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We show the presence of a first-order phase transition for a ferromagnetic Ising model on integer 2 dimensional lattice with a periodical external magnetic field. The external field takes two values h and -h, where h>0. The sites associated with positive and negative values of external field form a chessboard configuration with rectangular cells of sides L1xL2 sites. The phase transition holds if h is small enough. We prove a first-order phase transition using reflection positivity (RP) method.
In this talk we will discuss why the ten biggest known prime numbers are Mersenne numbers and discuss a primality test algorithm for Gaussian Mersenne and Eisenstein Mersenne Numbers.
Porous media with open porosity are three-dimensional (3D) structures, often consisting of a complex network of pores connected by throats. The morphology and connectivity of the pore space in porous media are commonly characterized by the pore and throat size distributions, the mean pore-throat aspect ratio and the mean connectivity number, i.e. the number of connections (throats) to each pore.