This paper addresses the development of homogenized energy models which characterize the ferroelastic switching mechanisms inherent to ferroelectric materials in a manner suitable for subsequent transducer and control design. In the first step of the development, we construct Helmholtz and Gibbs energy relations which quantify the potential and electrostatic energy associated with 90 and 180 di...

Proteins are life’s working horses and nature’s robots. They participate in every life process. They form supporting structures of cell, fibre, tissue, and organs; they are catalysts, speed up various life critical chemical reactions; they transfer signals so that we can see, hear, and smell; they protect us against intruders such as bacteria and virus; they regulate life cycles to keep that ev...

The fundamental law for protein folding is the Thermodynamic Principle: the amino acid sequence of a protein determines its native structure and the native structure has the minimum Gibbs free energy. If all chemical problems can be answered by quantum mechanics, there should be a quantum mechanics derivation of Gibbs free energy formula G(X) for every possible conformation X of the protein. We...

The conventional Gibbs energy minimization methods apply elemental amounts of system components as conservation constraints in the form of a stoichiometric conservation matrix. The linear constraints designate the limitations set on the components described by the system constituents. The equilibrium chemical potentials of the constituents are obtained as a linear combination of the component-s...

This paper deals with stationary Gibbsian point processes on the plane with an interaction that depends on the tiles of the Delaunay triangulation of points via a bounded triangle potential. It is shown that the class of these Gibbs processes includes all minimisers of the associated free energy density and is therefore nonempty. Conversely, each such Gibbs process minimises the free energy den...

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 to a composite periodic ferromagneticmaterial, i.e. a ferromagneticmaterial in which the heterogeneities are periodically distributed inside the media. We thus describe the Γ -limit of the GIBBS-LANDAU free energ...