Mixtureans

Mixtureans are a theoretical construct used to model the properties of mixtures. They are defined as abstract objects representing a specific combination of base components and the properties that arise from that mixture.

Definition: A mixturean is specified by a composition vector p = (p1,..., pk), where pi ≥ 0 and sum pi = 1, and a property function F that assigns to p a set of properties such as density, refractive index, rheology, or thermodynamic quantities.

Mathematical framework: Mixtureans are studied on the (k-1)-simplex; under ideal assumptions, properties are derived by linear interpolation of component properties; non-ideality introduces interaction terms or activity coefficients.

Computation: Given data for the base components, mixtureans are produced by varying p; predictive models may be linear or nonlinear; statistical methods from compositional data analysis are used.

Applications and example: In materials design or process engineering, mixtureans provide a compact way to reason about how changing composition affects properties. For a binary system of A and B with properties X_A and X_B, an ideal mixturean has X(p) = pX_A + (1-p)X_B; a non-ideal model adds interaction term.

See also: mixture model, compositional data analysis, phase diagram, thermodynamics.