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Academic literature on the topic 'Isoclinic planes'

Author: Grafiati
Published: 18 May 2024

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Journal articles on the topic "Isoclinic planes"

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Et-Taoui, Boumediene. "Quaternionic equiangular lines." Advances in Geometry 20, no. 2 (April 28, 2020): 273–84. http://dx.doi.org/10.1515/advgeom-2019-0021.

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AbstractLet 𝔽 = ℝ, ℂ or ℍ. A p-set of equi-isoclinic n-planes with parameter λ in 𝔽r is a set of pn-planes spanning 𝔽r each pair of which has the same non-zero angle arccos $\begin{array}{} \sqrt{\lambda} \end{array}$. It is known that via a complex matrix representation, a pair of isoclinic n-planes in ℍr with angle arccos $\begin{array}{} \sqrt{\lambda} \end{array}$ yields a pair of isoclinic 2n-planes in ℂ2r with angle arccos $\begin{array}{} \sqrt{\lambda} \end{array}$. In this article we characterize all the p-tuples of equi-isoclinic planes in ℂ2r which come via our complex representation from p-tuples of equiangular lines in ℍr. We then construct all the p-tuples of equi-isoclinic planes in ℂ4 and derive all the p-tuples of equiangular lines in ℍ2. Among other things it turns out that the quadruples of equiangular lines in ℍ2 are all regular, i.e. their symmetry groups are isomorphic to the symmetric group S4.
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Et-Taoui, B. "Equi-isoclinic planes of Euclidean spaces." Indagationes Mathematicae 17, no. 2 (June 2006): 205–19. http://dx.doi.org/10.1016/s0019-3577(06)80016-9.

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Blokhuis, Aart, Ulrich Brehm, and Boumediene Et-Taoui. "Complex conference matrices and equi-isoclinic planes in Euclidean spaces." Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry 59, no. 3 (December 19, 2017): 491–500. http://dx.doi.org/10.1007/s13366-017-0374-2.

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Wong, Yung-Chow, and Kam-Ping Mok. "Normally related n-planes and isoclinic n-planes in R2n and strongly linearly independent matrices of order n." Linear Algebra and its Applications 139 (October 1990): 31–52. http://dx.doi.org/10.1016/0024-3795(90)90386-q.

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Et-Taoui, Boumediene. "Infinite family of equi-isoclinic planes in Euclidean odd dimensional spaces and of complex symmetric conference matrices of odd orders." Linear Algebra and its Applications 556 (November 2018): 373–80. http://dx.doi.org/10.1016/j.laa.2018.07.014.

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Yang, Jian Hui, Rong Ling Sun, Zheng Hao Yang, Xin Yang Lin, and Hai Cheng Niu. "Constitutive Relations of Concrete under Plane Stresses Based on Generalized Octahedral Theory." Applied Mechanics and Materials 71-78 (July 2011): 342–52. http://dx.doi.org/10.4028/www.scientific.net/amm.71-78.342.

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Continuous (or generalized) octahedral element bodies can be obtained by intercepting a cube with three groups of failure (or yield) planes successively under true triaxial stress state, on which the stresses are twin stresses. Among the resulting polyhedral characteristic element bodies, isoclinal octahedron and orthogonal octahedron are of particular importance. Strength models of continuous octahedrons are then derived by stress analysis to arbitrary inclined sections in three dimensional stress space, and strain models by the principle of strain analysis, so the plane constitutive relations of concrete can be understood by plane problems transformed by stress-strain space according to the symmetry of an orthogonal octahedral octahedron where an arbitrary oblique plane is parallel to one of three rectangular coordinate axes.
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Morley, C. K., S. Jitmahantakul, C. von Hagke, J. Warren, and F. Linares. "Development of an intra-carbonate detachment during thrusting: The variable influence of pressure solution on deformation style, Khao Khwang Fold and Thrust Belt, Thailand." Geosphere 17, no. 2 (January 21, 2021): 602–25. http://dx.doi.org/10.1130/ges02267.1.

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Abstract Classic detachment zones in fold and thrust belts are generally defined by a weak lithology (typically salt or shale), often accompanied by high over-pressures. This study describes an atypical detachment that occurs entirely within a relatively strong Permian carbonate lithology, deformed during the Triassic Indosinian orogeny in Thailand under late diagenetic-anchimetamorphic conditions. The key differences between stratigraphic members that led to development of a detachment zone are bedding spacing and clay content. The lower, older, unit is the Khao Yai Member (KYM), which is a dark-gray to black, well-bedded, clay-rich limestone. The upper unit, the Na Phra Lan Member (NPM), comprises more massive, medium- to light-gray, commonly recrystallized limestones and marble. The KYM displays much tighter to even isoclinal, shorter-wavelength folds than the NPM. Pressure solution played a dominant role throughout the structural development—first forming early diagenetic bedding; later tectonic pressure solution preferentially followed this bedding instead of forming axial planar cleavage. The detachment zone between the two members is transitional over tens of meters. Moving up-section, tight to isoclinal folds with steeply inclined axial surfaces are replaced by folds with low-angle axial planes, thrusts, and thrust wedging, bed-parallel shearing, and by pressure solution along bedding-parallel seams (that reduce fold amplitude). In outcrops 100–300 m long, reduction of line-length shortening on folds from >50% to <10% shortening upwards indicates that deformation in the NPM is being accommodated differently from the KYM, probably predominantly by shortening on longer wavelength and/or spacing folds and thrusts, given the low amount of strain observed within the NPM, which excludes widespread layer-parallel thickening.
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SRIVASTAVA, DEEPAK C. "Geometrical similarity in successively developed folds and sheath folds in the basement rocks of the northwestern Indian Shield." Geological Magazine 148, no. 1 (August 20, 2010): 171–82. http://dx.doi.org/10.1017/s0016756810000610.

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AbstractAn intensely deformed gneiss–migmatite terrane and a relatively undeformed granulite–granitoid terrane constitute the bulk of Precambrian basement in the northwestern Indian Shield. This article traces the structural evolution in the gneiss–migmatite terrane, where traditional methods of structural analysis are difficult to apply, and shows how successively developed folds can assume identical geometry and orientation at an advanced stage of progressive ductile shearing. The gneiss–migmatite terrane exemplifies a regional-scale ductile shear zone that preserves the history of polyphase folding and sheath folding. Geometrical similarity between individual/domain-scale sheath folds and mesoscopic/regional-scale folds implies that sheath folding is common at all scales in the gneiss–migmatite terrane. As the mylonite foliation that traces successive folds is curviplanar, the successively initiated hinge lines were curvilinear from their inception in the shear zone. At the advanced stage of ductile shearing, the hinge line curvatures were accentuated due to their rotation towards subvertically directed maximum stretching (X), and variably oriented fold axial planes were brought into approximate parallelism with the upright principal plane (XY) of the bulk strain ellipsoid. Eventually all the folds, irrespective of their relative order of development, became strongly non-cylindrical, extremely tight, isoclinal and approximately co-planar with respect to each other. It is due to the above geometrical modifications during ductile shearing that folds, irrespective of their order of development, now appear identical with respect to isoclinal geometry, axial plane orientation and hinge line curvilinearity. Evidence from the fold orientations, the deformed lineation patterns and the sheath fold geometry suggest that the shearing occurred in a general shear type of bulk strain, and NNW–SSE-directed subhorizontal compression resulted in subvertically directed stretching in the gneiss–migmatite terrane.
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Hicock, Stephen R., and Aleksis Dreimanis. "Deformation till in the Great Lakes region: implications for rapid flow along the south-central margin of the Laurentide Ice Sheet." Canadian Journal of Earth Sciences 29, no. 7 (July 1, 1992): 1565–79. http://dx.doi.org/10.1139/e92-123.

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Structural and lithologic data indicate that, while deposited under actively moving ice, considerable portions of three muddy calcareous subglacial tills in the Great Lakes region probably experienced some component of ductile deformation. Viscous till flow and ductile shear are invoked to explain a combination of features such as recumbent isoclinal folds, unlithified sediment clasts, mixed ostracode shells, reversed stone lee ends, girdle and transverse fabrics, irregular stone pavements, fine striae following stone curves, and inconsistent stone striae and a-axes. Deforming, fine-textured subglacial till is considered as a subhorizontal shear zone, rheologically layered with associated structures (in descending order): ductile (e.g., isoclinal folds), brittle–ductile (e.g., fissility), and brittle (e.g., till wedges). Rheology would be controlled mainly by till pore water content, matrix texture, and stone content. Spatial and temporal superposition of rheologies and subglacial processes probably occurred while some fine tills were forming. Fine deformation till may be especially common around areas of the Great Lakes region where proglacial mud and weak bedrock were remoulded as ice travelled along major basins and troughs. In such areas, under a wet-based glacier, resulting till would have been too weak to sustain a large shear stress or inhibit rapid ice flow over it. Instead, in these places, the till was probably water saturated, accounting for most of the glacial flow, and protected the substrate from extensive deformation while effectively acting as a lubricant to overriding ice. Areas of fine deformation till probably represent areas of former low subglacial fluid conductivity and rapid glacial flow. In other areas, subglacial sheet flow of meltwater may have accelerated glacial flow. These two types of areas may have been connected at times under zones of ice streaming and (or) surging.
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Borradaile, G., P. Sarvas, R. Dutka, R. Stewart, and M. Stubley. "Transpression in slates along the margin of an Archean gneiss belt, northern Ontario—magnetic fabrics and petrofabrics." Canadian Journal of Earth Sciences 25, no. 7 (July 1, 1988): 1069–77. http://dx.doi.org/10.1139/e88-104.

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Archean slates along the northern boundary of the Quetico subprovince of the Superior Province show marked variations of the structural facing direction within coplanar primary cleavage surfaces. These are interpreted as being due to sheath folds near the faulted east–west boundary of the slates with the metavolcanic Wabigoon Belt. Sheath folds with axial traces nearly parallel to the belt boundary are macroscopic, primary, and isoclinal and are believed to result from pervasive dextral transpression of the northern margin of the Quetico subprovince. Magnetic fabrics confirm the presence of a single penetrative flattening tectonic microfabric and considerable north–south shortening on the scale of hand specimens and outcrops. The magnetic fabric is due to the alignment of metamorphic sheet silicates, with a subordinate contribution due to the preferred dimensional orientation of detrital magnetite grains. In some low-strain environments at the hinges of sheath folds and at the sandy bases of graded beds relict sedimentary magnetic fabrics are preserved. However, a tectonic magnetic fabric is usual, with flat susceptibility ellipsoids parallel to axial planes and with variably oriented maximum susceptibility directions. To the south, farther into the interior of the Quetico subprovince, the primary folds become more homoaxial and the metamorphic grade rises rather steeply, and still farther south, small-scale polyphase deformation becomes evident especially where the rocks are remobilized.
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Dissertations / Theses on the topic "Isoclinic planes"

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Lehbab, Imène. "Problèmes métriques dans les espaces de Grassmann." Electronic Thesis or Diss., Mulhouse, 2023. http://www.theses.fr/2023MULH6508.

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Il s'agit d'une contribution dans le domaine de la géométrie métrique du plan projectif complexe CP2 et de la variété de Grassmann réelle des plans dans R6. On s'intéresse à l'étude de tous les p-uplets, p ≥ 3, de droites équiangulaires dans C3 et des p-uplets de plans équi-isoclins dans R6. Sachant que 9 est le nombre maximum de droites équiangulaires que l'on peut construire dans C3, on décrit une méthode qui permet de construire tous les p-uplets de droites équiangulaires pour tout pϵ[3,9]. En particulier, on construit dans C3 cinq classes de congruence de quadruplets de droites équiangulaires dont une dépend d'un paramètre réel ɣ que l'on étend à une famille infinie de sextuplets de droites équiangulaires dépendant du même paramètre réel ɣ. En outre, on donne les angles pour lesquels nos sextuplets s'étendent au-delà et jusqu'aux 9-uplets. On sait qu'il existe un p-uplet, p≥3, de plans équi-isoclins engendrant Rr, r≥4, de paramètre c, 0
This work contributes to the field of metric geometry of the complex projective plane CP2 and the real Grassmannian manifold of the planes in R6. More specifically, we study all p-tuples, p ≥ 3, of equiangular lines in C3 or equidistant points in CP2, and p-tuples of equi-isoclinic planes in R6. Knowing that 9 is the maximum number of equiangular lines that can be constructed in C3, we develop a method to obtain all p-tuples of equiangular lines for all p ϵ [3,9]. In particular, we construct in C3 five congruence classes of quadruples of equiangular lines, one of which depends on a real parameter ɣ, which we extend to an infinite family of sextuples of equiangular lines depending on the same real parameter ɣ. In addition, we give the angles for which our sextuples extend beyond and up to 9-tuples. We know that there exists a p-tuple, p ≥ 3, of equi-isoclinic planes generating Rr, r ≥ 4, with parameter c, 0< c <1, if and only if there exists a square symmetric matrix, called Seidel matrix, of p × p square blocks of order 2, whose diagonal blocks are all zero and the others are orthogonal matrices in O(2) and whose smallest eigenvalue is equal to - 1/c and has multiplicity 2p-r. In this thesis, we investigate the case r=6 and we also show that we can explicitly determine the spectrum of all Seidel matrices of order 2p, p ≥ 3 whose off-diagonal blocks are in {R0, S0} where R0 and S0 are respectively the zero-angle rotation and the zero-angle symmetry. We thus show an unexpected link between some p-tuples of equi-isoclinic planes in Rr and simple graphs of order p
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Conference papers on the topic "Isoclinic planes"

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Wilde, D. J. "Two Generalizations of the Isometric Projection in Geometric Design." In ASME 1987 Design Technology Conferences. American Society of Mechanical Engineers, 1987. http://dx.doi.org/10.1115/detc1987-0045.

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Abstract The well-known pictorial drafting technique of isometric drawing is here generalized in two ways, called “isoclinal” and “axial”, or collectively, “symmetric”. Although the isoclinal projection preserves the useful property of foreshortening adjacent edges equally, and the axial projection foreshortens adjacent edges equally, the directions for these projections usually differ from that for isometric projection. Formulas are derived for the isoclinal and axial directions and their foreshortening factors and rotation matrices. Although intended for three-dimensional computer-aided design, the symmetric projections can also be performed on a drawing board with a protractor. Graphic examples involving design of non-rectangular connectors for three skew structural members and adjacent plates in space are presented.
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Stjepan Bogdan. "Fuzzy Controller Design Based on the Phase Plane Isoclines." In 2006 14th Mediterranean Conference on Control and Automation. IEEE, 2006. http://dx.doi.org/10.1109/med.2006.235699.

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Bogdan, Stjepan, and Zdenko Kovacic. "Fuzzy Controller Design Based on the Phase Plane Isoclines." In 2006 14th Mediterranean Conference on Control and Automation. IEEE, 2006. http://dx.doi.org/10.1109/med.2006.328846.

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Noufal, Abdelwahab, Safeya Alkatheeri, Khalid Obaid, Abdulla Shehab, Hamda Al Shehhi, and Saleh Al Hadarem. "Abu Dhabi Tectonic Evolution: Novel Model Impacting Hydrocarbon Potentiality and Trapping Mechanism." In ADIPEC. SPE, 2023. http://dx.doi.org/10.2118/216263-ms.

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Abstract There is evidence that the Oman Mountains deformation is being continued by massive thrust fault systems in the Eastern Abu Dhabi basins. These are large-scale thrust faults with a strike-slip component that most likely include a fault damage zone encircling the fault core, a zone of strong rock shearing, and complicated zones of deformation involving numerous fault planes. The initial event was caused by the compressional movement of the Masirah, which faulted and folded again during the Semail tectonic events. Large faults are typically modeled on seismic as a single, large slip plane, but the outcrop analogs demonstrate the case is far more intricate, according to understanding of fault zone complexity and fault rock attributes from field observations. To understand the strength characteristics and seismic behavior of faults in the subsurface, more in-depth information of the growth and structural style of thrust systems on outcrop analogues is essential considering the future exploration in eastern Abu Dhabi. Architecture, geometry, and tectonic uplift resulting from accumulated slip on the faults are all expressed at the surface for sub-surface thrust faults. The three-dimensional geometry of these fault planes and slip distributions, which provide suggestions to fault evolution and structural styles of the thrust systems in the subsurface, can be better understood by characterizing the structural patterns along-strike morphology of such styles. The fold-thrust belt can be further divided into sub-belts, including the imbricate thrust sub-belt, which is characterized by imbricate stepped-thrust sheets, the thrust-fold sub-belt, which is composed of equally developed thrusts and related folds, and the detachmentfold sub-belt, which is composed of box, chevron, and closed overturned-isoclinal folds on the oblique surface. Imbricate thrust system, passive-roof duplex (triangle zone), fault-related folds, back-thrust system, pop-up structure, and other types of structures have all been identified or inferred. A reasonable model for folding evolution in Abu Dhabi subsurface is presented answering the questions of the many interpretations for folding patterns, such as: If these folds related to the compressional forces, then why they did not represent series of anticlines and synclines? Why have they dissected? Why showing different amplitudes from the deflection to the hinge zones? And finally, why the main geometry is open folding style and did not showing steep dipping limbs towards the direction of the compression more than the other limb? This paper is presenting a trial to answer these questions lightening the tectonic evolution of Abu Dhabi basins reflecting the fields formation and evolution. Thrusting deformation developed preferentially along the main detachment layers, moving upward from the Upper Jurassic through the Cretaceous to Tertiary. The approach presented a new model for Abu Dhabi tectonic evolution, which will impact understanding of the hydrocarbon potentiality and trapping mechanism.
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