Chapter

Compositional Data Analysis

Volume 187 of the series Springer Proceedings in Mathematics & Statistics pp 117-125

Date:

Space-Time Compositional Models: An Introduction to Simplicial Partial Differential Operators

  • E. Jarauta-BragulatAffiliated withDepartment of Enginyeria Civil I Ambiental, Universitat Politècnica de Catalunya Email author 
  • , J. J. EgozcueAffiliated withDepartment of Enginyeria Civil I Ambiental, Universitat Politècnica de Catalunya

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Abstract

A function assigning a composition to space-time points is called a compositional or simplicial field. These fields can be analyzed using the compositional analysis tools. 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.

Keywords

Compositional derivative Aitchison geometry Mass continuity Gradient Gauss divergence theorem