Difference between revisions of "Isotropy" - New World Encyclopedia
From New World Encyclopedia
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* ''Mathematics'': Isotropy is also a concept in [[mathematics]]. Some [[manifold]]s are isotropic, meaning that the [[geometry]] on the manifold is the same regardless of direction. A similar concept is [[homogeneous space|homogeneity]]. A manifold can be homogeneous without being isotropic. But if it is inhomogeneous, it is necessarily anisotropic. | * ''Mathematics'': Isotropy is also a concept in [[mathematics]]. Some [[manifold]]s are isotropic, meaning that the [[geometry]] on the manifold is the same regardless of direction. A similar concept is [[homogeneous space|homogeneity]]. A manifold can be homogeneous without being isotropic. But if it is inhomogeneous, it is necessarily anisotropic. | ||
| − | * ''Cosmology'': The [[Big Bang]] theory of the evolution of the observable universe assumes that space is isotropic. It also assumes that space is homogeneous. These two assumptions together are | + | * ''Cosmology'': The [[Big Bang]] theory of the evolution of the observable universe assumes that, on large scales, space is isotropic. It also assumes that space is homogeneous.<ref>One needs to distinguish between the terms "isotropic" and "homogeneous." Isotropic is defined as "the same in all directions," and homogeneous is defined as "the same at all locations." [http://curious.astro.cornell.edu/question.php?number=508 Curious About Astronomy: What do "homogeneity" and "isotropy" mean?] Retrieved April 19, 2007.</ref> These two assumptions together are part of the [[Cosmological Principle]], and they are supported by investigations probing the large-scale structure of the universe and analyses of the cosmic microwave background radiation. |
* ''Cell biology'': If the properties of the [[Cell (biology) | cell wall]] are more or less the same everywhere, it is said to be isotropic. The interior of the cell is anisotropic due to intracellular [[Organelle | organelles]]. | * ''Cell biology'': If the properties of the [[Cell (biology) | cell wall]] are more or less the same everywhere, it is said to be isotropic. The interior of the cell is anisotropic due to intracellular [[Organelle | organelles]]. | ||
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* ''Radio broadcasting'': In [[radio]], an [[isotropic antenna]] is an idealized "[[radiator|radiating element]]" used as a [[reference]]; an [[antenna (electronics)|antenna]] that broadcasts power equally (calculated by the [[Poynting vector]]) in all directions. In practice, an isotropic antenna cannot exist, as equal radiation in all directions would be a violation of the [[Helmholtz equation|Helmholtz wave equation]]. The gain of an arbitrary antenna is usually reported in [[decibel]]s relative to an isotropic antenna, and is expressed as dBi or dB(i). | * ''Radio broadcasting'': In [[radio]], an [[isotropic antenna]] is an idealized "[[radiator|radiating element]]" used as a [[reference]]; an [[antenna (electronics)|antenna]] that broadcasts power equally (calculated by the [[Poynting vector]]) in all directions. In practice, an isotropic antenna cannot exist, as equal radiation in all directions would be a violation of the [[Helmholtz equation|Helmholtz wave equation]]. The gain of an arbitrary antenna is usually reported in [[decibel]]s relative to an isotropic antenna, and is expressed as dBi or dB(i). | ||
| − | * ''Physiology'': In skeletal muscle cells ( | + | * ''Physiology'': In skeletal muscle cells (or [[muscle fibers]]), the term "isotropic" refers to the light bands ([[I bands]]) that contribute to the striated pattern of the cells. |
* ''Materials'': In the study of [[Mechanics|mechanical]] properties of materials, "isotropic" means having identical values of a property in all [[crystallographic]] directions. | * ''Materials'': In the study of [[Mechanics|mechanical]] properties of materials, "isotropic" means having identical values of a property in all [[crystallographic]] directions. | ||
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* [[Cell]] | * [[Cell]] | ||
* [[Crystal]] | * [[Crystal]] | ||
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| + | == Notes == | ||
| + | <references/> | ||
== References == | == References == | ||
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* Wolf, Joseph Albert. 1966. ''The Geometry and Structure of Isotropy-Irreducible Homogeneous Spaces''. [s.l: s.n.]. ASIN B0007J1J68. | * Wolf, Joseph Albert. 1966. ''The Geometry and Structure of Isotropy-Irreducible Homogeneous Spaces''. [s.l: s.n.]. ASIN B0007J1J68. | ||
| + | |||
| + | == External links == | ||
| + | |||
| + | * NDT Resource Center. 2007. [http://www.ndt-ed.org/EducationResources/CommunityCollege/Materials/Structure/anisotropy.htm Anisotropy and Isotropy.] ''NDT Resource Center''. Retrieved April 19, 2007. | ||
| + | |||
| + | * Becker, Kate. 2003. [http://curious.astro.cornell.edu/question.php?number=508 Curious About Astronomy: What do "homogeneity" and "isotropy" mean?] ''Cornell University''. Retrieved April 19, 2007. | ||
[[Category:Physical sciences]] | [[Category:Physical sciences]] | ||
Revision as of 15:50, 19 April 2007
The space of our universe contains innumerable objects, but a fundamental assumption of the Big Bang theory is that space itself is isotropic and homogeneous. Shown here is the deepest visible-light image of the cosmos, derived from data gathered by the Hubble Space Telescope.
Isotropy (the opposite of anisotropy) is the property of being independent of 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: Isotropy is also a concept in mathematics. Some manifolds are isotropic, meaning that the geometry on the manifold is the same regardless of direction. A similar concept is homogeneity. A manifold can be homogeneous without being isotropic. But if it is inhomogeneous, it is necessarily anisotropic.
- Cosmology: The Big Bang theory of the evolution of the observable universe assumes that, on large scales, space is isotropic. It also assumes that space is homogeneous.[1] These two assumptions together are part of the Cosmological Principle, and they are supported by investigations probing the large-scale structure of the universe and analyses of the cosmic microwave background radiation.
- Cell biology: If the properties of the cell wall are more or less the same everywhere, it is said to be isotropic. The interior of the cell is anisotropic due to intracellular organelles.
- 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. In practice, an isotropic antenna cannot exist, as equal radiation in all directions would be a violation of the Helmholtz wave equation. The gain of an arbitrary antenna is usually reported in decibels relative to an isotropic antenna, and is expressed as dBi or dB(i).
- Physiology: In skeletal muscle cells (or muscle fibers), the term "isotropic" refers to the light bands (I bands) that contribute to the striated pattern of the cells.
- Materials: In the study of mechanical properties of materials, "isotropic" means having identical values of a property in all crystallographic directions.
- 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. 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.
See also
Notes
- ↑ One needs to distinguish between the terms "isotropic" and "homogeneous." Isotropic is defined as "the same in all directions," and homogeneous is defined as "the same at all locations." Curious About Astronomy: What do "homogeneity" and "isotropy" mean? Retrieved April 19, 2007.
ReferencesISBN links support NWE through referral fees
- Petrie, Ted. 1985. Spherical Isotropy Representations. Paris: Presses Universitaires de France. ASIN: B0007CABWI.
- Stokes, Harold T., and Dorian M. Hatch. 1988. Isotropy Subgroups of the 230 Crystallographic Space Groups. Singapore: World Scientific. ISBN 9971507722.
- Wolf, Joseph Albert. 1966. The Geometry and Structure of Isotropy-Irreducible Homogeneous Spaces. [s.l: s.n.]. ASIN B0007J1J68.
External links
- NDT Resource Center. 2007. Anisotropy and Isotropy. NDT Resource Center. Retrieved April 19, 2007.
- Becker, Kate. 2003. Curious About Astronomy: What do "homogeneity" and "isotropy" mean? Cornell University. Retrieved April 19, 2007.
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