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Chongmin Song - One of the best experts on this subject based on the ideXlab platform.
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convergence and accuracy of displacement based finite element formulations over arbitrary Polygons laplace interpolants strain smoothing and scaled boundary Polygon formulation
Finite Elements in Analysis and Design, 2014Co-Authors: Sundararajan Natarajan, Irene Chiong, Chongmin SongAbstract:Abstract Three different displacement based finite element formulations over arbitrary Polygons are studied in this paper. The formulations considered are the conventional Polygonal finite element method (FEM) with Laplace interpolants, the cell-based smoothed Polygonal FEM with simple averaging technique and the scaled boundary Polygon formulation. For the purpose of numerical integration, we employ the sub-triangulation for Polygonal FEM and classical Gaussian quadrature for the smoothed FEM and the scaled boundary Polygon formulation. The accuracy and the convergence properties of these formulations are studied with a few benchmark problems in the context of linear elasticity and the linear elastic fracture mechanics. The extension of scaled boundary Polygon to higher order Polygons is also discussed.
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displacement based finite element formulations over Polygons a comparison between laplace interpolants strain smoothing and scaled boundary Polygon formulation
arXiv: Numerical Analysis, 2013Co-Authors: Sundararajan Natarajan, Ean Tat Ooi, Irene Chiong, Chongmin SongAbstract:Three different displacement based finite element formulations over arbitrary Polygons are studied in this paper. The formulations considered are: the conventional Polygonal finite element method (FEM) with Laplace interpolants, the cell-based smoothed Polygonal FEM with simple averaging technique and the scaled boundary Polygon formulation. For the purpose of numerical integration, we employ the sub-traingulation for the Polygonal FEM and classical Gaussian quadrature for the smoothed FEM and for the scaled boundary Polygon formulation. The accuracy and the convergence properties of these formulations are studied with a few benchmark problems in the context of linear elasticity and the linear elastic fracture mechanics. The extension of scaled boundary Polygon to higher order Polygons is also discussed.
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Polygon scaled boundary finite elements for crack propagation modelling
International Journal for Numerical Methods in Engineering, 2012Co-Authors: Ean Tat Ooi, Chongmin Song, F Tinloi, Zhenjun YangAbstract:SUMMARY An automatic crack propagation modelling technique using Polygon elements is presented. A simple algorithm to generate a Polygon mesh from a Delaunay triangulated mesh is implemented. The Polygon element formulation is constructed from the scaled boundary finite element method (SBFEM), treating each Polygon as a SBFEM subdomain and is very efficient in modelling singular stress fields in the vicinity of cracks. Stress intensity factors are computed directly from their definitions without any nodal enrichment functions. An automatic remeshing algorithm capable of handling any n-sided Polygon is developed to accommodate crack propagation. The algorithm is simple yet flexible because remeshing involves minimal changes to the global mesh and is limited to only Polygons on the crack paths. The efficiency of the Polygon SBFEM in computing accurate stress intensity factors is first demonstrated for a problem with a stationary crack. Four crack propagation benchmarks are then modelled to validate the developed technique and demonstrate its salient features. The predicted crack paths show good agreement with experimental observations and numerical simulations reported in the literature. Copyright © 2012 John Wiley & Sons, Ltd.
D R Marchant - One of the best experts on this subject based on the ideXlab platform.
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thermal contraction crack Polygons on mars classification distribution and climate implications from hirise observations
Journal of Geophysical Research, 2009Co-Authors: Joseph S Levy, J W Head, D R MarchantAbstract:morphology is shown to be consistent with thermal contraction cracking of an ice-rich mantling unit, consistent with observations of sediment wedge thermal contraction crack Polygons forming in ice-cemented sediment at the Phoenix landing site. Polygon groups are distributed symmetrically in both northern and southern hemispheres, suggesting strong climate controls on Polygon morphology. Northern hemisphere Polygonally patterned surfaces are found to decrease in age from low to high latitude, spanning surface ages from 1 to <0.1 Ma, suggesting more recent deposition of ice-rich material at high latitudes than at low latitudes. Six of the seven classes of Polygons are interpreted to be capable of forming because of the combined effects of thermal contraction cracking and differential sublimation, suggesting that sublimation and sand wedge Polygons dominate Martian high latitudes. Gully Polygon systems present at midlatitudes suggest that small amounts of liquid water may have been involved in thermal contraction crack Polygon processes, producing composite wedge Polygons. No evidence is found for the presence of pervasive small-scale ice wedge Polygons.
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formation of patterned ground and sublimation till over miocene glacier ice in beacon valley southern victoria land antarctica
Geological Society of America Bulletin, 2002Co-Authors: D R Marchant, Adam R Lewis, William M Phillips, E J Moore, Roland Souchez, George H Denton, David E Sugden, Noel Potter, Gary P LandisAbstract:A thin glacial diamicton, informally termed Granite drift, occupies the floor of central Beacon Valley in southern Victoria Land, Antarctica. This drift is 40 Ar/ 39 Ar analyses of presumed in situ ash-fall deposits that occur within Granite drift. At odds with the great age of this ice are high-centered Polygons that cut Granite drift. If Polygon development has reworked and retransported ash-fall deposits, then they are untenable as chronostratigraphic markers and cannot be used to place a minimum age on the underlying glacier ice. Our results show that the surface of Granite drift is stable at Polygon centers and that enclosed ash-fall deposits can be used to define the age of underlying glacier ice. In our model for patterned-ground development, active regions lie only above Polygon troughs, where enhanced sublimation of underlying ice outlines high-centered Polygons. The rate of sublimation is influenced by the development of porous gravel-and-cobble lag deposits that form above thermal-contraction cracks in the underlying ice. A negative feedback associated with the development of secondary-ice lenses at the base of Polygon troughs prevents runaway ice loss. Secondary-ice lenses contrast markedly with glacial ice by lying on a δD versus δ 18 O slope of 5 rather than a precipitation slope of 8 and by possessing a strongly negative deuterium excess. The latter indicates that secondary-ice lenses likely formed by melting, downward percolation, and subsequent refreezing of snow trapped preferentially in deep Polygon troughs. The internal stratigraphy of Granite drift is related to the formation of surface Polygons and surrounding troughs. The drift is composed of two facies: A nonweathered, matrix-supported diamicton that contains >25% striated clasts in the >16 mm fraction and a weathered, clast-supported diamicton with varnished and wind-faceted gravels and cobbles. The weathered facies is a coarse-grained lag of Granite drift that occurs at the base of Polygon troughs and in lenses within the nonweathered facies. The concentration of cosmogenic 3 He in dolerite cobbles from two profiles through the nonweathered drift facies exhibits steadily decreasing values and shows the drift to have formed by sublimation of underlying ice. These profile patterns and the 3 He surface-exposure ages of 1.18 ± 0.08 Ma and 0.18 ± 0.01 Ma atop these profiles indicate that churning of clasts by cryoturbation has not occurred at these sites in at least the past 10 5 and 10 6 yr. Although Granite drift is stable at Polygon centers, low-frequency slump events occur at the margin of active Polygons. Slumping, together with weathering of surface clasts, creates the large range of cosmogenic-nuclide surface-exposure ages observed for Granite drift. Maximum rates of sublimation near active thermal-contraction cracks, calculated by using the two 3 He depth profiles, range from 5 m/m.y. to 90 m/m.y. Sublimation rates are likely highest immediately following major slump events and decrease thereafter to values well below our maximum estimates. Nevertheless, these rates are orders of magnitude lower than those computed on theoretical grounds. During eruptions of the nearby McMurdo Group volcanic centers, ash-fall debris collects at the surface of Granite drift, either in open thermal-contraction cracks or in deep troughs that lie above contraction cracks; these deposits subsequently lower passively as the underlying glacier ice sublimes. The fact that some regions of Granite drift have escaped modification by patterned ground for at least 8.1 Ma indicates long-term geomorphic stability of individual Polygons. Once established, Polygon toughs likely persist for as long as 10 5 –10 6 yr. Our model of patterned-ground formation, which applies to the hyperarid, cold-desert, polar climate of Antarctica, may also apply to similar-sized Polygons on Mars that occur over buried ice in Utopia Planitia.
Frans Oort - One of the best experts on this subject based on the ideXlab platform.
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newton Polygons and formal groups conjectures by manin and grothendieck
arXiv: Algebraic Geometry, 2000Co-Authors: Frans OortAbstract:We consider p-divisible groups (also called Barsotti-Tate groups) in characteristic p, their deformations, and we draw some conclusions. For such a group we can define its Newton Polygon (abbreviated NP). This is invariant under isogeny. For an abelian variety (in characteristic p) the Newton Polygon of its p-divisible group is ``symmetric''. In 1963 Manin conjectured that conversely any symmetric Newton Polygon is ``algebroid''; i.e., it is the Newton Polygon of an abelian variety. This conjecture was shown to be true and was proved with the help of the ``Honda-Serre-Tate theory''. We give another proof. Grothendieck showed that Newton Polygons ``go up'' under specialization: no point of the Newton Polygon of a closed fiber in a family is below the Newton Polygon of the generic fiber. In 1970 Grothendieck conjectured the converse: any pair of comparable Newton Polygons appear for the generic and special fiber of a family. This was extended by Koblitz in 1975 to a conjecture about a sequence of comparable Newton Polygons. We prove these conjectures.
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newton Polygons and formal groups conjectures by manin and grothendieck
Annals of Mathematics, 2000Co-Authors: Frans OortAbstract:We consider p-divisible groups (also called Barsotti-Tate groups) in characteristic p, their deformations, and we draw some conclusions. For such a group we can define its Newton Polygon (abbreviated NP). This is invariant under isogeny. For an abelian variety (in characteristic p) the Newton Polygon of its p-divisible group is "symmetric". In 1963 Manin conjectured that conversely any symmetric Newton Polygon is "algebroid"; i.e., it is the Newton Polygon of an abelian variety. This conjecture was shown to be true and was proved with the help of the "HondaSerre-Tate theory". We give another proof in Section 5. Grothendieck showed that Newton Polygons "go up" under specialization: no point of the Newton Polygon of a closed fiber in a family is below the Newton Polygon of the generic fiber. In 1970 Grothendieck conjectured the converse: any pair of comparable Newton Polygons appear for the generic and special fiber of a family. This was extended by Koblitz in 1975 to a conjecture about a sequence of comparable Newton Polygons. In Section 6 we show these conjectures to be true. These results are obtained by deforming the most special abelian varieties or p-divisible groups we can think of. In describing deformations we use the theory of displays; this was proposed by Mumford, and has been developed in [17], [18], and recently elaborated in [32] and [33]; also see [11], [31]. Having described a deformation we like to read off the Newton Polygon of the generic fiber. In most cases it is difficult to determine the Newton Polygon from the matrix defined by F on a basis for the (deformed) Dieudonne module. In general I have no procedure to do this (e.g. in case we deform away from a formal group where the Dieudonne module is not generated by one element). However in the special case we consider here, a(Go) = 1, a noncommutative version of the theorem of Cayley-Hamilton ("every matrix satisfies its own
Joseph S Levy - One of the best experts on this subject based on the ideXlab platform.
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thermal contraction crack Polygons on mars classification distribution and climate implications from hirise observations
Journal of Geophysical Research, 2009Co-Authors: Joseph S Levy, J W Head, D R MarchantAbstract:morphology is shown to be consistent with thermal contraction cracking of an ice-rich mantling unit, consistent with observations of sediment wedge thermal contraction crack Polygons forming in ice-cemented sediment at the Phoenix landing site. Polygon groups are distributed symmetrically in both northern and southern hemispheres, suggesting strong climate controls on Polygon morphology. Northern hemisphere Polygonally patterned surfaces are found to decrease in age from low to high latitude, spanning surface ages from 1 to <0.1 Ma, suggesting more recent deposition of ice-rich material at high latitudes than at low latitudes. Six of the seven classes of Polygons are interpreted to be capable of forming because of the combined effects of thermal contraction cracking and differential sublimation, suggesting that sublimation and sand wedge Polygons dominate Martian high latitudes. Gully Polygon systems present at midlatitudes suggest that small amounts of liquid water may have been involved in thermal contraction crack Polygon processes, producing composite wedge Polygons. No evidence is found for the presence of pervasive small-scale ice wedge Polygons.
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The role of thermal contraction crack Polygons in cold-desert fluvial systems
Antarctic Science, 2008Co-Authors: Joseph S Levy, James W. Head, David R. MarchantAbstract:Thermal contraction crack Polygons modify the generation, transport, and storage of water in Wright Valley gullies. Water generation is contributed to by trapping of windblown snow in Polygon troughs. Water transport is modified by changes to the ice-cement table and active layer topography caused by Polygon trough formation. Water storage is modified by sediment grain-size distribution within Polygons in gully distal hyporheic zones. Patterned ground morphological variation can serve as an indicator of fluvial modification, ranging from nearly unmodified composite-wedge Polygons to Polygons forming in association with gully channels. Thermal contraction crack Polygons may also constrain the gully formation sequence, suggesting the continuous presence of permafrost beneath the Wright Valley gullies during the entire period of gully emplacement. This analysis provides a framework for understanding the relationships between Polygons and gullies observed on Mars. If comparable stratigraphic relationships can be documented, the presence of an analogous impermeable ice-cemented layer beneath the gullies can be inferred, Suggesting an atmospheric source for Martian gully-carving fluids.
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Distribution and origin of patterned ground on Mullins Valley debris-covered glacier, Antarctica: The roles of ice flow and sublimation
Antarctic Science, 2006Co-Authors: Joseph S Levy, David R. Marchant, James W. HeadAbstract:We map Polygonally patterned ground formed in sublimation tills that overlie debris-covered glaciers in Mullins Valley and central Beacon Valley, in southern Victoria Land, Antarctica, and distinguish five morphological zones. Where the Mullins Valley debris-covered glacier debouches into Beacon Valley, Polygonal patterning transitions from radial (orthogonal) intersections to non-oriented (hexagonal) intersections, providing a time-series of Polygon evolution within a single microclimate. We offer the following model for Polygon formation and evolution in the Mullins Valley system. Near-vertical cracks that ultimately outline Polygons are produced by thermal contraction in the glacier ice. Some of these cracks may initially be oriented radial to maximum surface velocities by pre-existing structural stresses and material weaknesses in the glacier ice. In areas of relatively rapid flow, Polygons are oriented down-valley forming an overall fan pattern radial to maximum ice velocity. As glacier flow moves the cracks down-valley, minor variations in flow rate deform Polygons, giving rise to deformed radial Polygons. Non-oriented (largely hexagonal) Polygons commonly form in regions of stagnant and/or near-stagnant ice. We propose that orientation and morphology of contraction-crack Polygons in sublimation tills can thus be used as an indicator of rates of subsurface ice flow.
Sundararajan Natarajan - One of the best experts on this subject based on the ideXlab platform.
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convergence and accuracy of displacement based finite element formulations over arbitrary Polygons laplace interpolants strain smoothing and scaled boundary Polygon formulation
Finite Elements in Analysis and Design, 2014Co-Authors: Sundararajan Natarajan, Irene Chiong, Chongmin SongAbstract:Abstract Three different displacement based finite element formulations over arbitrary Polygons are studied in this paper. The formulations considered are the conventional Polygonal finite element method (FEM) with Laplace interpolants, the cell-based smoothed Polygonal FEM with simple averaging technique and the scaled boundary Polygon formulation. For the purpose of numerical integration, we employ the sub-triangulation for Polygonal FEM and classical Gaussian quadrature for the smoothed FEM and the scaled boundary Polygon formulation. The accuracy and the convergence properties of these formulations are studied with a few benchmark problems in the context of linear elasticity and the linear elastic fracture mechanics. The extension of scaled boundary Polygon to higher order Polygons is also discussed.
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displacement based finite element formulations over Polygons a comparison between laplace interpolants strain smoothing and scaled boundary Polygon formulation
arXiv: Numerical Analysis, 2013Co-Authors: Sundararajan Natarajan, Ean Tat Ooi, Irene Chiong, Chongmin SongAbstract:Three different displacement based finite element formulations over arbitrary Polygons are studied in this paper. The formulations considered are: the conventional Polygonal finite element method (FEM) with Laplace interpolants, the cell-based smoothed Polygonal FEM with simple averaging technique and the scaled boundary Polygon formulation. For the purpose of numerical integration, we employ the sub-traingulation for the Polygonal FEM and classical Gaussian quadrature for the smoothed FEM and for the scaled boundary Polygon formulation. The accuracy and the convergence properties of these formulations are studied with a few benchmark problems in the context of linear elasticity and the linear elastic fracture mechanics. The extension of scaled boundary Polygon to higher order Polygons is also discussed.
