Abstract The thick mantle lithosphere beneath cratons consists of strongly reduced rocks that have reacted with oxidized melts. These low-silica, incipient melts are rich in CO 2 and H O react surrounding forming an enriched zone at the base lithosphere, which is source region for many diamonds. Here, we reproduce these reactions novel experiments oxidised, hydrous carbonate-rich reduced, deple...

In recent years a number of methods have been developed for subdividing the surface of the earth to meet the needs of applications in dynamic modeling, survey sampling, and information storage and display. One set of methods uses the surfaces of Platonic solids, or regular polyhedra, as approximations to the surface of the earth. Diamond partitions are similar to recursive subdivisions of the t...

Mathematical and scientific computing problems are often approached using a divide and conquer paradigm in which a large problem domain is solved by combining results from smaller subdomains. In this very broad context, we focus on nested spatial decompositions of regularly sampled domains obtained by the regular simplex bisection scheme. Specifically, we utilize clusters of such simplices, ref...

We study a recurrence defined on a three dimensional lattice and prove that its values are Laurent polynomials in the initial conditions with all coefficients equal to one. This recurrence was studied by Propp and by Fomin and Zelivinsky. Fomin and Zelivinsky were able to prove Laurentness and conjectured that the coefficients were 1. Our proof establishes a bijection between the terms of the L...

Abstract We use the octahedron recurrence, which generalizes quadratic recurrence found by Kuo for standard Aztec diamonds, in order to compute boundary one-refined and two-refined partition functions two-periodic diamonds. In a first approach, geometric tangent method allows derive parametric form of arctic curve, separating solid liquid phases. This is done using recent reformulation without ...

We study a recurrence defined on a three dimensional lattice and prove that its values are Laurent polynomials in the initial conditions with all coefficients equal to one. This recurrence was studied by Propp and by Fomin and Zelivinsky. Fomin and Zelivinsky were able to prove Laurentness and conjectured that the coefficients were 1. Our proof establishes a bijection between the terms of the L...