25:
1248:, in order to mimic hierarchically ordered biological soft matter. 3D printing, especially Fused Deposition Modeling, can introduce anisotropy into printed parts. This is due to the fact that FDM is designed to extrude and print layers of thermoplastic materials. This creates materials that are strong when tensile stress is applied in parallel to the layers and weak when the material is perpendicular to the layers.
357:
124:
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are more likely to move anisotropically, since they are restricted in their movement (they move more in the dimension parallel to the fiber tract rather than in the two dimensions orthogonal to it), whereas water molecules dispersed in the rest of the brain have less restricted movement and therefore
1276:
devices, where the anisotropy of the features is needed to impart desired optical, electrical, or physical properties to the device. Anisotropic etching can also refer to certain chemical etchants used to etch a certain material preferentially over certain crystallographic planes (e.g., KOH etching
686:
In metals, anisotropic elasticity behavior is present in all single crystals with three independent coefficients for cubic crystals, for example. For face-centered cubic materials such as nickel and copper, the stiffness is highest along the <111> direction, normal to the close-packed planes,
432:
in a way that is isotropic, that is independent of spatial orientation around the heat source. Heat conduction is more commonly anisotropic, which implies that detailed geometric modeling of typically diverse materials being thermally managed is required. The materials used to transfer and reject
1227:
exhibit anisotropic mechanical properties, due to orientation of the reinforcement material. In many fiber-reinforced composites like carbon fiber or glass fiber based composites, the weave of the material (e.g. unidirectional or plain weave) can determine the extent of the anisotropy of the bulk
531:
instruments measure this conductivity or resistivity, and the results are used to help find oil and gas in wells. The mechanical anisotropy measured for some of the sedimentary rocks like coal and shale can change with corresponding changes in their surface properties like sorption when gases are
323:
properties of fluorescence from samples excited with plane-polarized light, is used, e.g., to determine the shape of a macromolecule. Anisotropy measurements reveal the average angular displacement of the fluorophore that occurs between absorption and subsequent emission of a photon.
1505:
601:
is changed. Tendon fibers appear hyperechoic (bright) when the transducer is perpendicular to the tendon, but can appear hypoechoic (darker) when the transducer is angled obliquely. This can be a source of interpretation error for inexperienced practitioners.
678:
properties, like the elastic constants, are anisotropic, even for materials with cubic symmetry. The Young's modulus relates stress and strain when an isotropic material is elastically deformed; to describe elasticity in an anisotropic material,
1615:
999:
347:
Images of a gravity-bound or man-made environment are particularly anisotropic in the orientation domain, with more image structure located at orientations parallel with or orthogonal to the direction of gravity (vertical and horizontal).
1243:
can be engineered to have directionally dependent properties through processing techniques or introduction of anisotropy-inducing elements. Researchers have built composite materials with aligned fibers and voids to generate anisotropic
456:
describes light propagation in these media. An "axis of anisotropy" is defined as the axis along which isotropy is broken (or an axis of symmetry, such as normal to crystalline layers). Some materials can have multiple such
687:
and smallest parallel to <100>. Tungsten is so nearly isotropic at room temperature that it can be considered to have only two stiffness coefficients; aluminium is another metal that is nearly isotropic.
634:
material, anisotropy is associated with the crystal symmetry in the sense that more symmetric crystal types have fewer independent coefficients in the tensor description of a given property. When a material is
480:
wavespeed. Measuring the effects of anisotropy in seismic data can provide important information about processes and mineralogy in the Earth; significant seismic anisotropy has been detected in the Earth's
1385:
1381:
where 'i' denotes incident direction and 'v' denotes viewing direction (as if from a satellite or other instrument). And let P be the Planar Albedo, which represents the total reflectance from the scene.
1079:
to cubic materials is waived in the
Tensorial anisotropy index A that takes into consideration all the 27 components of the fully anisotropic stiffness tensor. It is composed of two major parts
1379:
639:, the directional dependence on properties is often related to the processing techniques it has undergone. A material with randomly oriented grains will be isotropic, whereas materials with
1509:
850:
1320:(BRDF)) from a reflective surface are often not isotropic in nature. This makes calculations of the total energy being reflected from any scene a difficult quantity to calculate. In
1228:
material. The tunability of orientation of the fibers allows for application-based designs of composite materials, depending on the direction of stresses applied onto the material.
1187:
1679:
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276:(AF) is a method of enhancing the image quality of textures on surfaces that are far away and steeply angled with respect to the point of view. Older techniques, such as
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is the variation of seismic wavespeed with direction. Seismic anisotropy is an indicator of long range order in a material, where features smaller than the seismic
814:
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1324:
applications, anisotropy functions can be derived for specific scenes, immensely simplifying the calculation of the net reflectance or (thereby) the net
206:. An anisotropic object or pattern has properties that differ according to direction of measurement. For example, many materials exhibit very different
507:
in one direction (e.g. parallel to a layer), is different from that in another (e.g. perpendicular to a layer). This property is used in the gas and
622:
in engineering applications. A material with physical properties that are symmetric about an axis that is normal to a plane of isotropy is called a
391:, the source of the radiation. Cosmic anisotropy has also been seen in the alignment of galaxies' rotation axes and polarization angles of quasars.
335:. In this context, anisotropic systems refer to the electron distribution of molecules with abnormally high electron density, like the pi system of
1305:
display more isotropy. This difference in fractional anisotropy is exploited to create a map of the fiber tracts in the brains of the individual.
1620:
1329:
1317:
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This first component includes the modified Zener ratio and additionally accounts for directional differences in the material, which exist in
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has the fluidity of a normal liquid, but has an average structural order relative to each other along the molecular axis, unlike water or
1865:"The Energy Balance of Groundwater Flow Applied to Subsurface Drainage in Anisotropic Soils by Pipes or Ditches With Entrance Resistance"
1754:
1706:
551:, the difference between horizontal and vertical permeability must be taken into account; otherwise the results may be subject to error.
2113:
Wang, Xin; Jiang, Man; Gou, Jihua; Hui, David (1 February 2017). "3D printing of polymer matrix composites: A review and prospective".
1696:
476:(e.g., crystals, cracks, pores, layers, or inclusions) have a dominant alignment. This alignment leads to a directional variation of
300:, as used to filter particles, is a filter with increasingly smaller interstitial spaces in the direction of filtration so that the
245:
than across it because of the directional non-uniformity of the grain (the grain is the same in one direction, not all directions).
328:
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Igneous rock like granite also shows the anisotropy due to the orientation of the minerals during the solidification process.
402:, so that its magnetic field is oriented in a preferred direction. Plasmas may also show "filamentation" (such as that seen in
305:
301:
380:
131:
2078:
Sano, Koki; Ishida, Yasuhiro; Aida, Tazuko (16 October 2017). "Synthesis of
Anisotropic Hydrogels and Their Applications".
1828:
Saurabh, Suman; Harpalani, Satya (2 January 2019). "Anisotropy of coal at various scales and its variation with sorption".
127:
1781:"Anisotropic Thermal and Electrical Properties of Thin Thermal Interface Layers of Graphite Nanoplatelet-Based Composites"
2006:"Homogenization of carbon/polymer composites with anisotropic distribution of particles and stochastic interface defects"
1220:
covers the influence of stiffness coefficients that are nonzero only for non-cubic materials and remains zero otherwise.
89:
1988:
1948:
1750:
1500:{\displaystyle P(\Omega _{i})=\int _{\Omega _{v}}\gamma (\Omega _{i},\Omega _{v}){\hat {n}}\cdot d{\hat {\Omega }}_{v}}
847:, as the ratio between the empirically determined shear modulus for the cubic material and its (isotropic) equivalent:
376:
61:
1871:
1335:
339:. This abnormal electron density affects the applied magnetic field and causes the observed chemical shift to change.
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or blurring of textures. By reducing detail in one direction more than another, these effects can be reduced easily.
108:
1231:
Amorphous materials such as glass and polymers are typically isotropic. Due to the highly randomized orientation of
68:
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descriptions of material properties can be used to determine the directional dependence of that property. For a
308:
regions increasingly remove smaller particles, resulting in greater flow-through and more efficient filtration.
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1133:, the former referring to components existing in cubic tensor and the latter in anisotropic tensor so that
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42:
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It is of interest because, with knowledge of the anisotropy function as defined, a measurement of the
1746:
1610:{\displaystyle A(\Omega _{i},\Omega _{v})={\frac {\gamma (\Omega _{i},\Omega _{v})}{P(\Omega _{i})}}}
1257:
994:{\displaystyle a_{r}={\frac {G}{E/}}={\frac {2(1+\nu )G}{E}}\equiv {\frac {2C_{44}}{C_{11}-C_{12}}}.}
312:
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will be often be anisotropic. Textured materials are often the result of processing techniques like
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Physicists use the term anisotropy to describe direction-dependent properties of materials.
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Tian, Xiaojuan; Itkis, Mikhail E; Bekyarova, Elena B; Haddon, Robert C (8 April 2013).
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technique that involves measuring the fractional anisotropy of the random motion (
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is often anisotropic for the same reason. When calculating groundwater flow to
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1915:"Granite | Properties, Formation, Composition, Uses » Geology Science"
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9 pp. The corresponding free WellDrain program can be downloaded from:
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262:, an anisotropic surface changes in appearance as it rotates about its
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DoITPoMS Teaching and
Learning Package: "Introduction to Anisotropy"
24:
2154:"Gauge, and knitted fabric generally, is an anisotropic phenomenon"
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674:, are often dependent on the direction of measurement. Fourth-rank
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processes to create well defined microscopic features with a high
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The corresponding free EnDrain program can be downloaded from:
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1300:) of water molecules in the brain. Water molecules located in
820:. Therefore, for cubic materials, we can think of anisotropy,
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1736:"Detection of Anisotropy in the Cosmic Blackbody Radiation"
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material, for instance. The second component of this index
527:(low conductivity), whereas shales have lower resistivity.
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reported about their detection of the cosmic anisotropy in
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1650:) yields a measure of the total scene reflectance (planar
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2004:
Sokołowski, Damian; Kamiński, Marcin (1 September 2018).
421:, which contain no structural ordering of the molecules.
194:
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1941:
Properties of
Materials: Anisotropy, Symmetry, Structure
1778:
566:. Anisotropy in minerals is most reliably seen in their
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caused by the movement of the earth with respect to the
448:("optical anisotropy"), and exhibit properties such as
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In geometry, property of being directionally dependent
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233:An example of anisotropy is light coming through a
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1374:{\displaystyle \gamma (\Omega _{i},\Omega _{v})}
1239:are in general described as isotropic. However,
2112:
1772:
1318:Bidirectional reflectance distribution function
1072:. For an isotropic material, the ratio is one.
2077:
1309:Remote sensing and radiative transfer modeling
614:, is a material's directional dependence of a
532:produced from the coal and shale reservoirs.
1654:) for that specific incident geometry (say,
585:Anisotropy is also a well-known property in
523:. Sand-bearing hydrocarbon assets have high
503:material can exhibit electrical anisotropy;
658:Mechanical properties of materials such as
383:in 1977. Their experiment demonstrated the
683:(or compliance) tensors are used instead.
2021:
1943:(1st ed.). Oxford University Press.
1812:
589:imaging describing a different resulting
464:
214:when measured along different axes, e.g.
109:Learn how and when to remove this message
1978:
1894:"Subsurface Land Drainage By Tube Wells"
1256:Anisotropic etching techniques (such as
570:. An example of an isotropic mineral is
355:
304:regions filter out larger particles and
122:
2080:Angewandte Chemie International Edition
618:. This is a critical consideration for
2161:
1877:from the original on 19 February 2009.
1623:from a single viewing direction (say,
1268:. These features are commonly used in
1003:The latter expression is known as the
1830:International Journal of Coal Geology
1272:(microelectromechanical systems) and
425:are examples of anisotropic liquids.
381:cosmic microwave background radiation
342:
248:
241:, which is easier to split along its
132:cosmic microwave background radiation
1730:Smoot G. F.; Gorenstein M. V. &
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47:adding citations to reliable sources
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1938:
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1760:from the original on 9 October 2022
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499:formations with distinct layers of
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1751:University of California, Berkeley
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1281:produces pyramid-like structures)
1182:{\displaystyle A^{T}=A^{I}+A^{A}.}
377:University of California, Berkeley
14:
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2127:10.1016/j.compositesb.2016.11.034
1983:(2nd ed.). Waveland Pr Inc.
1707:All pages with titles containing
1697:All pages with titles containing
1328:of a scene. For example, let the
606:Materials science and engineering
1981:Mechanical Behavior of Materials
1968:(1st ed.). Clarendon Press.
142:
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1966:Physical Properties of Crystals
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624:transversely isotropic material
515:-bearing sands in sequences of
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2115:Composites Part B: Engineering
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1913:MAT, Mahmut (19 April 2018).
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433:heat from the heat source in
1979:Courtney, Thomas H. (2005).
1743:Lawrence Berkeley Laboratory
1223:Fiber-reinforced or layered
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1674:{\displaystyle \Omega _{i}}
1643:{\displaystyle \Omega _{v}}
690:For an isotropic material,
558:are anisotropic, including
10:
2190:
1892:Oosterbaan, R. J. (2002).
1863:Oosterbaan, R. J. (1997).
1842:10.1016/j.coal.2018.11.008
351:
2023:10.1007/s00707-018-2174-7
1747:Space Sciences Laboratory
1258:deep reactive-ion etching
593:of soft tissues, such as
554:Most common rock-forming
364:displaying the nature of
313:fluorescence spectroscopy
2144:"Overview of Anisotropy"
1290:Diffusion tensor imaging
1235:in polymeric materials,
597:, when the angle of the
670:, and high-temperature
505:electrical conductivity
437:are often anisotropic.
410:) that is directional.
317:fluorescence anisotropy
296:A chemical anisotropic
2169:Orientation (geometry)
2092:10.1002/anie.201708196
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1057:{\displaystyle C_{ij}}
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537:hydraulic conductivity
465:Geophysics and geology
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319:, calculated from the
266:, as is the case with
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2054:"Fabric Weave Styles"
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1213:{\displaystyle A^{A}}
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1126:{\displaystyle A^{A}}
1101:
1099:{\displaystyle A^{I}}
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1027:{\displaystyle a_{r}}
996:
842:
840:{\displaystyle a_{r}}
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743:
741:{\displaystyle G=E/,}
511:industry to identify
389:early Universe matter
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274:Anisotropic filtering
212:mechanical properties
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809:{\displaystyle \nu }
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529:Formation evaluation
43:improve this article
2058:Composite Envisions
1939:Newnham, Robert E.
1797:2013NatSR...3E1710T
1225:composite materials
620:materials selection
444:are anisotropic to
396:Magnetic anisotropy
282:trilinear filtering
1785:Scientific Reports
1734:(5 October 1977).
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470:Seismic anisotropy
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249:Fields of interest
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818:Poisson's ratio
801:
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794:Young's modulus
777:
774:
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750:
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706:
695:
692:
691:
660:Young's modulus
637:polycrystalline
632:monocrystalline
610:Anisotropy, in
608:
583:
509:oil exploration
467:
428:Some materials
423:Liquid crystals
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2010:Acta Mechanica
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771:
770:shear modulus
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450:birefringence
447:
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385:Doppler shift
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60: –
59:
55:
54:Find sources:
48:
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37:
32:This article
30:
26:
21:
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2118:
2114:
2108:
2083:
2079:
2073:
2061:. Retrieved
2057:
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1934:
1922:. Retrieved
1918:
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1858:
1833:
1829:
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1788:
1784:
1774:
1764:15 September
1762:. Retrieved
1732:Muller R. A.
1725:
1708:
1698:
1618:
1316:fields (see
1312:
1302:fiber tracts
1288:
1285:Neuroscience
1274:microfluidic
1266:aspect ratio
1255:
1230:
1222:
1074:
1002:
689:
685:
657:
649:wire drawing
645:cold rolling
609:
591:echogenicity
584:
576:
553:
534:
495:
468:
459:optical axes
439:
430:conduct heat
427:
414:
412:
408:plasma globe
393:
371:
362:plasma globe
346:
326:
321:polarization
310:
295:
272:
257:
232:
224:conductivity
137:
136:
120:
105:
96:
86:
79:
72:
65:
58:"Anisotropy"
53:
41:Please help
36:verification
33:
2121:: 442–458.
1924:16 February
1709:anisotropic
1191:orthotropic
1077:Zener ratio
1005:Zener ratio
525:resistivity
513:hydrocarbon
501:sedimentary
435:electronics
2163:Categories
1964:Nye, J.F.
1717:References
1699:anisotropy
1326:irradiance
1064:refers to
672:creep rate
599:transducer
497:Geological
491:inner core
478:elasticity
474:wavelength
419:chloroform
373:Physicists
216:absorbance
138:Anisotropy
69:newspapers
2174:Asymmetry
2040:126198766
2032:1619-6937
1850:133624963
1836:: 14–25.
1663:Ω
1632:Ω
1593:Ω
1572:Ω
1559:Ω
1552:γ
1534:Ω
1521:Ω
1486:^
1483:Ω
1473:⋅
1467:^
1449:Ω
1436:Ω
1429:γ
1418:Ω
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1347:Ω
1340:γ
1246:hydrogels
973:−
942:≡
927:ν
897:ν
804:ν
727:ν
681:stiffness
664:ductility
404:lightning
292:Chemistry
235:polarizer
2100:29034553
1872:Archived
1791:: 1710.
1755:Archived
1685:See also
1314:Radiance
1237:polymers
1034:, where
564:feldspar
556:minerals
541:aquifers
442:crystals
302:proximal
286:aliasing
278:bilinear
208:physical
204:isotropy
99:May 2017
1814:3632880
1793:Bibcode
1279:silicon
792:is the
768:is the
641:texture
595:tendons
366:plasmas
352:Physics
337:benzene
83:scholar
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2038:
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1652:albedo
1292:is an
796:, and
748:where
676:tensor
651:, and
628:Tensor
572:garnet
560:quartz
547:or to
545:drains
489:, and
487:mantle
400:plasma
315:, the
306:distal
298:filter
268:velvet
226:, and
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2036:S2CID
1897:(PDF)
1875:(PDF)
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1846:S2CID
1758:(PDF)
1739:(PDF)
549:wells
521:shale
483:crust
446:light
440:Many
406:or a
375:from
243:grain
90:JSTOR
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2096:PMID
2065:2019
2028:ISSN
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1766:2013
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1270:MEMS
1106:and
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517:sand
280:and
239:wood
128:WMAP
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