anisotropi

Anisotropy (often written anisotropi in some languages) is the directional dependence of a material or system’s properties. An anisotropic property has different values when measured along different directions, whereas an isotropic property is the same in all directions.

Anisotropy arises from structure that lacks complete rotational symmetry, such as crystal lattices, aligned fibers, or layered media. For linear response properties, the directional dependence is described by tensors; a second-order tensor maps a direction to a response and has principal axes that define the directions of maximum and minimum response.

Common examples include optical anisotropy, where the refractive index varies with polarization and propagation direction (birefringence); mechanical or elastic anisotropy, where stiffness differs with orientation (wood, composites, and many crystals); thermal anisotropy, in which heat conduction differs by direction (graphite is a classic case); electrical and magnetic anisotropy, affecting conductivity, permittivity, and the preferred direction of magnetization; and acoustic or seismic anisotropy, where wave speeds depend on direction.

Anisotropy has practical implications for material design, engineering, geophysics, and cosmology. It is measured using experiments and techniques such as polarized light microscopy, X-ray diffraction to determine crystal texture, ultrasound or seismic surveys, and tensorial data analysis. In cosmology, anisotropy refers to directional variations in the cosmic microwave background, providing information about the early universe.