A general finite element framework for the application to different types of phase transforming alloys and under general thermo-mechanical loadings is presented. The developed technique is exemplified on cubic to tetragonal transformations of shape memory alloys.

For a number of virus- and bacterium genomes we use the concept of block entropy from information theory and compare it with the corresponding configurational energy, defined via the ionization energies of the nucleotides and a hopping term for their interactions in the sense of a tight-binding...

The statistical proprieties of complex systems can differ deeply for those of classical systems governed by Boltzmann–Gibbs entropy. In particular, the probability distribution function observed in several complex systems shows a power-law behavior in the tail which disagrees with the standard...

For interface-tracking simulation of two-phase flows with a high density ratio, we propose a computational method, NS–PFM, combining Navier–Stokes (NS) equations with phase-field model (PFM) based on the free energy theory. Through the numerical simulations, it was confirmed that (1) the...

We derive the free energy of the chiral Potts model by the infinite lattice “inversion relation” method. This method is non-rigorous in that it always needs appropriate analyticity assumptions. Guided by previous calculations based on exact finite-lattice functional relations, we find that...

The microscopic approach to calculating the free energy of a three-dimensional Ising-like system in a homogeneous external field is developed in the higher non-Gaussian approximation (the ρ6 model) at temperatures above the critical value of Tc (Tc is the phase-transition temperature in the...

There have lately been several suggestions for parametrized distances on a graph that generalize the shortest path distance and the commute time or resistance distance. The need for developing such distances has risen from the observation that the above-mentioned common distances in many...

This article investigates the effect for random pinning models of long range power-law decaying correlations in the environment. For a particular type of environment based on a renewal construction, we are able to sharply describe the phase transition from the delocalized phase to the localized...

We study the Hopfield model where the ratio α of patterns to sites grows large. We prove that the free energy with inverse temperature β and external field B behaves like βα+γ, where γ=P(2β,B) is the limiting free energy of the Sherrington–Kirkpatrick model with inverse temperature 2β...

The large discrepancy between the values of the free energy for DNA dinucleotides (or dimers) measured by different teams has raised a debate, yet unsettled. Here the free energy is fitted by a three parameter empiric formula derived in the framework of the crystal basis model of genetic code....