Resumen de Space-time compositional models: an introduction to simplicial partial differential operators

Eusebi Jarauta Bragulat , Juan José Egozcue Rubí

• A function assigning a composition to space-time points is called a compositional or simplicial field. These fields can be analysed using the compositional analysis tools. A study of linear models for evolutionary compositions depending on one variable, usually time, was formulated by Egozcue and Jarauta-Bragulat (2014) in terms of the so-called simplicial linear differential equations. The foundations of differential and integral calculus for simplex-valued functions of one real variable, was presented by Egozcue, Jarauta-Bragulat and D´ıaz-Barrero (2011). In order to study compositions depending on space and/or time, reformulation and interpretation of traditional partial differential operators is required. These operators such as: partial derivatives, compositional gradient, directional derivative and divergence are of primary importance to state alternative models of processes as diffusion, advection and waves, from the compositional perspective. This kind of models, usually based on continuity of mass, circulation of a vector field along a curve and flux through surfaces, should be analyzed when compositional operators are used instead of the traditional gradient or divergence. This study is aimed at setting up the definitions, mathematical basis and interpretation of such operators.