Isotropy is uniformity in all directions. Precise definitions depend on the subject area. The word is made up from Greek iso (equal) and tropos (direction). Exceptions, or inequalities, are frequently indicated by the prefix an, hence anisotropy. Anisotropy (pronounced with stress on the third syllable ˌænaɪˈsɒtrəpi is the property of being directionally dependent as opposed to Isotropy, which means homogeneity 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. 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 Measurement is the process of estimating the magnitude of some attribute of an object such as its length or weight relative to some standard ( unit of measurement) such as In Particle physics, an elementary particle or fundamental particle is a particle not known to have substructure that is it is not known to be made

• Within mathematics, Isotropy has a few different meanings:
  • Isotropic manifolds: Some manifolds are isotropic, meaning that the geometry on the manifold is the same regardless of direction. Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and In Mathematics, an isotropic manifold is a Manifold in which the Geometry doesn't depend on directions A manifold is a mathematical space in which every point has a neighborhood which resembles Euclidean space, but in which the global structure may be Geometry ( Greek γεωμετρία; geo = earth metria = measure is a part of Mathematics concerned with questions of size shape and relative position A similar concept is homogeneity. In Mathematics, particularly in the theories of Lie groups Algebraic groups and Topological groups a homogeneous space for a group A manifold can be homogeneous without being isotropic. But if it is inhomogeneous, it is necessarily anisotropic.
  • Isotropic quadratic form: A quadratic form q is said to be isotropic if there is a non-zero vector v such that q(v)=0. In mathematics a Quadratic form over a field F is said to be isotropic if there is a non-zero vector on which it evaluates to zero In Mathematics, a quadratic form is a Homogeneous polynomial of degree two in a number of variables
  • Isotropic coordinates on an Isotropic chart for Lorentzian manifolds. In the theory of Lorentzian manifolds Spherically symmetric spacetimes admit a family of nested round spheres. In Differential geometry, a pseudo-Riemannian manifold (also called a semi-Riemannian manifold) is a generalization of a Riemannian manifold.

• Cosmology: The Big Bang theory of the evolution of the observable universe assumes that space is isotropic. The Big Bang is the cosmological model of the Universe that is best supported by all lines of scientific evidence and Observation. It also assumes that space is homogeneous. These two assumptions together are known as the Cosmological Principle. The cosmological principle is an assumption invoked in Cosmology that when applied severely restricts the large variety of possible cosmological theories As of 2006, the observations suggest that, on distance scales much larger than galaxies, galaxy clusters are "Great" features, but small compared to so-called multi-verse scenarios. Year 2006 ( MMVI) was a Common year starting on Sunday of the Gregorian calendar. The Great Wall (also called Coma Wall) sometimes specifically referred to as the CfA2 Great Wall, is the second largest known super-structure in the

• Cell biology: If the properties of the cell wall are more or less the same everywhere, it is said to be isotropic. The cell is the structural and functional unit of all known living Organisms It is the smallest unit of an organism that is classified as living and is often called The interior of the cell is anisotropic due to intracellular organelles. In Cell biology, an organelle (pronunciation /ɔː(rgəˡnɛl/ is a specialized subunit within a cell that has a specific function and is usually separately enclosed

• Radio broadcasting: In radio, an isotropic antenna is an idealized "radiating element" used as a reference; an antenna that broadcasts power equally (calculated by the Poynting vector) in all directions. Radio is the transmission of signals by Modulation of electromagnetic waves with frequencies below those of visible Light. An isotropic radiator is a theoretical Point source of waves which exhibits the same magnitude or properties when measured in all directions Radiators and convectors are types of Heat exchangers designed to transfer Thermal energy from one medium to another for the purpose of cooling In general a reference is a relation between objects in which one object designates by linking to another object An antenna is a Transducer designed to transmit or Receive electromagnetic waves In other words antennas convert electromagnetic waves into In Physics, the Poynting vector can be thought of as representing the Energy Flux (in W/m2 of an Electromagnetic field. In practice, an isotropic antenna cannot exist, as equal radiation in all directions would be a violation of the Helmholtz wave equation. The Helmholtz equation, named for Hermann von Helmholtz, is the Elliptic partial differential equation (\nabla^2 + k^2 A = 0 The gain of an arbitrary antenna is usually reported in decibels relative to an isotropic antenna, and is expressed as dBi or dB(i). The decibel ( dB) is a logarithmic unit of measurement that expresses the magnitude of a physical quantity (usually power or intensity relative to

• Physiology: In skeletal muscle cells (a. k. a. muscle fibers), the term "isotropic" refers to the light bands (I bands) that contribute to the striated pattern of the cells. Skeletal muscle is a type of Striated muscle, which usually attaches to tendons In Physiology, isotropic bands are skeletal muscle cells (aka

• Materials: In the study of mechanical properties of materials, "isotropic" means having identical values of a property in all crystallographic directions. Mechanics ( Greek) is the branch of Physics concerned with the behaviour of physical bodies when subjected to Forces or displacements Crystallography is the experimental science of determining the arrangement of Atoms in Solids In older usage it is the scientific study of Crystals The

• Optics: Optical isotropy means having the same optical properties in all directions. The individual reflectance or transmittance of the domains is averaged if the macroscopic reflectance or transmittance is to be calculated. In photometry and Heat transfer, reflectivity is the fraction of incident radiation reflected by a surface In Optics and Spectroscopy, transmittance is the fraction of incident light at a specified Wavelength that passes through a sample This can be verified simply by investigating, e. g. , a polycrystalline material under a polarizing microscope having the polarizers crossed: If the crystallites are larger than the resolution limit, they will be visible. Polycrystalline materials are solids that are composed of many Crystallites of varying size and orientation

• Microfabrication: 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. Microfabrication or micromanufacturing are the terms to describe processes of fabrication of miniature structures of Micrometre sizes and smaller Microchipsjpg|right|thumb|200px|Microchips ( EPROM memory with a transparent window showing the integrated circuit inside Microelectromechanical systems ( MEMS) is the technology of the very small and merges at the nano-scale into Nanoelectromechanical systems (NEMS and Nanotechnology

• Thermal expansion: A solid is said to be isotropic if the expansion of solid is equal in all directions when thermal energy is provided to the solid. All metals are isotropic.

• Economics and Geography: An isotropic region is a region which has the same properties everywhere. Such a region is a construction needed in many types of models.

See also

• Rotational invariance
• Isotropic bands
• Isotropic coordinates
• Transverse isotropy

In Mathematics, a function defined on an Inner product space is said to have rotational invariance if its value does not change when arbitrary Rotations In Physiology, isotropic bands are skeletal muscle cells (aka In the theory of Lorentzian manifolds Spherically symmetric spacetimes admit a family of nested round spheres. A transversely isotropic material is symmetric about an axis that is normal to a plane of Isotropy.

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