We define matrix models that converge to the generating functions of a wide variety of loop models with fugacity taken in sets with an accumulation point. The latter can also be seen as moments of a non-commutative law on a subfactor planar algebra. We apply this construction to compute the generating functions of the Potts model on a random planar map.

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Introduction: Oxygen fugacity (fO2) is an important factor in planetary formation and evolution. Certain minerals or assemblages of minerals are stable only under certain fO2 conditions (at a constant T and P) and can be recorders of ambient fO2 during geologic processes. The best estimate of oxygen fugacity from mineral assemblages has implications, from large-scale models of planetary evoluti...

biotite samples from different units of boroujerd granitoid complex (bgc) of the sanandaj-sirjan zone, western iran, have beenanalyzed by electron microprobe for major elements. biotite analyses from three units of quartzdiorite, granodiorite and monzograniteof bgc have their own distinct non-overlapping compositional fields in the annite – siderophyllite – phlogopite – eastonitequadrilateral (...

Introduction: Primitive achondrites (IAB irons/winonaites; acapulcoites/lodranites; and brachinites) have chondritic compositions, but nonchondritic textures (from metamorphic through partially melted) [1]. Because of this, they offer a unique insight into the first stages of the differentiation process on asteroids. Acapulcoites and lodranites have textural and mineralogical evidence that they...

Oxygen fugacity in metal-bearing systems controls some fundamental aspects of the geochemistry of the early Earth, such as the FeO and siderophile trace element content of the mantle, volatile species that influence atmospheric composition, and conditions for organic compounds synthesis. Redox and metal-silicate equilibria in the early Earth are sensitive to oxygen fugacity (fO(2)), yet are poo...

A systematic study of the properties of particle and charge correlation functions in the two-dimensional Coulomb gas confined to a one-dimensional domain is under-taken. Two versions of this system are considered: one in which the positive and negative charges are constrained to alternate in sign along the line, and the other where there is no charge ordering constraint. Both systems undergo a ...

Proper evaluation of the Gibbs free energy and other properties of seawater and other aqueous solutions is essential in the analysis of desalination systems. Standard seawater has been studied extensively and property data are readily accessible. However, many aqueous solutions requiring desalination have significantly different composition from seawater and seawater data is generally not accur...