1259:, 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.
36:
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135:
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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
1287:
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
697:
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,
443:
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
1238:
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
542:
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
334:
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.
1516:
612:
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.
689:
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,
1626:
1010:
358:
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).
1254:
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
467:
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
698:
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.
645:
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
491:
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
1396:
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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.
1090:
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
1390:
650:, 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
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861:
1331:(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
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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.
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287:(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
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applications, anisotropy functions can be derived for specific scenes, immensely simplifying the calculation of the net reflectance or (thereby) the net
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217:. An anisotropic object or pattern has properties that differ according to direction of measurement. For example, many materials exhibit very different
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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
633:
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
402:, the source of the radiation. Cosmic anisotropy has also been seen in the alignment of galaxies' rotation axes and polarization angles of quasars.
346:. In this context, anisotropic systems refer to the electron distribution of molecules with abnormally high electron density, like the pi system of
1316:
display more isotropy. This difference in fractional anisotropy is exploited to create a map of the fiber tracts in the brains of the individual.
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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
1876:"The Energy Balance of Groundwater Flow Applied to Subsurface Drainage in Anisotropic Soils by Pipes or Ditches With Entrance Resistance"
1765:
562:, the difference between horizontal and vertical permeability must be taken into account; otherwise the results may be subject to error.
2124:
Wang, Xin; Jiang, Man; Gou, Jihua; Hui, David (1 February 2017). "3D printing of polymer matrix composites: A review and prospective".
1999:
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487:(e.g., crystals, cracks, pores, layers, or inclusions) have a dominant alignment. This alignment leads to a directional variation of
311:, as used to filter particles, is a filter with increasingly smaller interstitial spaces in the direction of filtration so that the
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than across it because of the directional non-uniformity of the grain (the grain is the same in one direction, not all directions).
119:
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Igneous rock like granite also shows the anisotropy due to the orientation of the minerals during the solidification process.
413:, so that its magnetic field is oriented in a preferred direction. Plasmas may also show "filamentation" (such as that seen in
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57:
2089:
Sano, Koki; Ishida, Yasuhiro; Aida, Tazuko (16 October 2017). "Synthesis of
Anisotropic Hydrogels and Their Applications".
1839:
Saurabh, Suman; Harpalani, Satya (2 January 2019). "Anisotropy of coal at various scales and its variation with sorption".
1792:"Anisotropic Thermal and Electrical Properties of Thin Thermal Interface Layers of Graphite Nanoplatelet-Based Composites"
2017:"Homogenization of carbon/polymer composites with anisotropic distribution of particles and stochastic interface defects"
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covers the influence of stiffness coefficients that are nonzero only for non-cubic materials and remains zero otherwise.
100:
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222:
1511:{\displaystyle P(\Omega _{i})=\int _{\Omega _{v}}\gamma (\Omega _{i},\Omega _{v}){\hat {n}}\cdot d{\hat {\Omega }}_{v}}
858:, as the ratio between the empirically determined shear modulus for the cubic material and its (isotropic) equivalent:
72:
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350:. This abnormal electron density affects the applied magnetic field and causes the observed chemical shift to change.
53:
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or blurring of textures. By reducing detail in one direction more than another, these effects can be reduced easily.
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Amorphous materials such as glass and polymers are typically isotropic. Due to the highly randomized orientation of
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descriptions of material properties can be used to determine the directional dependence of that property. For a
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regions increasingly remove smaller particles, resulting in greater flow-through and more efficient filtration.
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It is of interest because, with knowledge of the anisotropy function as defined, a measurement of the
1803:
1621:{\displaystyle A(\Omega _{i},\Omega _{v})={\frac {\gamma (\Omega _{i},\Omega _{v})}{P(\Omega _{i})}}}
1201:
1005:{\displaystyle a_{r}={\frac {G}{E/}}={\frac {2(1+\nu )G}{E}}\equiv {\frac {2C_{44}}{C_{11}-C_{12}}}.}
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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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1926:"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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DoITPoMS Teaching and
Learning Package: "Introduction to Anisotropy"
2165:"Gauge, and knitted fabric generally, is an anisotropic phenomenon"
685:, 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:
1311:) of water molecules in the brain. Water molecules located in
831:. Therefore, for cubic materials, we can think of anisotropy,
29:
1747:"Detection of Anisotropy in the Cosmic Blackbody Radiation"
1204:
material, for instance. The second component of this index
538:(low conductivity), whereas shales have lower resistivity.
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reported about their detection of the cosmic anisotropy in
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1661:) yields a measure of the total scene reflectance (planar
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2015:
Sokołowski, Damian; Kamiński, Marcin (1 September 2018).
432:, which contain no structural ordering of the molecules.
205:
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1952:
Properties of
Materials: Anisotropy, Symmetry, Structure
577:. Anisotropy in minerals is most reliably seen in their
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caused by the movement of the earth with respect to the
459:("optical anisotropy"), and exhibit properties such as
27:
In geometry, property of being directionally dependent
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244:An example of anisotropy is light coming through a
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60:. Unsourced material may be challenged and removed.
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141:image of the (extremely tiny) anisotropies in the
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1385:{\displaystyle \gamma (\Omega _{i},\Omega _{v})}
1250:are in general described as isotropic. However,
1329:Bidirectional reflectance distribution function
1083:. For an isotropic material, the ratio is one.
1320:Remote sensing and radiative transfer modeling
625:, is a material's directional dependence of a
543:produced from the coal and shale reservoirs.
8:
1665:) for that specific incident geometry (say,
596:Anisotropy is also a well-known property in
534:. Sand-bearing hydrocarbon assets have high
514:material can exhibit electrical anisotropy;
669:Mechanical properties of materials such as
394:in 1977. Their experiment demonstrated the
694:(or compliance) tensors are used instead.
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1954:(1st ed.). Oxford University Press.
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600:imaging describing a different resulting
225:when measured along different axes, e.g.
120:Learn how and when to remove this message
1905:"Subsurface Land Drainage By Tube Wells"
1267:Anisotropic etching techniques (such as
581:. An example of an isotropic mineral is
315:regions filter out larger particles and
2091:Angewandte Chemie International Edition
1733:
629:. This is a critical consideration for
1888:from the original on 19 February 2009.
1634:from a single viewing direction (say,
1279:. These features are commonly used in
1014:The latter expression is known as the
1841:International Journal of Coal Geology
1283:(microelectromechanical systems) and
436:are examples of anisotropic liquids.
392:cosmic microwave background radiation
252:, which is easier to split along its
143:cosmic microwave background radiation
7:
1741:Smoot G. F.; Gorenstein M. V. &
58:adding citations to reliable sources
1771:from the original on 9 October 2022
510:formations with distinct layers of
1762:University of California, Berkeley
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1292:produces pyramid-like structures)
1193:{\displaystyle A^{T}=A^{I}+A^{A}.}
388:University of California, Berkeley
25:
2138:10.1016/j.compositesb.2016.11.034
1994:(2nd ed.). Waveland Pr Inc.
1718:All pages with titles containing
1708:All pages with titles containing
1339:of a scene. For example, let the
617:Materials science and engineering
1992:Mechanical Behavior of Materials
1979:(1st ed.). Clarendon Press.
153:
34:
1977:Physical Properties of Crystals
635:transversely isotropic material
526:-bearing sands in sequences of
45:needs additional citations for
2126:Composites Part B: Engineering
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409:, for example, may occur in a
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1924:MAT, Mahmut (19 April 2018).
444:heat from the heat source in
1990:Courtney, Thomas H. (2005).
1754:Lawrence Berkeley Laboratory
1234:Fiber-reinforced or layered
1685:{\displaystyle \Omega _{i}}
1654:{\displaystyle \Omega _{v}}
701:For an isotropic material,
569:are anisotropic, including
2201:
1903:Oosterbaan, R. J. (2002).
1874:Oosterbaan, R. J. (1997).
1853:10.1016/j.coal.2018.11.008
2034:10.1007/s00707-018-2174-7
1758:Space Sciences Laboratory
1269:deep reactive-ion etching
604:of soft tissues, such as
565:Most common rock-forming
375:displaying the nature of
324:fluorescence spectroscopy
2155:"Overview of Anisotropy"
1301:Diffusion tensor imaging
1246:in polymeric materials,
608:, when the angle of the
681:, and high-temperature
516:electrical conductivity
448:are often anisotropic.
421:) that is directional.
328:fluorescence anisotropy
307:A chemical anisotropic
2180:Orientation (geometry)
2103:10.1002/anie.201708196
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1068:{\displaystyle C_{ij}}
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548:hydraulic conductivity
476:Geophysics and geology
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330:, calculated from the
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2065:"Fabric Weave Styles"
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1224:{\displaystyle A^{A}}
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1137:{\displaystyle A^{A}}
1112:
1110:{\displaystyle A^{I}}
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1038:{\displaystyle a_{r}}
1007:
853:
851:{\displaystyle a_{r}}
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752:{\displaystyle G=E/,}
522:industry to identify
400:early Universe matter
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285:Anisotropic filtering
223:mechanical properties
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820:{\displaystyle \nu }
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540:Formation evaluation
54:improve this article
2069:Composite Envisions
1950:Newnham, Robert E.
1808:2013NatSR...3E1710T
1236:composite materials
631:materials selection
455:are anisotropic to
407:Magnetic anisotropy
293:trilinear filtering
1796:Scientific Reports
1745:(5 October 1977).
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579:optical properties
481:Seismic anisotropy
426:anisotropic liquid
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354:Real-world imagery
260:Fields of interest
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2097:(10): 2532–2543.
1816:10.1038/srep01710
1702:Circular symmetry
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796:{\displaystyle E}
772:{\displaystyle G}
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883:
865:
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838:
833:
832:
829:Poisson's ratio
809:
808:
805:Young's modulus
785:
784:
761:
760:
703:
702:
671:Young's modulus
648:polycrystalline
643:monocrystalline
621:Anisotropy, in
619:
594:
520:oil exploration
478:
439:Some materials
434:Liquid crystals
365:
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2149:External links
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2021:Acta Mechanica
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2001:978-1577664253
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679:yield strength
664:heat treatment
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465:Crystal optics
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806:
790:
782:
781:shear modulus
766:
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461:birefringence
458:
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447:
442:
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431:
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408:
403:
401:
397:
396:Doppler shift
393:
389:
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248:. Another is
247:
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81:
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74:
71: –
70:
66:
65:Find sources:
59:
55:
49:
48:
43:This article
41:
37:
32:
31:
19:
2129:
2125:
2119:
2094:
2090:
2084:
2072:. Retrieved
2068:
2059:
2024:
2020:
2010:
1991:
1985:
1976:
1970:
1951:
1945:
1933:. Retrieved
1929:
1919:
1898:
1869:
1844:
1840:
1834:
1799:
1795:
1785:
1775:15 September
1773:. Retrieved
1743:Muller R. A.
1736:
1719:
1709:
1629:
1327:fields (see
1323:
1313:fiber tracts
1299:
1296:Neuroscience
1285:microfluidic
1277:aspect ratio
1266:
1241:
1233:
1085:
1013:
700:
696:
668:
660:wire drawing
656:cold rolling
620:
602:echogenicity
595:
587:
564:
545:
506:
479:
470:optical axes
450:
441:conduct heat
438:
425:
423:
419:plasma globe
404:
382:
373:plasma globe
357:
337:
332:polarization
321:
306:
283:
268:
243:
235:conductivity
148:
147:
131:
116:
107:
97:
90:
83:
76:
69:"Anisotropy"
64:
52:Please help
47:verification
44:
18:Anisotropies
2132:: 442–458.
1935:16 February
1720:anisotropic
1202:orthotropic
1088:Zener ratio
1016:Zener ratio
536:resistivity
524:hydrocarbon
512:sedimentary
446:electronics
2174:Categories
1975:Nye, J.F.
1728:References
1710:anisotropy
1337:irradiance
1075:refers to
683:creep rate
610:transducer
508:Geological
502:inner core
489:elasticity
485:wavelength
430:chloroform
384:Physicists
227:absorbance
149:Anisotropy
80:newspapers
2185:Asymmetry
2051:126198766
2043:1619-6937
1861:133624963
1847:: 14–25.
1674:Ω
1643:Ω
1604:Ω
1583:Ω
1570:Ω
1563:γ
1545:Ω
1532:Ω
1497:^
1494:Ω
1484:⋅
1478:^
1460:Ω
1447:Ω
1440:γ
1429:Ω
1424:∫
1408:Ω
1371:Ω
1358:Ω
1351:γ
1257:hydrogels
984:−
953:≡
938:ν
908:ν
815:ν
738:ν
692:stiffness
675:ductility
415:lightning
303:Chemistry
246:polarizer
2111:29034553
1883:Archived
1802:: 1710.
1766:Archived
1696:See also
1325:Radiance
1248:polymers
1045:, where
575:feldspar
567:minerals
552:aquifers
453:crystals
313:proximal
297:aliasing
289:bilinear
219:physical
215:isotropy
110:May 2017
1825:3632880
1804:Bibcode
1290:silicon
803:is the
779:is the
652:texture
606:tendons
377:plasmas
363:Physics
348:benzene
94:scholar
2109:
2074:23 May
2049:
2041:
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1958:
1859:
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1663:albedo
1303:is an
807:, and
759:where
687:tensor
662:, and
639:Tensor
583:garnet
571:quartz
558:or to
556:drains
500:, and
498:mantle
411:plasma
326:, the
317:distal
309:filter
279:velvet
237:, and
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75:
67:
2047:S2CID
1908:(PDF)
1886:(PDF)
1879:(PDF)
1857:S2CID
1769:(PDF)
1750:(PDF)
560:wells
532:shale
494:crust
457:light
451:Many
417:or a
386:from
254:grain
101:JSTOR
87:books
2107:PMID
2076:2019
2039:ISSN
1996:ISBN
1956:ISBN
1937:2024
1777:2013
1756:and
1632:BRDF
1341:BRDF
1281:MEMS
1117:and
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546:The
530:and
528:sand
291:and
250:wood
139:WMAP
73:news
2134:doi
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