Inphysics andgeometry,isotropy (from Ancient Greekἴσος (ísos)'equal' and τρόπος (trópos)'turn, way') is uniformity in allorientations. Precise definitions depend on the subject area. Exceptions, or inequalities, are frequently indicated by the prefixa- oran-, henceanisotropy.Anisotropy is also used to describe situations where properties vary systematically, dependent on direction.Isotropic radiation has the same intensity regardless of the direction ofmeasurement, and an isotropic field exerts the same action regardless of how the testparticle is oriented.
Aquadratic formq is said to be isotropic if there is a non-zero vectorv such thatq(v) = 0; such av is anisotropic vector or null vector. In complex geometry, a line through the origin in the direction of an isotropic vector is anisotropic line.
Thevector field generated by a point source is said to beisotropic 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 distributionmust be isotropic in therest frame of the decaying particle - regardless of the detailed physics of the decay. This follows fromrotational invariance of theHamiltonian, which in turn is guaranteed for a spherically symmetric potential.
Gases
Thekinetic 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 thepermittivity, 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 individualreflectance ortransmittance 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, apolycrystalline material under a polarizing microscope having the polarizers crossed: If the crystallites are larger than the resolution limit, they will be visible.
Thecosmological principle, which underpins much of modern cosmology (including theBig 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-calledmultiverse scenarios.[citation needed]
In the study ofmechanical properties of materials, "isotropic" means having identical values of a property in all directions. This definition is also used ingeology andmineralogy. Glass and metals are examples of isotropic materials.[3] Common anisotropic materials includewood (because its material properties are different parallel to and perpendicular to the grain) and layered rocks such asslate.
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 incarbon fiber materials andrebars inreinforced concrete are oriented to withstand tension.
In industrial processes, such asetching 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 inmicrofabrication ofintegrated circuits andMEMS 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 acomputed tomography is said to have isotropicvoxel spacing when the space between any two adjacent voxels is the same along each axisx, 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 indicesi, j, k.[6]
