WordNet

invariant with respect to direction (同)isotropous
(physics) the property of being isotropic; having the same value when measured in different directions (同)symmetry
not invariant with respect to direction; "anisotropic crystals"
in an anisotropic manner
in an isotropic manner

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出典(authority):フリー百科事典『ウィキペディア（Wikipedia）』「2013/09/12 01:05:08」(JST)

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Not to be confused with isotope.

"Isotropic" redirects here. For the eye condition described as esotropic, see Esotropia.

Isotropy is uniformity in all orientations; it is derived from the Greek isos (ίσος, equal) and tropos (τρόπος, way). Precise definitions depend on the subject area. Exceptions, or inequalities, are frequently indicated by the prefix 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[edit source | edit]

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. A similar concept is homogeneity. 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.
Isotropic coordinates on an Isotropic chart for Lorentzian manifolds.
Isotropy group: An isotropy group is the group of isomorphisms from any object to itself in a groupoid.^[1]

Physics[edit source | edit]

Quantum mechanics or Particle physics: 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.; Kinetic theory is also an example of 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, there will be an equal number moving in one direction as any other hence demonstrating isotropy.

Fluid dynamics: 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.

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.

Electromagnetics: 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 most simple instance being free space.

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.

Cosmology: The Big Bang theory of the evolution of the observable universe assumes that space is isotropic.^[2] It also assumes that space is homogeneous.^[3] These two assumptions together are known as the Cosmological Principle. 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.

Materials science[edit source | edit]

This sand grain made of volcanic glass is isotropic, and thus, stays extinct when rotated between polarization filters on a petrographic microscope

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.^[4] Common anisotropic materials include wood, because its material properties are different parallel and perpendicular to the grain, and layered minerals 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.

Microfabrication[edit source | edit]

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.

Antenna (radio)[edit source | edit]

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).

Biology[edit source | edit]

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.

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.

Pharmacology: 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.^[5] Most recently, isotropic formulations have been used extensively in dermatology for drug delivery.^[6]

Other sciences[edit source | edit]

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.

References[edit source | edit]

^ A groupoid is a category where all morphisms are isomorphisms, i.e., invertible. If is any object, then denotes its isotropy group: the group of isomorphisms from to .
^ http://map.gsfc.nasa.gov/universe/bb_theory.html
^ http://map.gsfc.nasa.gov/universe/bb_theory.html
^ "Anisotropy and Isotropy".
^ Landman L. “The Epidermal Permeability Barrier.” Anat Embryol (Berl) 1988; 178:1-13 [1]
^ Gregoriadis G. “Lipsomes in Drug Delivery.” Harwood Academic Publishers, 1993; [2]

UpToDate Contents

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1. 胸膜のプラーク、肥厚、および腫瘍の画像 imaging of pleural plaques thickening and tumors
2. 胸部CTの原理 principles of computed tomography of the chest
3. 胸部MRI magnetic resonance imaging of the thorax
4. 肺結節のCTおよびPET computed tomographic and positron emission tomographic scanning of pulmonary nodules
5. 肺癌の画像検査 imaging of lung cancer

English Journal

The promotion of HL-1 cardiomyocyte beating using anisotropic collagen-GAG scaffolds.

Gonnerman EA, Kelkhoff DO, McGregor LM, Harley BA.SourceDept. Chemical and Biomolecular Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA.
Biomaterials.Biomaterials.2012 Dec;33(34):8812-21. doi: 10.1016/j.biomaterials.2012.08.051. Epub 2012 Sep 12.
Biomaterials for myocardial tissue engineering must balance structural, mechanical and bioactivity concerns. This work describes the interaction between HL-1 cardiomyocytes and a series of geometrically anisotropic collagen-GAG (CG) scaffolds with aligned tracks of ellipsoidal pores designed to mimi
PMID 22979989

Electron Spin Resonance and optical absorption spectroscopic studies of manganese centers in aluminium lead borate glasses.

Sivaramaiah G, Lakshmanarao J.SourceDepartment of Physics, Government College for Men, Kadapa 516004, India. Electronic address: gsivaram7@yahoo.co.in.
Spectrochimica acta. Part A, Molecular and biomolecular spectroscopy.Spectrochim Acta A Mol Biomol Spectrosc.2012 Dec;98:105-9. doi: 10.1016/j.saa.2012.08.023. Epub 2012 Aug 19.
Electron Spin Resonance (ESR) and optical absorption studies of 5Al(2)O(3)+75H(3)BO(3)+(20-x)PbO+xMnSO(4) (where x=0.5, 1,1.5 and 2mol% of MnSO(4)) glasses at room temperature have been studied. The ESR spectrum of all the glasses exhibits resonance signals with effective isotropic g values at ≈2.
PMID 23000927

Japanese Journal

Hydrogen-Related Dangling Bonds in Hydrogenated Amorphous Silicon

森垣和夫,疋田春水
広島工業大学研究紀要 33, 135-142, 36192-00-00
… The relationship between isotropic and anisotropic hyperfine interaction constants of the dangling-bond electron at the hydrogen-related dangling bond with a hydrogen nucleus at a nearby site is examined for various types of a-Si:H samples, including ESR data taken from the literatures. …
NAID 120005403262

Observation and Analysis of Neutron-Induced Single-Event Burnout in Silicon Power Diodes

Shoji T.,Nishida S.,Hamada K.,Tadano H.
IEEE transactions on power electronics 30(5), 2474-2480, 2015-05
… The axial symmetry of damage region reflects the spatially isotropic thermal diffusion that occurred. …
NAID 120005540936

Multidirectional available high-frequency response with zero-field resonance above 8 GHz in epitaxial α-Fe(001) films

Gao Cunxu,Wang Yutian,Li Chengyi,Wei Yanping,Chen Zhendong,Chai Guozhi,Xue Desheng
Appl. Phys. Express 8(5), 053001, 2015-04-07
… The results show an in-plane isotropic static permeability above 50 with a multidirectional zero-field resonance frequency (f<inf>r</inf>) higher than 8 GHz in the films. …
NAID 150000110569

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