anisotropy: one construct, many systems

In materials science, anisotropy is the dependence of a material's physical properties on direction within the crystal; magnetocrystalline anisotropy, for example, makes some crystal axes easy and others hard to magnetize. Nikolai Akulov's 1931 paper Zur Theorie der Feinstruktur der Magnetisierungskurven der Einkristalle in Zeitschrift für Physik gave the phenomenological theory and the anisotropy constants still in use. Here the direction-dependence belongs to a material and is measured in the laboratory.[1]

Unit

One anisotropy constant (e.g., K1), in energy per unit volume

Recovery means

Measure a property along different crystal axes and find it differs with direction

Measured by

Determined by torque magnetometry or directional property tests, expressed as anisotropy constants

In cosmology, anisotropy refers to the small variations in the temperature of the cosmic microwave background from one direction to another, the imprint of density fluctuations in the early universe. George Smoot and the COBE team reported the first detection in Structure in the COBE differential microwave radiometer first-year maps in The Astrophysical Journal. Here the same direction-dependence shows up as a statistical pattern of temperature across the sky at the level of tens of microkelvin.[2]

Unit

One temperature fluctuation ΔT/T across an angular scale, in microkelvin

Recovery means

Map CMB temperature over the sky and detect direction-to-direction differences after removing the dipole

Measured by

Characterized by the angular power spectrum from all-sky microwave maps