Relevant bibliographies by topics / Finite geometry; projective geometry

Academic literature on the topic 'Finite geometry; projective geometry'

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Published: 10 December 2022
Last updated: 28 January 2023

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Journal articles on the topic "Finite geometry; projective geometry"

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Newelski, Ludomir. "Geometry of *-Finite Types." Journal of Symbolic Logic 64, no. 4 (December 1999): 1375–95. http://dx.doi.org/10.2307/2586784.

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AbstractAssume T is a superstable theory with < 2ℵ0 countable models. We prove that any *- algebraic type of -rank > 0 is m-nonorthogonal to a *-algebraic type of -rank 1. We study the geometry induced by m-dependence on a *-algebraic type p* of -rank 1. We prove that after some localization this geometry becomes projective over a division ring . Associated with p* is a meager type p. We prove that p is determined by p* up to nonorthogonality and that underlies also the geometry induced by forking dependence on any stationarization of p. Also we study some *-algebraic *-groups of -rank 1 and prove that any *-algebraic *-group of -rank 1 is abelian-by-finite.
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Connes, Alain, and Caterina Consani. "Projective geometry in characteristic one and the epicyclic category." Nagoya Mathematical Journal 217 (March 2015): 95–132. http://dx.doi.org/10.1215/00277630-2887960.

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AbstractWe show that the cyclic and epicyclic categories which play a key role in the encoding of cyclic homology and the lambda operations, are obtained from projective geometry in characteristic one over the infinite semifield of max-plus integers ℤmax. Finite-dimensional vector spaces are replaced by modules defined by restriction of scalars from the one-dimensional free module, using the Frobenius endomorphisms of ℤmax. The associated projective spaces are finite and provide a mathematically consistent interpretation of Tits's original idea of a geometry over the absolute point. The self-duality of the cyclic category and the cyclic descent number of permutations both acquire a geometric meaning.
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Dodson, C. T. J. "Fréchet geometry via projective limits." International Journal of Geometric Methods in Modern Physics 11, no. 07 (August 2014): 1460017. http://dx.doi.org/10.1142/s0219887814600172.

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Fréchet spaces of sections arise naturally as configurations of a physical field. Some recent work in Fréchet geometry is briefly reviewed and some suggestions for future work are offered. An earlier result on the structure of second tangent bundles in the finite-dimensional case was extended to infinite-dimensional Banach manifolds and Fréchet manifolds that could be represented as projective limits of Banach manifolds. This led to further results concerning the characterization of second tangent bundles and differential equations in the more general Fréchet structure needed for applications.
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Connes, Alain, and Caterina Consani. "Projective geometry in characteristic one and the epicyclic category." Nagoya Mathematical Journal 217 (March 2015): 95–132. http://dx.doi.org/10.1017/s0027763000026969.

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AbstractWe show that the cyclic and epicyclic categories which play a key role in the encoding of cyclic homology and the lambda operations, are obtained from projective geometry in characteristic one over the infinite semifield ofmax-plus integersℤmax. Finite-dimensional vector spaces are replaced by modules defined by restriction of scalars from the one-dimensional free module, using the Frobenius endomorphisms of ℤmax. The associated projective spaces arefiniteand provide a mathematically consistent interpretation of Tits's original idea of a geometry over the absolute point. The self-duality of the cyclic category and the cyclic descent number of permutations both acquire a geometric meaning.
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Kohn, Kathlén, and Kristian Ranestad. "Projective Geometry of Wachspress Coordinates." Foundations of Computational Mathematics 20, no. 5 (November 11, 2019): 1135–73. http://dx.doi.org/10.1007/s10208-019-09441-z.

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Abstract We show that there is a unique hypersurface of minimal degree passing through the non-faces of a polytope which is defined by a simple hyperplane arrangement. This generalizes the construction of the adjoint curve of a polygon by Wachspress (A rational finite element basis, Academic Press, New York, 1975). The defining polynomial of our adjoint hypersurface is the adjoint polynomial introduced by Warren (Adv Comput Math 6:97–108, 1996). This is a key ingredient for the definition of Wachspress coordinates, which are barycentric coordinates on an arbitrary convex polytope. The adjoint polynomial also appears both in algebraic statistics, when studying the moments of uniform probability distributions on polytopes, and in intersection theory, when computing Segre classes of monomial schemes. We describe the Wachspress map, the rational map defined by the Wachspress coordinates, and the Wachspress variety, the image of this map. The inverse of the Wachspress map is the projection from the linear span of the image of the adjoint hypersurface. To relate adjoints of polytopes to classical adjoints of divisors in algebraic geometry, we study irreducible hypersurfaces that have the same degree and multiplicity along the non-faces of a polytope as its defining hyperplane arrangement. We list all finitely many combinatorial types of polytopes in dimensions two and three for which such irreducible hypersurfaces exist. In the case of polygons, the general such curves are elliptic. In the three-dimensional case, the general such surfaces are either K3 or elliptic.
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Aggarwal, M. L., Lih-Yuan Deng, and Mukta Datta Mazumder. "Optimal Fractional Factorial Plans Using Finite Projective Geometry." Communications in Statistics - Theory and Methods 37, no. 8 (February 22, 2008): 1258–65. http://dx.doi.org/10.1080/03610920701713351.

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Kalmbach H.E., Gudrun. "Projective Gravity." International Journal of Contemporary Research and Review 9, no. 03 (March 13, 2018): 20181–83. http://dx.doi.org/10.15520/ijcrr/2018/9/03/466.

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In [1] and [3] it was pointed out that octonians can replace an infinite dimensional Hilbert space and psi-waves descriptions concerning the states of deuteron which are finite in number. It is then clear that gravity needs projective and projection geometry to be described in a unified way with the three other basic forces of physics.
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Ben-Yaacov, Itay, Ivan Tomašić, and Frank O. Wagner. "The Group Configuration in Simple Theories and its Applications." Bulletin of Symbolic Logic 8, no. 2 (June 2002): 283–98. http://dx.doi.org/10.2178/bsl/1182353874.

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AbstractIn recent work, the authors have established the group configuration theorem for simple theories, as well as some of its main applications from geometric stability theory, such as the binding group theorem, or, in the ω-categorical case, the characterization of the forking geometry of a finitely based non-trivial locally modular regular type as projective geometry over a finite field and the equivalence of pseudolinearity and local modularity.The proof necessitated an extension of the model-theoretic framework to include almost hyperimaginaries, and the study of polygroups.
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Games, Richard A. "The Geometry of m-Sequences: Three-Valued Crosscorrelations and Quadrics in Finite Projective Geometry." SIAM Journal on Algebraic Discrete Methods 7, no. 1 (January 1986): 43–52. http://dx.doi.org/10.1137/0607005.

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Beil, Charlie. "Nonnoetherian geometry." Journal of Algebra and Its Applications 15, no. 09 (August 22, 2016): 1650176. http://dx.doi.org/10.1142/s0219498816501760.

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We introduce a theory of geometry for nonnoetherian commutative algebras with finite Krull dimension. In particular, we establish new notions of normalization and height: depiction (a special noetherian overring) and geometric codimension. The resulting geometries are algebraic varieties with positive-dimensional points, and are thus inherently nonlocal. These notions also give rise to new equivalent characterizations of noetherianity that are primarily geometric. We then consider an application to quiver algebras whose simple modules of maximal dimension are one dimensional at each vertex. We show that the vertex corner rings of [Formula: see text] are all isomorphic if and only if [Formula: see text] is noetherian, if and only if the center [Formula: see text] of [Formula: see text] is noetherian, if and only if [Formula: see text] is a finitely generated [Formula: see text]-module. Furthermore, we show that [Formula: see text] is depicted by a commutative algebra generated by the cycles in its quiver. We conclude with an example of a quiver algebra where projective dimension and geometric codimension, rather than height, coincide.
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Dissertations / Theses on the topic "Finite geometry; projective geometry"

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Fleming, Patrick Scott. "Finite projective planes and related topics." Laramie, Wyo. : University of Wyoming, 2006. http://proquest.umi.com/pqdweb?did=1225126281&sid=1&Fmt=2&clientId=18949&RQT=309&VName=PQD.

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Cook, Gary Russell. "Arcs in a finite projective plane." Thesis, University of Sussex, 2011. http://sro.sussex.ac.uk/id/eprint/7510/.

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The projective plane of order 11 is the dominant focus of this work. The motivation for working in the projective plane of order 11 is twofold. First, it is the smallest projective plane of prime power order such that the size of the largest (n, r)-arc is not known for all r ∈ {2,...,q + 1}. It is also the smallest projective plane of prime order such that the (n; 3)-arcs are not classified. Second, the number of (n, 3)-arcs is significantly higher in the projective plane of order 11 than it is in the projective plane of order 7, giving a large number of (n, 3)-arcs for study. The main application of (n, r)-arcs is to the study of linear codes. As a forerunner to the work in the projective plane of order eleven two algorithms are used to raise the lower bound on the size of the smallest complete n-arc in the projective plane of order thirty-one from 12 to 13. This work presents the classification up to projective equivalence of the complete (n, 3)- arcs in PG(2, 11) and the backtracking algorithm that is used in its construction. This algorithm is based on the algorithm used in [3]; it is adapted to work on (n, 3)-arcs as opposed to n-arcs. This algorithm yields one representative from every projectively inequivalent class of (n, 3)-arc. The equivalence classes of complete (n, 3)-arcs are then further classified according to their stabilizer group. The classification of all (n, 3)-arcs up to projective equivalence in PG(2, 11) is the foundation of an exhaustive search that takes one element from every equivalence class and determines if it can be extended to an (n′, 4)-arc. This search confirmed that in PG(2, 11) no (n, 3)-arc can be extended to a (33, 4)-arc and that subsequently m4(2, 11) = 32. This same algorithm is used to determine four projectively inequivalent complete (32, 4)-arcs, extended from complete (n, 3)-arcs. Various notions under the general title of symmetry are defined both for an (n, r)-arc and for sets of points and lines. The first of these makes the classification of incomplete (n; 3)- arcs in PG(2, 11) practical. The second establishes a symmetry based around the incidence structure of each of the four projectively inequivalent complete (32, 4)-arcs in PG(2, 11); this allows the discovery of their duals. Both notions of symmetry are used to analyze the incidence structure of n-arcs in PG(2, q), for q = 11, 13, 17, 19. The penultimate chapter demonstrates that it is possible to construct an (n, r)-arc with a stabilizer group that contains a subgroup of order p, where p is a prime, without reference to an (m < n, r)-arc, with stabilizer group isomorphic to ℤ1. This method is used to find q-arcs and (q + 1)-arcs in PG(2, q), for q = 23 and 29, supporting Conjecture 6.7. The work ends with an investigation into the effect of projectivities that are induced by a matrix of prime order p on the projective planes. This investigation looks at the points and subsets of points of order p that are closed under the right action of such matrices and their structure in the projective plane. An application of these structures is a restriction on the size of an (n, r)-arc in PG(2, q) that can be stabilized by a matrix of prime order p.
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Hamed, Zainab Shehab. "Arcs of degree four in a finite projective plane." Thesis, University of Sussex, 2018. http://sro.sussex.ac.uk/id/eprint/77816/.

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The projective plane, PG(2;q), over a Galois field Fq is an incidence structure of points and lines. A (k;n)-arc K in PG(2;q) is a set of k points such that no n+1 of them are collinear but some n are collinear. A (k;n)-arc K in PG(2;q) is called complete if it is not contained in any (k+1;n)-arc. The existence of arcs for particular values of k and n pose interesting problems in finite geometry. It connects with coding theory and graph theory, with important applications in computer science. The main problem, known as the packing problem, is to determine the largest size mn(2;q) of K in PG(2;q). This problem has received much attention. Here, the work establishes complete arcs with a large number of points. In contrast, the problem to determine the smallest size tn(2;q) of a complete (k;n)-arc is mostly based on the lower bound arising from theoretical investigations. This thesis has several goals. The first goal is to classify certain (k;4)-arcs for k = 6,...,38 in PG(2;13). This classification is established through an approach in Chapter 2. This approach uses a new geometrical method; it is a combination of projective inequivalence of (k;4)-arcs up to k = 6 and certain sdinequivalent (k;4)-arcs that have sd-inequivalent classes of secant distributions for k = 7,...,38. The part related to projectively inequivalent (k;4)-arcs up to k=6 starts by fixing the frame points f1;2;3;88g and then classify the projectively inequivalent (5;4)-arcs. Among these (5;4)-arcs and (6;4)-arcs, the lexicographically least set are found. Now, the part regarding sd-inequivalent (k;4)-arcs in this method starts by choosing five sd-inequivalent (7;4)-arcs. This classification method may not produce all sd-inequivalent classes of (k;4)-arcs. However, it was necessary to employ this method due to the increasing number of (k;4)-arcs in PG(2;13) and the extreme computational difficulty of the problem. It reduces the constructed number of (k;4)-arcs in each process for large k. Consequently, it reduces the executed time for the computation which could last for years. Also, this method decreases the memory usage needed for the classification. The largest size of (k;4)-arc established through this method is k = 38. The classification of certain (k;4)-arcs up to projective equivalence, for k = 34,35,36,37,38, is also established. This classification starts from the 77 incomplete (34;4)-arcs that are constructed from the sd-inequivalent (33;4)-arcs given in Section 2.29, Table 2.35. Here, the largest size of (k;4)-arc is still k = 38. In addition, the previous process is re-iterated with a different choice of five sd-inequivalent (7;4)-arcs. The purpose of this choice is to find a new size of complete (k;4)-arc for k > 38. This particular computation of (k;4)-arcs found no complete (k;4)-arc for k > 38. In contrast, a new size of complete (k;4)-arc in PG(2;13) is discovered. This size is k = 36 which is the largest complete (k;4)-arc in this computation. This result raises the second largest size of complete (k;4)-arc found in the first classification from k = 35 to k = 36. The second goal is to discuss the incidence structure of the orbits of the groups of the projectively inequivalent (6;4)-arcs and also the incidence structures of the orbits of the groups other than the identity group of the sd-inequivalent (k;4)-arcs. In Chapter 3, these incidence structures are given for k = 6,7,8,9,10,11,12,13,14,38. Also, the pictures of the geometric configurations of the lines and the points of the orbits are described. The third goal is to find the sizes of certain sd-inequivalent complete (k;4)-arcs in PG(2;13). These sizes of complete (k;4)-arcs are given in Chapter 4 where the smallest size of complete (k;4)-arc is at most k = 24 and the largest size is at least k = 38. The fourth goal is to give an example of an associated non-singular quartic curve C for each complete (k;4)-arc and to discuss the algebraic properties of each curve in terms of the number I of inflexion points, the number jC \K j of rational points on the corresponding arc, and the number N1 of rational points of C . These curves are given in Chapter 5. Also, the algebraic properties of complete arcs of the most interesting sizes investigated in this thesis are studied. In addition, there are two examples of quartic curves C (g0 1) and C (g0 2) attaining the Hasse-Weil- Serre upper bound for the number N1 of rational points on a curve over the finite field of order thirteen. This number is 32. The fifth goal is to classify the (k;4)-arcs in PG(2;13) up to projective inequivalence for k < 10. This classification is established in Chapter 6. It starts by fixing a triad, U1, on the projective line, PG(1;13). Here, the number of projectively inequivalent (k;4)-arcs are tested by using the tool given in Chapter 2. Then, among the number of the projectively inequivalent (10;4)-arcs found, the classification of sd-inequivalent (k;4)-arcs for k = 10 is made. The number of these sd-inequivalent arcs is 36. Then, the 36 sd-inequivalent arcs are extended. The aim here is to investigate if there is a new size of sd-inequivalent (k;4)-arc for k > 38 that can be obtained from these arcs. The largest size of sd-inequivalent (k;4)-arc in this process is the same as the largest size of the sd-inequivalent (k;4)-arc established in Chapter 2, that is, k = 38. In addition, the classification of (k;n)-arcs in PG(2;13) is extended from n = 4 to n = 6. This extension is given in Chapter 7 where some results of the classification of certain (k;6)-arcs for k = 9; : : : ;25 are obtained using the same method as in Chapter 2 for k = 7,...,38. This process starts by fixing a certain (8;6)-arc containing six collinear points in PG(2;13).
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Pichanick, E. V. D. "Bounds for complete arcs in finite projective planes." Thesis, University of Sussex, 2016. http://sro.sussex.ac.uk/id/eprint/63459/.

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This thesis uses algebraic and combinatorial methods to study subsets of the Desarguesian plane IIq = PG(2, q). Emphasis, in particular, is given to complete (k, n)-arcs and plane projective curves. Known Diophantine equations for subsets of PG(2, q), no more than n of which are collinear, have been applied to k-arcs of arbitrary degree. This yields a new lower bound for complete (k, n)-arcs in PG(2, q) and is a generalization of a classical result of Barlotti. The bound is one of few known results for complete arcs of arbitrary degree and establishes new restrictions upon the parameters of associated projective codes. New results governing the relationship between (k, 3)-arcs and blocking sets are also provided. Here, a sufficient condition ensuring that a blocking set is induced by a complete (k, 3)-arc in the dual plane q is established and shown to complement existing knowledge of relationships between k-arcs and blocking sets. Combinatorial techniques analyzing (k, 3)-arcs in suitable planes are then introduced. Utilizing the numeric properties of non-singular cubic curves, plane (k, 3)-arcs satisfying prescribed incidence conditions are shown not to attain existing upper bounds. The relative sizes of (k, 3)-arcs and non-singular cubic curves are also considered. It is conjectured that m3(2, q), the size of the largest complete (k, 3)-arc in PG(2, q), exceeds the number of rational points on an elliptic curve. Here, a sufficient condition for its positive resolution is given using combinatorial analysis. Exploiting its structure as a (k, 3)-arc, the elliptic curve is then considered as a method of constructing cubic arcs and results governing completeness are established. Finally, classical theorems relating the order of the plane q to the existence of an elliptic curve with a specified number of rational points are used to extend theoretical results providing upper bounds to t3(2, q), the size of the smallest possible complete (k, 3)-arc in PG(2, q).
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Oxenham, Martin Glen. "On n-covers of PG (3,q) and related structures /." Title page, contents and introduction only, 1991. http://web4.library.adelaide.edu.au/theses/09PH/09pho98.pdf.

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Giuzzi, Luca. "Hermitian varieties over finite fields." Thesis, University of Sussex, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.326913.

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White, Clinton T. Wilson R. M. "Two cyclic arrangement problems in finite projective geometry : parallelisms and two-intersection sets /." Diss., Pasadena, Calif. : California Institute of Technology, 2002. http://resolver.caltech.edu/CaltechETD:etd-06052006-143933.

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Culbert, Craig W. "Spreads of three-dimensional and five-dimensional finite projective geometries." Access to citation, abstract and download form provided by ProQuest Information and Learning Company; downloadable PDF file, 101 p, 2009. http://proquest.umi.com/pqdweb?did=1891555371&sid=3&Fmt=2&clientId=8331&RQT=309&VName=PQD.

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Vereecke, Sam K. J. "Some properties of arcs, caps and quadrics in projective spaces in finite order." Thesis, University of Sussex, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.263915.

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Grout, Jason Nicholas. "The Minimum Rank Problem Over Finite Fields." Diss., CLICK HERE for online access, 2007. http://contentdm.lib.byu.edu/ETD/image/etd1995.pdf.

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Books on the topic "Finite geometry; projective geometry"

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Projective geometries over finite fields. 2nd ed. Oxford: Clarendon Press, 1998.

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A, Thas J., ed. General Galois geometries. Oxford: Clarendon Press, 1991.

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Barlotti, A. Finite Geometric Structures and their Applications. Berlin, Heidelberg: Springer-Verlag Berlin Heidelberg, 2011.

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Katcher, Pollatsek Harriet Suzanne, ed. Difference sets: Connecting algebra, combinatorics and geometry. Providence, Rhode Island: American Mathematical Society, 2013.

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Coxeter, H. S. M. Projective geometry. 2nd ed. New York: Springer-Verlag, 1987.

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Projective geometry. New York: Springer-Verlag, 1988.

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Samuel, Pierre. Projective Geometry. New York, NY: Springer New York, 1988. http://dx.doi.org/10.1007/978-1-4612-3896-6.

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Fortuna, Elisabetta, Roberto Frigerio, and Rita Pardini. Projective Geometry. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-42824-6.

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Bădescu, Lucian. Projective Geometry and Formal Geometry. Basel: Birkhäuser Basel, 2004. http://dx.doi.org/10.1007/978-3-0348-7936-1.

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Projective geometry and formal geometry. Basel: Birkhäuser, 2004.

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Book chapters on the topic "Finite geometry; projective geometry"

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Coxeter, H. S. M. "A Finite Projective Plane." In Projective Geometry, 91–101. New York, NY: Springer New York, 1987. http://dx.doi.org/10.1007/978-1-4612-6385-2_10.

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Lord, Eric. "Finite Geometries." In Symmetry and Pattern in Projective Geometry, 145–71. London: Springer London, 2013. http://dx.doi.org/10.1007/978-1-4471-4631-5_7.

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Braun, David, Nicolas Magaud, and Pascal Schreck. "Formalizing Some “Small” Finite Models of Projective Geometry in Coq." In Artificial Intelligence and Symbolic Computation, 54–69. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-99957-9_4.

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Poonen, Bjorn. "The S-Integral Points on the Projective Line Minus Three Points via Finite Covers and Skolem’s Method." In Arithmetic Geometry, Number Theory, and Computation, 583–87. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-80914-0_21.

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Audin, Michèle. "Projective Geometry." In Geometry, 143–82. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-642-56127-6_6.

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Holme, Audun. "Projective Space." In Geometry, 221–32. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/978-3-662-04720-0_11.

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Holme, Audun. "Projective Space." In Geometry, 313–23. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-14441-7_12.

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Holme, Audun. "Axiomatic Projective Geometry." In Geometry, 177–94. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/978-3-662-04720-0_8.

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Holme, Audun. "Axiomatic Projective Geometry." In Geometry, 265–82. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-14441-7_9.

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Ostermann, Alexander, and Gerhard Wanner. "Projective Geometry." In Geometry by Its History, 319–44. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-29163-0_11.

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Conference papers on the topic "Finite geometry; projective geometry"

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Rosu, H. C. "MUBs: From Finite Projective Geometry to Quantum Phase Enciphering." In QUANTUM COMMUNICATION, MEASUREMENT AND COMPUTING. AIP, 2004. http://dx.doi.org/10.1063/1.1834443.

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deBues, Timothy T., Darrell W. Pepper, and Yitung Chen. "2-D H-Adaptive Finite Element Method for Gas Gun Design." In ASME 2003 International Mechanical Engineering Congress and Exposition. ASMEDC, 2003. http://dx.doi.org/10.1115/imece2003-41929.

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The Joint Actinide Shock Physics Experimental Research (JASPER) facility utilizes a two-stage light gas gun to conduct equation of state experiments. The gun has a launch tube bore diameter of 28 mm, and is capable of launching projectiles at a velocity of 7.5 km/s using compressed hydrogen as a propellant. A numerical study is conducted to determine the effects that launch tube exit geometry changes have on attitude of the projectile in flight. A comparison of two launch tube exit geometries is considered. The first case is standard muzzle geometry where the wall of the bore and the outer surface of the launch tube form a right angle. The second case includes a beveled transition from the wall of the bore to the outer surface of the launch tube. An h-adaptive, Petrov-Galerkin finite element method is employed to model the axisymmetric compressible flow equations. Numerical solutions indicate that pressure variations occur on the back face of the projectile from case to case.
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Sridharala, Srujanbabu, Mohamed B. Trabia, Brendan O'Toole, Vinod Chakka, and Mostafiz Chowdhury. "Optimization of Finite Element Modeling Methodology for Projectile Models." In ASME 2006 International Mechanical Engineering Congress and Exposition. ASMEDC, 2006. http://dx.doi.org/10.1115/imece2006-15685.

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Gun-fired projectiles are subjected to severe loads over extremely short duration. There is a need to better understand the effects of these loads on components within a projectile. While experimental data can be helpful in understanding projectile launch phenomena, collecting such data is usually difficult. There are also limitations on the reliability of sensors under these circumstances. Finite element modeling (FEM) can be used to model the projectile launch event. Currently, engineers usually use large number of elements to accurately model the projectile launch event, which results in an extremely long computational time. FEM results in these cases are always subject to questions regarding accuracy of the results and proof of mesh stability This paper presents an expert system that can reduce computational time needed to perform FEM of gun-fired projectiles. The proposed approach can result in reducing computational time while ensuring that accuracy of results is not affected. Recommendations of the expert system are reached through two stages. In the first stage, an equivalent projectile with simple geometry is created to reduce the complexity of the model. In the second stage, parameters controlling mesh density of the equivalent projectile are used as variables in an optimization scheme with the objective of reducing computational time. Accuracy of the acceleration results from an optimized model with respect to a model with an extremely fine mesh is used as an inequality constraint within the optimization search. A projectile model meshed with aspect ratios obtained from the optimization search produces good agreement with the finite element results of the original densely-meshed projectile model while significantly reducing computational time. It is anticipated that this approach can make it easier to conduct parametric analysis or optimization studies for projectile design.
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Norato, Julián A. "A Geometry Projection Method for the Optimal Distribution of Short Fiber Reinforcements." In ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/detc2015-47406.

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This paper presents an optimization method for optimally distributing short fibers of variable length for the reinforcement of structural components for stiffness. Unlike standard density-based and level set topology optimization methods that generally render material distributions with variable member size, the proposed method projects an explicit geometry model onto a continuous density field. The proposed method inherits the benefits of density-based topology optimization methods, namely simplified and efficient primal and sensitivity analyses on a fixed grid, fast convergence, robustness, and amenability to standard finite element methods for the analysis and to nonlinear programming algorithms for the optimization. The explicit geometry representation of the fibers provides a suitable description of the short fibers, and therefore the designs produced by the proposed method have potential for manufacturing using, for example, processing methods for the fabrication of micro-architectured materials. Examples of reinforcement distribution design for two-dimensional structures in plane stress demonstrate the method.
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Pintar, Frank A., Srirangam Kumaresan, Brian Stemper, Narayan Yoganandan, and Thomas A. Gennarelli. "Finite Element Modeling of Penetrating Traumatic Brain Injuries." In ASME 2000 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2000. http://dx.doi.org/10.1115/imece2000-2602.

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Abstract Recent advances in the treatment of penetrating gunshot wounds to the head have saved lives. These advances are largely reported using retrospective analysis of patients with recommendations for treatment. Biomechanical quantification of intracranial deformation/stress distribution associated with the type of weapon (e.g., projectile geometry) will advance clinical understanding of the mechanics of penetrating wounds. The present study was designed to delineate the biomechanical behavior of the human head under penetrating impact of two different projectile geometries using a nonlinear, three-dimensional finite element model. The human head model included the skull and brain. The qualitative comparison of the model output with each type of projectile during various time steps indicates that the deformation/stress progresses as the projectile penetrates the tissue. There is also a distinct difference in the patterns of displacement for each type of projectile. The present study is a first step in the study of the biomechanics of penetrating traumatic brain injuries.
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Stolfi, J. "Oriented projective geometry." In the third annual symposium. New York, New York, USA: ACM Press, 1987. http://dx.doi.org/10.1145/41958.41966.

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Ponyavin, Valery, Yitung Chen, Darrell W. Pepper, and Hsuan-Tsung Hsieh. "Numerical Modeling of Unsteady Gas Flow Around the Projectile in the Light Gas Gun." In ASME 2004 International Mechanical Engineering Congress and Exposition. ASMEDC, 2004. http://dx.doi.org/10.1115/imece2004-59640.

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In this study, an attempt to calculate the characteristics of gas flow around a projectile during the motion of the projectile in the Joint Actinide Shock Physics Experimental Research (JASPER) light-gas gun is undertaken. The flow is considered as axisymmetric, nonstationary, nonisothermal, compressible, and turbulent. For calculating the flow around the projectile, the finite volume method was employed. A comparison between two launch tube exit geometries was made. The first case was standard muzzle geometry, where the wall of the bore and the outer surface of the launch tube form a 90 degree angle. The second case included a 26.6 degree bevel transition from the wall of the bore to the outer surface of the launch tube. The results of the calculations are represented in figures depicting the flow at different moments of time. The figures show the fields of velocity, pressure and density, as well as the appearance of shock waves inside the geometry. Some comparisons with calculations of the same problem but using finite-element method were made. The obtained results can be further used for optimization JASPER geometry. The results also can be used for calculating the gun barrels for the strength and the oscillatory stability. In our future study we will couple structural analysis of the gun barrel material with the gas dynamic calculation of motion of the projectile in the gun barrel with the use of advanced computational methods.
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Zhang, Shanglong, and Julián A. Norato. "A Geometry Projection Method for the Optimal Design of Panel Reinforcements With Ribs Made of Plates." In ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/detc2016-59985.

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The stiffness of plate structures can be significantly improved by adding reinforcing ribs. In this paper, we are in particular concerned with stiffening of panels using ribs made of constant-thickness plates that may be, for example, welded to the panel. These ribs are common in, for example, the reinforcement of ship hulls, aircraft wings, pressure vessels and storage tanks. Existing methods either produce rib designs that cannot be fabricated with plates, or employ heuristics that produce non-optimal designs. This paper presents a method for optimally designing the topology, locations and dimensions of rectangular ribs to reinforce a panel. To this end, we smoothly project an analytic, explicit geometry representation of a set of ribs onto a continuous density field over a design envelope. This density field is discretized in an element-wise manner on a uniform grid for analysis. The initial design consists of a prescribed set of ribs, constrained to remain perpendicular to the panel to facilitate manufacturing and joining of the ribs. The advantages of our method are two-fold. On one hand, as in classical density-based topology optimization, we circumvent re-meshing by using a fixed finite element grid for the analysis, and the differentiability of the projection allows us to employ efficient and robust gradient-based optimization methods. On the other hand, the explicit geometry representation provides a direct translation into CAD, it produces reinforcement designs that conform to available plate cutting and joining processes, and it allows us to impose a constraint on the minimum separation between any two ribs to guarantee clear gaps for weld gun access. Also, bounds on the ribs dimensions can be naturally and directly accommodated. We present numerical examples of our panel reinforcement design under different types of loadings to demonstrate the applicability of the proposed method.
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Podshivalov, Lev, Anath Fischer, and Pinhas Z. Bar-Yoseph. "Performance Assessment of Hexahedral Meshing Methods for Design and Mechanical Analysis of Composite Materials." In ASME 2012 11th Biennial Conference on Engineering Systems Design and Analysis. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/esda2012-82247.

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Composite materials can be designed and modeled as material volumes with inclusions of several materials. These multiple inclusions are randomly distributed in a unit cube volume according to the material parameters (density, dimensions, orientation etc.). Then, the finite element (FE) analysis method is applied on the resulting structure to estimate the equivalent material properties. Therefore, these models should to be meshed prior to mechanical FE analysis. Automatic high quality hexahedral meshing is considered a very complex task. Hence, despite extensive research, currently there are no robust methods that can handle grain-based geometry. Meshing a composite material modeled by multiple inclusions presents a number of challenges: (a) the meshing needs to be robust to dimensions, position and orientation of the inclusions; (b) mesh continuity must be achieved on the boundaries between the volume (also known as the matrix) and the inclusions; (c) the mesh needs to approximate the original geometric model with high accuracy; and (d) high quality mesh elements are required for mechanical analysis. Structured and unstructured meshing methods can be used for handling this task. In this research two meshing methods were developed to generate high quality meshes: (a) structured meshing created by warping the grid according to the model’s geometry, and (b) unstructured meshing created by projecting the nodes onto the boundaries of the inclusions to achieve exact geometric representation. The performance of these methods was then evaluated and compared on composite materials with ellipsoidal inclusions. Among the performance criteria for these methods are mesh element quality, geometry approximation error, stress concentrations near the boundaries, and computational complexity. The results indicate that the proposed methods can be used for design and mechanical analysis of composite materials. Moreover, in homogenization applications the structured warped mesh is compatible in terms of performance and element quality to the unstructured mesh.
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Bokor, J., and Z. Szabo. "Projective geometry and feedback stabilization." In 2017 IEEE 21st International Conference on Intelligent Engineering Systems (INES). IEEE, 2017. http://dx.doi.org/10.1109/ines.2017.8118537.

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Reports on the topic "Finite geometry; projective geometry"

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Ivey, Thomas A. Geometry and Topology of Finite-gap Vortex Filaments. GIQ, 2012. http://dx.doi.org/10.7546/giq-7-2006-187-202.

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Sherrill, Manolo. Development of the finite slab geometry in the NORA code. Office of Scientific and Technical Information (OSTI), September 2020. http://dx.doi.org/10.2172/1671054.

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Kistler, B. L. A study of the process of using Pro/ENGINEER geometry models to create finite element models. Office of Scientific and Technical Information (OSTI), February 1997. http://dx.doi.org/10.2172/481613.

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Shum, D. K., J. W. Bryson, and J. G. Merkle. Potential change in flaw geometry of an initially shallow finite-length surface flaw during a pressurized-thermal-shock transient. Office of Scientific and Technical Information (OSTI), September 1993. http://dx.doi.org/10.2172/10186644.

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Shabana, Ahmed A. Integration of Computational Geometry, Finite Element, and Multibody System Algorithms for the Development of New Computational Methodology for High-Fidelity Vehicle Systems Modeling and Simulation. ADDENDUM. Fort Belvoir, VA: Defense Technical Information Center, November 2013. http://dx.doi.org/10.21236/ada593312.

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Roesler, Jeffery, Roberto Montemayor, John DeSantis, and Prakhar Gupta. Evaluation of Premature Cracking in Urban Concrete Pavement. Illinois Center for Transportation, January 2021. http://dx.doi.org/10.36501/0197-9191/21-001.

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This study investigated the causes for premature, transverse cracking on urban jointed plain concrete pavements in Illinois. A field survey of 67 sections throughout Illinois coupled with ultrasonic evaluation was completed to synthesize the extent of premature cracking on urban JPCP. The visual survey showed some transverse and longitudinal cracks were a result of improper slab geometry (excessive slab length and width). Ultrasonic tests over the contraction joints determined some notched joints had not activated and adjacent transverse cracks were likely formed as a result. Three-dimensional finite-element analyses confirmed that cracking would not develop as a result of normal environmental factors and slab-base frictional restraint. The concrete mixture also did not appear to be a contributing factor to the premature cracks. Finally, the lack of lubrication on dowel bars was determined to potentially be a primary mechanism that could restrain the transverse contraction joints, produce excessive tensile stresses in the slab, and cause premature transverse cracks to develop.
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Riveros, Guillermo, Felipe Acosta, Reena Patel, and Wayne Hodo. Computational mechanics of the paddlefish rostrum. Engineer Research and Development Center (U.S.), September 2021. http://dx.doi.org/10.21079/11681/41860.

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Purpose – The rostrum of a paddlefish provides hydrodynamic stability during feeding process in addition to detect the food using receptors that are randomly distributed in the rostrum. The exterior tissue of the rostrum covers the cartilage that surrounds the bones forming interlocking star shaped bones. Design/methodology/approach – The aim of this work is to assess the mechanical behavior of four finite element models varying the type of formulation as follows: linear-reduced integration, linear-full integration, quadratic-reduced integration and quadratic-full integration. Also presented is the load transfer mechanisms of the bone structure of the rostrum. Findings – Conclusions are based on comparison among the four models. There is no significant difference between integration orders for similar type of elements. Quadratic-reduced integration formulation resulted in lower structural stiffness compared with linear formulation as seen by higher displacements and stresses than using linearly formulated elements. It is concluded that second-order elements with reduced integration and can model accurately stress concentrations and distributions without over stiffening their general response. Originality/value – The use of advanced computational mechanics techniques to analyze the complex geometry and components of the paddlefish rostrum provides a viable avenue to gain fundamental understanding of the proper finite element formulation needed to successfully obtain the system behavior and hot spot locations.
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FINITE ELEMENT SIMULATION FOR ULTRA-HIGH-PERFORMANCE CONCRETE-FILLED DOUBLE-SKIN TUBES EXPOSED TO FIRE. The Hong Kong Institute of Steel Construction, August 2022. http://dx.doi.org/10.18057/icass2020.p.263.

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Ultra-high-performance concrete (UHPC) or ultra-high-strength concrete (UHSC) are alternatively used to reduce construction materials, thereby achieving more sustainable constructions. Moreover, engaging the advantages of concrete cores and outer steel tubes in concrete-filled steel tubes (CFST) or ductile concrete-filled double-skin tubes (CFDST) is of great interest for the better performance of such members under fire. Nevertheless, current design provisions do not provide design models for UHPC-filled double-skin tubes under fire, and existing finite-element (FE) methodologies available in the literature may not accurately simulate the behaviour of CFDST exposed to fire. Therefore, this paper develops a comprehensive FE protocol implementing the scripting technique to model CFDST members for heat transfer and coupled (simultaneously or sequentially) thermal-stress analyses. Various modelling parameters incorporated in the proposed FE routine include the cross-sectional geometry (circular, elliptical, hexagonal, octagonal, and rectangular), the size (width, diameter, and wall thickness), interactions, meshing, thermal- and mechanical-material properties, and boundary conditions. The detailed algorithm for heat transfer analysis is presented and elaborated via a flow chart. Validations, verifications, and robustness of the developed FE models are established based on extensive comparison studies with existing fire tests available in the literature. As a result, and to recognize the value of the current FE methodology, an extensive parametric study is conducted for different affecting parameters (e.g., nominal steel ratio, hollowness ratio, concrete cylindrical strength, yield strength of metal tubes, and width-to-thickness ratio). Extensive FE results are used for optimizing the fire design of such members. Consequently, a simplified and accurate analytical model that can provide the axial load capacity of CFDST columns under different fire ratings is presented
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PERFORMANCE OF STUD SHEAR CONNECTIONS IN COMPOSITE SLABS WITH VARIOUS CONFIGURATIONS (ICASS’2020). The Hong Kong Institute of Steel Construction, August 2022. http://dx.doi.org/10.18057/icass2020.p.351.

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This research project aims to examine the structural behaviour of stud shear connections with both solid concrete slabs and composite slabs under standard and modified push-out tests. A total of 27 push-out tests were carried out to provide test data of typical stud shear connections. It should be noted that the modified push-out tests were proposed in which the stud shear connections were subjected to combined shear and pull-out forces. Advanced finite element models using ABAQUS have also been established and calibrated carefully against the test data. Systematic numerical investigations are conducted to provide new understandings on load transfer mechanisms of these stud shear connections. Moreover, a comprehensive parametric study is carried out using various material properties of the concrete and various geometry of the profiled steel decking. A configuration parameter ηd and a reduction factor ηt are proposed for use in conjunction with the reduction factor kd given in EN 1994-1- 1 to incorporate the effects of installation positions of headed shear stud, trough widths of profiled decks, and presence of significant pull-out forces.
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CALCULATION OF THE RESISTANCE WITH DIFFERENT STIFFNESS CONNECTIONS AGAINST PROGRESSIVE COLLAPSE BASED ON THE COMPONENT METHOD. The Hong Kong Institute of Steel Construction, August 2022. http://dx.doi.org/10.18057/icass2020.p.108.

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"The collapse performance of steel frames generally depends on their ability to resist local damage, however, this ability depends on the behaviour of beam-to-column connections that have not yet to be identified in a methodical and reliable manner. Thus, it is critical to develop a simplified joint model, which could predict the structural collapse resistance to prevent progressive collapse. In this study, component models with different stiffness connections, namely the double web angle (DWA) connection, top-seat with double web angle connection (TSDWA) and welded flange-bolted web connection (WUF) were constructed based on the component method by simplifying its geometry and dividing into a number of basic springs. The proposed component-based connections models with detailed components were implemented within the finite element programme ANSYS, and the models were validated against previously experimental tests. The analysis results show that the component models can accurately reflect the load response and post-fracture path of the substructures with a cost-effective solution, which indicated that the component method has great theoretical significance and applicable value in progressive collapse analysis, and provided a simple and effective tool for the engineers to calculate the progressive collapse resistance."
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