Action at a distance in classical uniaxial ferromagnetic arrays

We examine in detail the theoretical foundations of striking long-range couplings emerging in arrays of fluid cells connected by narrow channels by using a lattice gas (Ising model) description of a system. We present a reexamination of the well known exact determination of the two-point correlation function along the edge of a channel using the transfer matrix technique and a new interpretation is provided. The explicit form of the correlation length is found to grow exponentially with the cross section of the channels at the bulk two-phase coexistence. The aforementioned result is recaptured by a refined version of the Fisher-Privman theory of first order phase transitions in which the Boltzmann factor for a domain wall is decorated with a contribution stemming from the point tension originated at its endpoints. The Boltzmann factor for a domain wall together with the point tension is then identified exactly thanks to two independent analytical techniques, providing a critical test of the Fisher-Privman theory. We then illustrate how to build up the network model from its elementary constituents, the cells and the channels. Moreover, we are able to extract the strength of the coupling between cells and express them in terms of the length and width and coarse grained quantities such as surface and point tensions. We then support our theoretical investigation with a series of corroborating results based on Monte Carlo simulations. We illustrate how the long range ordering occurs and how the latter is signaled by the thermodynamic quantities corresponding to both planar and three-dimensional Ising arrays.Comment: 36 pages, 19 figure

On right conjugacy closed loops of twice prime order

The right conjugacy closed loops of order 2p, where p is an odd prime, are classified up to isomorphism.Comment: Clarified definitions, added some remarks and a tabl

Reliability modelling of PEM fuel cells with hybrid Petri nets

In this paper, a novel model for dynamic reliability analysis of a PEM fuel cell system is developed using Modelica language in order to account for multi-state dynamics and aging. The modelling approach constitutes the combination of physical and stochastic sub-models with shared variables. The physical model consist of deterministic calculations of the system state described by variables such as temperature, pressure, mass flow rates and voltage output. Additionally, estimated component degradation rates are also taken into account. The non-deterministic model, on the other hand, is implemented with stochastic Petri nets which represent different events that can occur at random times during fuel cell lifetime. A case study of effects of a cooling system on fuel cell performance was investigated. Monte Carlo simulations of the process resulted in a distribution of system parameters, thus providing an estimate of best and worst scenarios of a fuel cell lifetime