Anisotropic space
Introduction
In the field of physics, anisotropy[a] is the general property of matter according to which qualities such as elasticity "Elasticity (solid mechanics)"), temperature, conductivity, speed of light propagation, etc., vary depending on the direction in which they are examined.[1] Something anisotropic may present different characteristics depending on the direction.[2] The anisotropy of materials is more pronounced in crystalline solids, due to their atomic structure and regular molecular.
In a general sense, we speak of anisotropy when any change in scale of a figure or body occurs, such as in an x - y graph, with different factors (or depending on a function) in each coordinate.
Anisotropic properties
In principle, any physical property that can be represented by a tensor magnitude is susceptible to anisotropic behavior. Among the properties that can present anisotropy are:
In the same way that numbers can "measure" the scalar magnitude of a property, mathematical groups "Group (mathematics)") can "measure" the symmetry of a property. Thus the type of anisotropy that a property presents can be characterized by a subgroup of a rotation symmetry group.
For example, if a certain property is invariant under the action of the group of rotations "Action (mathematical)") of three-dimensional space, then it is said to present isotropy. If it is not invariant, there will be a maximal subgroup of rotations such that under the action of said subgroup the action remains invariant. Depending on the maximal subgroup, the type of anisotropy can be classified into different:
Types of anisotropy
The types of anisotropy that a material presents are always associated with subgroups of the orthogonal group O(3), so each type of anisotropy is characterized by a point group. Among the types of anisotropy are: