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| {{confuse|isotope}}
| | == 805 == |
| {{redirect|Isotropic|the eye condition described as esotropic|Esotropia}}
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| '''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 [[Elementary particle|particle]] is oriented.
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| ==Mathematics==
| | クレセントシティはまた、実質的な利益を、他のクレセントシティは、間違いなく、途方に暮れたままに損失で少しクレセントシティを買うためにこの時間は唯一の状態なかった、そして、最も重要なこと、それは広場を買ったファミリーに追加されるxiaojiaを怒ら市、無力な、心は一部の人の意図である、という考えは失望撤退しなければならなかった [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-7.html カシオ 腕時計 gps]。<br><br>シティスクエアは、リリース後に販売される、その後、活動に加えて、列の完全なの温床となるよう考えているだろうが、再び恥ずかしさの味を味わって、彼はxiaojiaが今影響があってもこのステップに強いてきた期待していなかった [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-8.html casio 腕時計 スタンダード]。<br><br>日の返済期間は、まだ完了していない瞬間がやたらと汗をかいて気になる助けることができなかったが、ちょうどプラスの欄の下にBiは、最終的には見知らぬ人が、両側を切望しそこ運ばれた、一緒にバランスを考え出すために追加することができます到着するとしている雄弁全体午後代金引数、最後に見知らぬ人、20万安い価格で、プラスに完成した列は、ほぼその暗い顔、「色」を殺したい、心がいっぱいです |
| Within [[mathematics]], ''isotropy'' has a few different meanings:
| | 相关的主题文章： |
| ; [[Isotropic manifold]]s: 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.
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| ; [[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''.
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| ; [[Isotropic coordinates]] on an Isotropic chart for [[Lorentzian manifolds]].
| | <li>[http://andendless.com/cgi-bin/epad/epad.cgi http://andendless.com/cgi-bin/epad/epad.cgi]</li> |
| ; [[Isotropy group]]: An isotropy group is the group of [[isomorphism]]s from any [[object (category theory)|object]] to itself in a [[groupoid]].<ref>A [[groupoid]] <math>\mathcal G</math> is a [[category]] where all [[morphism]]s are [[isomorphism]]s, i.e., invertible. If <math>G \in \mathcal G</math> is any object, then <math>\mathcal G(G,G)</math> denotes its [[isotropy group]]: the group of isomorphisms from <math>G</math> to <math>G</math>.</ref>
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| | <li>[http://www.wannyann.com/cgi-bin/glight/glight.cgi http://www.wannyann.com/cgi-bin/glight/glight.cgi]</li> |
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| | <li>[http://anxinyt.com/plus/feedback.php?aid=310 http://anxinyt.com/plus/feedback.php?aid=310]</li> |
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| | </ul> |
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| ==Physics== | | == ゆっくりと持ち上げ == |
| ; [[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.
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| :[[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.
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| ; [[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.
| | 丁度そのことが何であるかを参照してくださいますが、見ていないが、彼女は可能な明らかに何かがあるとき、実際に瞬時に沸騰している身体の血液「流体」は、多くなるようなことを感じ、彼女の心に非常に強い引力が、出現する。<br><br>唇を「なめる」、そのようなシーンは本当に無限のルアー「混乱」シェン「陰陽」が充填されている「陰」Xiangshe優しく 'なめる'への [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-10.html カシオの時計] '気持ち'風水シェン清子どもたちが続いた瞬間、そのJiaoquは、タッチの漸進的出現の中の目が実際にショックを受けていることを、ショックを受けて押し込んだ「色」<br><br>「古代のフェニックス血精液？ [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-6.html casio 腕時計 メンズ] '<br>ゆっくりと持ち上げ<br>美しい目は、いくつかの約束で、瞬きシャオヤン、トーンを見つめ鳳凰清子どもたちは道路の各音節を強調し、衝撃を与えた [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-4.html カシオ 電波ソーラー時計]。<br><br>「古代のフェニックス血精液？ [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-8.html カシオ レディース 電波ソーラー腕時計] '<br><br>ウェンヤン、ダイナミックのシャオヤンの心は、わずかな表面が動いていなかった、きっぱりと言った： [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-3.html カシオ gps 時計] 'あなたは何を意味するのですか？' |
| | | 相关的主题文章： |
| ; [[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.
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| ; [[Electromagnetism|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.
| | <li>[http://www.qingvip.net/plus/feedback.php?aid=5 http://www.qingvip.net/plus/feedback.php?aid=5]</li> |
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| ; [[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.
| | <li>[http://oppositionunchained.com/wiki/index.php/User:Uyqwazyhmqga#.E6.9A.87.E3.81.A4.E3.81.B6.E3.81.97.E3.81.AB.E3.80.81.E5.8D.88.E5.BE.8C.E3.81.AB.E8.BF.91.E3.81.A5.E3.81.84.E3.81.9F.E3.81.A8.E3.81.8D.E3.81.BE.E3.81.A0.E6.9E.9C.E7.89.A9.E3.81.BE.E3.81.9B.E3.82.93.E3.81.A7.E3.81.97.E3.81.9F http://oppositionunchained.com/wiki/index.php/User:Uyqwazyhmqga#.E6.9A.87.E3.81.A4.E3.81.B6.E3.81.97.E3.81.AB.E3.80.81.E5.8D.88.E5.BE.8C.E3.81.AB.E8.BF.91.E3.81.A5.E3.81.84.E3.81.9F.E3.81.A8.E3.81.8D.E3.81.BE.E3.81.A0.E6.9E.9C.E7.89.A9.E3.81.BE.E3.81.9B.E3.82.93.E3.81.A7.E3.81.97.E3.81.9F]</li> |
| <div id="Cosmology"></div> | | |
| ; [[Cosmology]]: The [[Big Bang]] theory of the evolution of the observable universe assumes that space is isotropic.<ref>http://map.gsfc.nasa.gov/universe/bb_theory.html</ref> It also assumes that space is homogeneous.<ref>http://map.gsfc.nasa.gov/universe/bb_theory.html</ref> 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 Wall (astronomy)|"Great"]] features, but small compared to so-called multi-verse scenarios.
| | <li>[http://cgi.www5c.biglobe.ne.jp/~twidusk/cgi-bin/yybbs.cgi http://cgi.www5c.biglobe.ne.jp/~twidusk/cgi-bin/yybbs.cgi]</li> |
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| ===Materials science===
| | </ul> |
| [[Image:LvMS-Lvv.jpg|thumb|This sand grain made of [[volcanic]] glass is [[isotropic]], and thus, stays extinct when rotated between [[polarized|polarization filters]] on a [[petrographic microscope]]]] | |
| In the study of [[List of materials properties|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.<ref>{{cite web|title=Anisotropy and Isotropy|url=http://www.ndt-ed.org/EducationResources/CommunityCollege/Materials/Structure/anisotropy.htm}}</ref> Common anisotropic materials include [[wood]], because its material properties are different parallel and perpendicular to the grain, and layered minerals such as [[slate]].
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| 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 [[rebar]]s in [[reinforced concrete]] are oriented to withstand tension.
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| ===Microfabrication===
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| 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 [[Microelectromechanical systems|MEMS]] devices.
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| ===Antenna (radio)===
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| 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).
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| ==Biology==
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| ; [[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]]s.
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| ; [[Physiology]]: In skeletal muscle cells (a.k.a. [[muscle fibers]]), the term "[[isotropic bands|isotropic]]" refers to the light bands ([[I bands]]) that contribute to the striated pattern of the cells.
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| ; [[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.<ref>Landman L. “The Epidermal Permeability Barrier.” Anat Embryol (Berl) 1988; 178:1-13 [http://www.springerlink.com/content/x2v22259r84n6k75/]</ref> Most recently, [[isotropic formulations]] have been used extensively in dermatology for drug delivery.<ref>Gregoriadis G. “Lipsomes in Drug Delivery.” Harwood Academic Publishers, 1993; [http://books.google.com.au/books?hl=en&lr=&id=IqqYFne6deEC&oi=fnd&pg=PR7&dq=Liposomes+in+Drug+Delivery&ots=MSjlK_DRqc&sig=XKlC_NXQDndHXkVUepu8rIPaQrU]</ref>
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| ==Other sciences==
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| ; ''[[Economics]]'' and ''[[Geography]]'': An isotropic region is a region that has the same properties everywhere. Such a region is a construction needed in many types of models.
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| ==See also==
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| {{Wiktionary}}
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| * [[Rotational invariance]]
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| * [[Isotropic bands]]
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| * [[Isotropic coordinates]]
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| * [[Transverse isotropy]]
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| * [[Anisotropic]]
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| * [[Bi isotropic]]
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| ==References==
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| {{Reflist}}
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| [[Category:Orientation]]
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