Excess functions ........................................................................................................................................ 1 Mathematical explanation ..................................................................................................................... 1 Physical example: Molar volume of a pure substance ................................................

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.

................................................................................................ 3 Abbreviations ........................................................................................ 5 List of Papers & Statement ................................................................... 6 Introduction ......................................................................................

We modify the Lencka and Anderko fit of the chemical part of the compressibility factor of the AEOS model used to describe hydrogen fluoride. This modification results in improved agreement with experiment in the calculation of the heat capacity with little negative effect on the prediction of other properties. We report new parameters for this model and provide the equations for the fugacity c...

Subducted slabs, which include altered-oceanic crust and overlying sediments, impart geochemical redox fingerprints to arc magmas affect long-term evolution of the deep mantle. Yet, oxygen fugacity subducting slab remains poorly constrained. Light Rare Earth Element (LREE) chalcophile element (ChE) ratios may serve as proxies for downgoing slabs because difference in compatibility these groups ...

It is believed that the Moon formed following collision of a large planetesimal with early Earth. Over ∼4 Gyr since this event has been considerably less processed by geological activity than Earth, and may provide better record processes conditions in Earth-Moon system. There have many studies magmatic volatiles such as H, F, Cl, S C lunar materials. However, our ability to interpret variable ...

Excess functions ........................................................................................................................................ 1 Mathematical explanation ..................................................................................................................... 1 Physical example: Molar volume of a pure substance ................................................