In
physics and
geometry, isotropy (from
Ancient Greekἴσος (ísos) 'equal' and τρόπος (trópos) 'turn, way') is uniformity in all
orientations. Precise definitions depend on the subject area. Exceptions, or inequalities, are frequently indicated by the prefix a- or an-, hence anisotropy. Anisotropy is also used to describe situations where properties vary systematically, dependent on direction.
Isotropic radiation has the same intensity regardless of the direction of
measurement, and an isotropic field exerts the same action regardless of how the test
particle is oriented.
Mathematics
Within
mathematics, isotropy has a few different meanings:
A
quadratic formq is said to be isotropic if there is a non-zero vector v such that q(v) = 0; such a v is an
isotropic vector or null vector. In complex geometry, a line through the origin in the direction of an isotropic vector is an
isotropic line.
The
vector field generated by a point source is said to be isotropic if, for any spherical neighborhood centered at the point source, the magnitude of the vector determined by any point on the sphere is invariant under a change in direction. For an example, starlight appears to be isotropic.
When a spinless particle (or even an unpolarized particle with spin) decays, the resulting decay distribution must be isotropic in the
rest frame of the decaying particle - regardless of the detailed physics of the decay. This follows from
rotational invariance of the
Hamiltonian, which in turn is guaranteed for a spherically symmetric potential.
Gases
The
kinetic theory of gases also exemplifies isotropy. It is assumed that the molecules move in random directions and as a consequence, there is an equal probability of a molecule moving in any direction. Thus when there are many molecules in the gas, with high probability there will be very similar numbers moving in one direction as any other, demonstrating approximate isotropy.
Fluid flow is isotropic if there is no directional preference (e.g. in fully developed 3D turbulence). An example of anisotropy is in flows with a background density as gravity works in only one direction. The apparent surface separating two differing isotropic fluids would be referred to as an isotrope.
An isotropic medium is one such that the
permittivity, ε, and
permeability, μ, of the medium are uniform in all directions of the medium, the simplest instance being free space.
Optical isotropy means having the same optical properties in all directions. The individual
reflectance or
transmittance of the domains is averaged for micro-heterogeneous samples if the macroscopic reflectance or transmittance is to be calculated. This can be verified simply by investigating, for example, a
polycrystalline material under a polarizing microscope having the polarizers crossed: If the crystallites are larger than the resolution limit, they will be visible.
The
cosmological principle, which underpins much of modern cosmology (including the
Big Bang theory of the evolution of the observable universe), assumes that the universe is both isotropic and homogeneous, meaning that the universe has no preferred location (is the same everywhere) and has no preferred direction.[2] Observations[which?] made in 2006 suggest that, on distance-scales much larger than
galaxies,
galaxy clusters are
"Great" features, but small compared to so-called
multiverse scenarios.[citation needed]
In the study of
mechanical properties of materials, "isotropic" means having identical values of a property in all directions. This definition is also used in
geology and
mineralogy. Glass and metals are examples of isotropic materials.[3] Common anisotropic materials include
wood (because its material properties are different parallel to and perpendicular to the grain) and layered rocks such as
slate.
Isotropic materials are useful since they are easier to shape, and their behavior is easier to predict. Anisotropic materials can be tailored to the forces an object is expected to experience. For example, the fibers in
carbon fiber materials and
rebars in
reinforced concrete are oriented to withstand tension.
In industrial processes, such as
etching steps, "isotropic" means that the process proceeds at the same rate, regardless of direction. Simple chemical reaction and removal of a substrate by an acid, a solvent or a reactive gas is often very close to isotropic. Conversely, "anisotropic" means that the attack rate of the substrate is higher in a certain direction. Anisotropic etch processes, where vertical etch-rate is high but lateral etch-rate is very small, are essential processes in
microfabrication of
integrated circuits and
MEMS devices.
While it is well established that the skin provides an ideal site for the administration of local and systemic drugs, it presents a formidable barrier to the permeation of most substances.[4] Recently,
isotropic formulations have been used extensively in dermatology for drug delivery.[5]
A volume such as a
computed tomography is said to have isotropic
voxel spacing when the space between any two adjacent voxels is the same along each axis x, y, z. E.g., voxel spacing is isotropic if the center of voxel (i, j, k) is 1.38 mm from that of (i+1, j, k), 1.38 mm from that of (i, j+1, k) and 1.38 mm from that of (i, j, k+1) for all indices i, j, k.[6]