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

Conference paper

DOI: 10.1007/978-3-319-44811-4_8

Volume 187 of the book series Springer Proceedings in Mathematics & Statistics (PROMS)
Cite this paper as:
Jarauta-Bragulat E., Egozcue J.J. (2016) Space-Time Compositional Models: An Introduction to Simplicial Partial Differential Operators. In: Martín-Fernández J., Thió-Henestrosa S. (eds) Compositional Data Analysis. CoDaWork 2015. Springer Proceedings in Mathematics & Statistics, vol 187. Springer, Cham

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 

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of Enginyeria Civil I AmbientalUniversitat Politècnica de CatalunyaBarcelonaSpain