Field concept, scalar fields and vector fields

Field concept

In mathematics, a field is an item used to model the phenomena concerning the "extended" objects. In a simplified meaning, a field is the association of a value of parameter to every point in the space. In the largest sense, the term "value of the parameter" represents a tensor.

Scalar field / vector field

We remark:

• the scalar fields (0 order tensor): to each point of space is associated a number, e.g. the temperature, the pressure, or the density…
• the vector fields (1 st order tensor): to each point of space is associated a vector, e.g. the vector of gravity field, the vector of electric field, the local velocity of a fluid …

A vector field associates to each point of space a vector quantity defined by three real numbers, while a scalar field associates a real quantity expressed by only one real number.

Quantities handled by Flux

The quantities handled by Flux are scalar quantities and vector quantities. Depending on physical application, these quantities can be expressed by real or complex numbers.

Functions handled by Flux

The functions available in Flux allow the handling of the scalar and vector quantities expressed by real or complex numbers. These functions are generally described in the previous section.

The functions for handling quantities expressed by complex numbers are described in the following section.