investigated. For this goal, first nonlinear formulation of isotropic piezoelectric Euler-Bernoulli nano-beam is developed based on the size-dependent piezoelectricity theory then special beam type piezoelectric energy hardvester is probed for different parameters. Basic nonlinear equations of piezoelectric nano-beam are...

Characterization and DFT studies of cis, trans and vinyl derivatives of 1,4-butadiene using C20 in different temperatures

 In this research of cis, trans and vinyl monomeric derivatives of 1,4-butadiene were studied using C20 in different temperatures by Functional density theory (DFT). To this purpose, the materials were firstly optimized geometrically, then the calculations of the thermodynamic parameters were performed on all of them. In the following, changes in parameters of energy...

Iterative algorithms for families of variational inequalities fixed points and equilibrium problems

A Free Energy Foundation of Semantic Similarity in Automata and Languages

This paper develops a free energy theory from physics including the variational principles for automata and languages and also provides algorithms to compute the energy as well as efficient algorithms for estimating the nondeterminism in a nondeterministic finite automaton. This theory is then used as a foundation to define a semantic similarity metric for automata and languages. Since automata...