Relevant bibliographies by topics / Conformal representations

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Conformal representations'

Author: Grafiati
Published: 30 May 2022
Last updated: 31 May 2022

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Journal articles on the topic "Conformal representations"

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MATSUDA, SATOSHI. "REPRESENTATION BLOCKS OF CONFORMAL FIELDS FOR THE N=4SU(2)k SUPERCONFORMAL ALGEBRAS." International Journal of Modern Physics A 10, no. 11 (1995): 1671–91. http://dx.doi.org/10.1142/s0217751x95000802.

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The representation theories of the SU(2)k-extended N=4 superconformal algebras (SCA’s) with arbitrary level k are developed, based on their Feigin-Fuchs representations found recently by the present author. A basic unit of the representation blocks consisting of eight “boson-like” and eight “fermion-like” conformal fields is found to describe arbitrary representations of the N=4 SU(2)k SCA’s, including unitary and nonunitary representations. The transformation properties of the fundamental sets of the conformal fields under the N=4 SU(2)k superconformal symmetries are given. Then, the whole sets of the charge screening operators of the N=4 SU(2)k SCA’s are identified out of the 16 conformal fields in the basic unit of the representation blocks. The conditions for the eligible charge screening operators are analyzed in terms of the continuous parameters which enter in our vertex operator forms for the fundamental conformal fields of the representation blocks.
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EHOLZER, W. "FUSION ALGEBRAS INDUCED BY REPRESENTATIONS OF THE MODULAR GROUP." International Journal of Modern Physics A 08, no. 20 (1993): 3495–507. http://dx.doi.org/10.1142/s0217751x93001405.

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Using the representation theory of the subgroups SL 2(ℤp) of the modular group we investigate the induced fusion algebras in some simple examples. Only some of these representations lead to "good" fusion algebras. Furthermore, the conformal dimensions and the central charge of the corresponding rational conformal field theories are calculated. Two series of representations which can be realized by unitary theories are presented. We show that most of the fusion algebras induced by admissible representations are realized in well-known rational models.
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LLEDÓ, FERNANDO. "CONFORMAL COVARIANCE OF MASSLESS FREE NETS." Reviews in Mathematical Physics 13, no. 09 (2001): 1135–61. http://dx.doi.org/10.1142/s0129055x01000958.

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In the present paper we review in a fiber bundle context the covariant and massless canonical representations of the Poincaré group as well as certain unitary representations of the conformal group (in 4-dimensions). We give a simplified proof of the well-known fact that massless canonical representations with discrete helicity extend to unitary and irreducible representations of the conformal group mentioned before. Further we give a simple new proof that massless free nets for any helicity value are covariant under the conformal group. Free nets are the result of a direct (i.e. independent of any explicit use of quantum fields) and natural way of constructing nets of abstract C *-algebras indexed by open and bounded regions in Minkowski space that satisfy standard axioms of local quantum physics. We also give a group theoretical interpretation of the embedding ℐ. that completely characterizes the free net: it reduces the (algebraically) reducible covariant representation in terms of the unitary canonical ones. Finally, we also mention some of the expected algebraic properties of these models that are a direct consequence of the conformal covariance (essential duality, PCT-symmetry etc.).
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Kolesnikov, P. S. "Universal enveloping Poisson conformal algebras." International Journal of Algebra and Computation 30, no. 05 (2020): 1015–34. http://dx.doi.org/10.1142/s0218196720500289.

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Lie conformal algebras are useful tools for studying vertex operator algebras and their representations. In this paper, we establish close relations between Poisson conformal algebras and representations of Lie conformal algebras. We also calculate explicitly Poisson conformal brackets on the associated graded conformal algebras of universal associative conformal envelopes of the Virasoro conformal algebra and the Neveu–Schwartz conformal superalgebra.
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RYTTOV, THOMAS A., and FRANCESCO SANNINO. "CONFORMAL HOUSE." International Journal of Modern Physics A 25, no. 24 (2010): 4603–21. http://dx.doi.org/10.1142/s0217751x10050391.

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We investigate the gauge dynamics of nonsupersymmetric SU (N) gauge theories featuring the simultaneous presence of fermionic matter transforming according to two distinct representations of the underlying gauge group. We bound the regions of flavors and colors which can yield a physical infrared fixed point. As a consistency check we recover the previously investigated bounds of the conformal windows when restricting to a single matter representation. The earlier conformal windows can be imagined to be part now of the new conformal house. We predict the nonperturbative anomalous dimensions at the infrared fixed points. We further investigate the effects of adding mass terms to the condensates on the conformal house chiral dynamics and construct the simplest instanton induced effective Lagrangian terms.
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Kolesnikov, P. S. "Conformal representations of Leibniz algebras." Siberian Mathematical Journal 49, no. 3 (2008): 429–35. http://dx.doi.org/10.1007/s11202-008-0043-7.

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Carpi, Sebastiano, and Robin Hillier. "Loop groups and noncommutative geometry." Reviews in Mathematical Physics 29, no. 09 (2017): 1750029. http://dx.doi.org/10.1142/s0129055x17500295.

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We describe the representation theory of loop groups in terms of K-theory and noncommutative geometry. This is done by constructing suitable spectral triples associated with the level [Formula: see text] projective unitary positive-energy representations of any given loop group [Formula: see text]. The construction is based on certain supersymmetric conformal field theory models associated with [Formula: see text] in the setting of conformal nets. We then generalize the construction to many other rational chiral conformal field theory models including coset models and the moonshine conformal net.
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Wu, Henan. "Finite irreducible representations of map Lie conformal algebras." International Journal of Mathematics 28, no. 01 (2017): 1750002. http://dx.doi.org/10.1142/s0129167x17500021.

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In this paper, we study the finite representation theory of the map Lie conformal algebra [Formula: see text], where G is a finite simple Lie conformal algebra and A is a commutative associative algebra with unity over [Formula: see text]. In particular, we give a complete classification of nontrivial finite irreducible conformal modules of [Formula: see text] provided A is finite-dimensional.
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ALTSCHÜLER, D. "THE CRITICAL REPRESENTATIONS OF AFFINE LIE ALGEBRAS." Modern Physics Letters A 01, no. 10 (1986): 557–64. http://dx.doi.org/10.1142/s0217732386000701.

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A critical representation of an affine algebra Ĝ is a representation with central charge k=−g, g being the dual Coxeter number of the underlying simple Lie algebra G. These representations arise naturally in the study of conformal current algebras and BRS cohomology. The author shows how to construct them explicitly in a number of cases, and some intriguing open problems are mentioned.
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Morel, B., A. Sciarrino, and P. Sorba. "Unitary massless representations of conformal superalgebras." Physics Letters B 166, no. 1 (1986): 69–74. http://dx.doi.org/10.1016/0370-2693(86)91157-3.

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Dissertations / Theses on the topic "Conformal representations"

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Diemer, Tammo. "Conformal geometry, representation theory and linear fields." Bonn : Mathematisches Institut der Universität, 2004. http://catalog.hathitrust.org/api/volumes/oclc/62770144.html.

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Loke, Terence M. L. "Operator algebras and conformal field theory of the discrete series representations of Diff(S'1)." Thesis, University of Cambridge, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.338206.

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Pevzner, Michael. "Représentations des groupes de Lie conformes et quantification des espaces symétriques." Habilitation à diriger des recherches, Université de Reims - Champagne Ardenne, 2005. http://tel.archives-ouvertes.fr/tel-00320444.

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Шоман, Ольга Вікторівна. "Геометричне моделювання узагальнених паралельних множин". Thesis, Київський державний технічний університет будівництва i архітектури, 2007. http://repository.kpi.kharkov.ua/handle/KhPI-Press/20365.

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Дисертація на здобуття наукового ступеня доктора технічних наук зі спеціальності 05.01.01 – Прикладна геометрія, інженерна графіка. – Київський національний університет будівництва і архітектури, Київ, 2007. Дисертацію присвячено розробці теорії геометричного моделювання узагальнених паралельних множин для розв'язання задач формоутворення в часі геометричних об'єктів – наочних геометричних моделей динамічних явищ і процесів, що характеризуються хвильовими фронтами, поверхні яких у певні моменти часу утворюють просторову конформну сітку з лініями у напрямках руху цих фронтів, або характеризуються ізолініями, конформними до напрямків зміни фізичних параметрів. На основі введеної термінології запропоновано загальний підхід до геометричного моделювання проявів процесів і явищ різної фізичної природи. Розроблено теоретичні основи методу опису геометричних моделей паралельних множин на площині за допомогою рівнянь Гамільтона – Якобі у вигляді рівняння ейконала для кривих, що мають точки звороту або самі себе перетинають; методу опису геометричних моделей паралельних множин за допомогою нормальних рівнянь для поверхонь, які задано у параметричному вигляді; методу на основі конформних відображень, в якому запропоновано новий геометричний зміст функції комплексного потенціалу вихору і одержано нові геометричні моделі сімей квазіпаралельних ліній на комплексній площині. Удосконалено метод іміджевої екстраполяції для прогнозування геометричної форми ліній на площині, як елементів узагальнених паралельних множин. Розроблені методи дозволяють вивчати якісні зміни об'єктів, що моделюються.<br>Thesis for a doctor's degree in engineering sciences. Specialty: 05.01.01 – Applied geometry, engineering graphics. – Kyiv National University of Building and Architecture. – Kyiv, 2007. The dissertation is devoted to developing of the geometrical modelling theory of the general parallel sets for problems solving of geometrical objects form-formation in time which are visual geometrical models of dynamic phenomena and processes characterized by wave fronts surfaces which create the space conformal set in the moments of time with the lines on directions of these fronts moving or by isolines which are conformal to directions of physical parameters change. On introduced terminology basis the general approach to the geometrical modelling of different origin physical phenomena and processes displays is proposed. It was developed the theoretical basis of: the method of parallel sets geometrical models creation on the plane by means of Hamilton – Jacobi equation as eikonal equation for the curves with return and self-intersection points; the method of parallel sets geometrical models creation by means of normal equations for the surfaces in parameter form; the method based on conformal representations, in which the new geometrical meaning of twister complex potential function was proposed and the new geometrical models of quasi-parallel lines sets were obtained on the complex plane; the improved image extrapolation method for forecasting of geometrical form of lines on the plane as the elements of general parallel sets. These methods allow to research qualitative change of objects modelled.
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Kawai, S. "Boundary conformal field theory in free-field representation." Thesis, University of Oxford, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.249280.

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Mathéus, Frédéric. "Empilements de cercles : rigidité, discrétisation d'applications conformes." Université Joseph Fourier (Grenoble), 1994. http://www.theses.fr/1994GRE10234.

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Depuis une dizaine d'annees, les empilements de cercles ont fait l'objet d'abondantes recherches concernant des questions de rigidite, et une methode de discretisation de l'uniformisation de riemann. Le fait est que les empilements etudies jusqu'ici etaient tous plonges. L'objet de cette these est d'etudier ces questions d'approximation et de rigidite dans le cadre des empilements immerges. Ainsi, nous utilisons les empilements de cercles immerges finis pour discretiser des immersions conformes d'un compact du plan (chap. 1). La methode de deformation d'empilements de cercles employee alors permet de donner une nouvelle demonstration du theoreme de rodin-sullivan d'approximation de l'uniformisation de riemann (chap. 2). En particulier, on obtient une preuve simple du lemme de schwarz-pick pour les empilements de cercles. Nous etudions ensuite (chap. 3) la rigidite de certains empilements infinis immerges, les empilements infinis immerges proprement dans le plan et dans le disque
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Ström, David. "The Open Mapping Theorem for Analytic Functions and some applications." Thesis, Karlstad University, Faculty of Technology and Science, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-210.

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<p>This thesis deals with the Open Mapping Theorem for analytic functions on domains in the complex plane: A non-constant analytic function on an open subset of the complex plane is an open map.</p><p>As applications of this fundamental theorem we study Schwarz’s Lemma and its consequences concerning the groups of conformal automorphisms of the unit disk and of the upper halfplane.</p><p>In the last part of the thesis we indicate the first steps in hyperbolic geometry.</p><br><p>Denna uppsats behandlar satsen om öppna avbildningar för analytiska funktioner på domäner i det komplexa talplanet: En icke-konstant analytisk funktion på en öppen delmängd av det komplexa talplanet är en öppen avbildning.</p><p>Som tillämpningar på denna fundamentala sats studeras Schwarz’s lemma och dess konsekvenser för grupperna av konforma automorfismer på enhetsdisken och på det övre halvplanet.</p><p>I uppsatsens sista del antyds de första stegen inom hyperbolisk geometri.</p>
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Palcoux, Sébastien. "Série discrète unitaire, caractères, fusion de Connes et sous-facteurs pour l'algèbre Neveu-Schwarz." Phd thesis, Université de la Méditerranée - Aix-Marseille II, 2009. http://tel.archives-ouvertes.fr/tel-00514234.

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On donne une preuve complète de la classification des représentations d'énergie positive unitaires de l'algèbre Neveu-Schwarz, de telle manière qu'on obtient directement les caractères de la séries discrètes. Ensuite, on explicite leur loi de fusion de Connes et on prouve que les sous-facteurs de Jones-Wassermann sont irréductibles d'indice fini, on donne leur formule.
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Agrebaoui, Boujemaâ. "Sur la theorie des representations des algebres de kac-moody affines, la theorie des operateurs vertex et la theorie des champs conformes." Université Louis Pasteur (Strasbourg) (1971-2008), 1995. http://www.theses.fr/1995STR13090.

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Parmi les travaux cruciaux dans la theorie des representations, il y a ceux qui etudient la construction explicite de certaines representations de niveau un des algebres de kac-moody affines, en termes d'algebres d'operateurs vertex. Rappelons que le niveau d'une representation est l'action du centre de cette algebre. Il est difficile de construire les representations de niveau plus grand que un. C'est pour cela que les specialistes se sont interesses a la conjecture suivante qui est connue depuis une dizaine d'annees: toute representation irreductible de plus haut poids dominant et de niveau un entier n positif appait dans un produit tensoriel de n modules de niveau un (irreductibles). Le resultat principal de la premiere partie de ma these est la preuve de cette conjecture qui implique entre autre l'equivalence de certains resultats d'algebres d'operateurs vertex generalisees construites de deux points de vue differentes. Dans la seconde partie de ma these je m'interesse au modele de wess-zumino-witten (wzw) et le resultat principal est la donnee d'une interpretation de l'espace des blocs conformes comme un espace de champs primaires. Ces resultats sont connus auparavant par les physiciens
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HERNANDEZ, ORTEGA LINDA JOSELINNE. "Elaboración de un portafolio de inversión conformado por las divisas más representativas del mercado y de acciones de empresas en países emergentes del 2016 a 2018." Tesis de Licenciatura, UNIVERSIDAD AUTONOMA DEL ESTADO DE MEXICO, 2019. http://hdl.handle.net/20.500.11799/105297.

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El presente trabajo comprende la investigación del concepto de portafolio de inversión, de los mercados de divisas y de los mercados de acciones, su impacto económico y el funcionamiento que tienen dentro de la economía, con el propósito de poder elaborar un portafolio de inversión que esté integrado por acciones emitidas por empresas de países emergentes y por las divisas operadas en el mercado FOREX, utilizando la metodología de Markowitz para obtener las ponderaciones de los activos en el caso de la minimización del riesgo y la maximización del rendimiento. En el primer capítulo se hará referencia a las teorías planteadas para la elaboración de los portafolios de inversión, sirviendo como base para su comprensión y mejor entendimiento. Las definiciones planteadas servirán para brindar una introducción a las bases de los activos que conforman el portafolio, para posteriormente analizar de una manera más profunda en el segundo capitulo al mercado de divisas y al de acciones, comprendiendo su importancia económica y el impacto que han tenido ambos mercados con sus operaciones a nivel global. En el tercer capítulo del trabajo, se procederá a la elaboración del portafolio de inversión, con el objeto de comprobar la hipótesis y responder a la pregunta de investigación. Se analiza a detalle la selección de los activos, una breve descripción de cada uno de ellos y su comportamiento en los países respectivos de su emisión, justificando la selección de estos para el portafolio y concluyendo con la conformación del portafolio, calculando sus posibles riesgos, agregando las ponderaciones calculadas para cada activo y justificando la conformación de este.
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Books on the topic "Conformal representations"

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Todorov, Ivan T. Conformal description of spinning particles. Springer-Verlag, 1986.

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Dobrev, V. K. Representations of quantum groups and q-deformed invariant wave equations. Papierflieger, 1995.

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Conformal representation. Dover Publications, 1998.

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Bieberbach, Ludwig. Conformal mapping. American Mathematical Society, 2000.

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Courant, Richard. Dirichlet's principle, conformal mapping, and minimal surfaces. Dover Publications, 2005.

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Conformal maps of nonsmooth surfaces and their applications. Xlibris Corp., 2008.

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Mochizuki, Shinichi. Conformal and quasiconformal categorical representation of hyperbolic Riemann surfaces. Kyōto Daigaku Sūri Kaiseki Kenkyūjo, 2004.

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Grafarend, Erik W. Map projections: Cartographic information systems. Springer, 2006.

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Shakespeare, William. King Henry V: Or, The conquest of France, a tragedy. Printed exactly conformable to the representation, on its revival at the Theatre Royal. Drury Lane, October I, 1789. Pergamon Press, 1985.

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Trade, United States Congress House Committee on Ways and Means Subcommittee on. Proposals to conform the customs user fee on merchandise processing and the superfund tax differential with U.S. GATT obligations: Hearing before the Subcommittee on Trade of the Committee on Ways and Means, House of Representatives, One Hundred First Congress, first session, January 25, 1989. U.S. G.P.O., 1989.

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Book chapters on the topic "Conformal representations"

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Jackiw, Roman. "Representations of the Two-Dimensional Conformal Group." In Super Field Theories. Springer US, 1987. http://dx.doi.org/10.1007/978-1-4613-0913-0_7.

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Gu, Xianfeng, and Baba C. Vemuri. "Matching 3D Shapes Using 2D Conformal Representations." In Medical Image Computing and Computer-Assisted Intervention – MICCAI 2004. Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-540-30135-6_94.

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Todorov, Ivan T. "The Conformal Group of a Conformally Flat Space Time and Its Twistor Representations." In Conformal Description of Spinning Particles. Springer Berlin Heidelberg, 1986. http://dx.doi.org/10.1007/978-3-642-82868-3_3.

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Bincer, Adam M. "Massless Representations of the Poincaré Group and Conformal Invariance." In Symmetries in Science VI. Springer US, 1993. http://dx.doi.org/10.1007/978-1-4899-1219-0_8.

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Kohno, Toshitake. "Homological Representations of Braid Groups and the Space of Conformal Blocks." In Perspectives in Lie Theory. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-58971-8_16.

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Marussi, Antonio. "Some Integral Properties of the Conformal Representations of Surfaces on Surfaces." In Intrinsic Geodesy. Springer Berlin Heidelberg, 1985. http://dx.doi.org/10.1007/978-3-642-70243-3_16.

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Marussi, Antonio. "Some Remarks on the Use of Conformal Representations in Three-Dimensional Geodesy." In Intrinsic Geodesy. Springer Berlin Heidelberg, 1985. http://dx.doi.org/10.1007/978-3-642-70243-3_13.

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Görnitz, Th, and C. F. v. Weizsäcker. "De — sitter representations and the particle concept, studied in an ur-theoretical cosmological model." In Conformal Groups and Related Symmetries Physical Results and Mathematical Background. Springer Berlin Heidelberg, 1986. http://dx.doi.org/10.1007/3540171630_70.

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Marussi, Antonio. "An Analogy Between the Laws of Propagation of Light in Continuous Isotropic Refracting Media and Conformal Representations." In Intrinsic Geodesy. Springer Berlin Heidelberg, 1985. http://dx.doi.org/10.1007/978-3-642-70243-3_19.

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Henkel, Malte. "Representation Theory of the Virasoro Algebra." In Conformal Invariance and Critical Phenomena. Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/978-3-662-03937-3_4.

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Conference papers on the topic "Conformal representations"

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RETAKH, ALEXANDER. "STRUCTURE AND REPRESENTATIONS OF CONFORMAL ALGEBRAS." In Proceedings of the International Conference on Algebras, Modules and Rings. WORLD SCIENTIFIC, 2006. http://dx.doi.org/10.1142/9789812774552_0018.

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Kolesnikov, P. S. "On Representations of Dialgebras and Conformal Algebras." In The International Conference on Algebra 2010 - Advances in Algebraic Structures. WORLD SCIENTIFIC, 2011. http://dx.doi.org/10.1142/9789814366311_0028.

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Todorov, Ivan, and Vladimir Dobrev. "Minimal Representations and Reductive Dual Pairs in Conformal Field Theory." In LIE THEORY AND ITS APPLICATIONS IN PHYSICS: VIII International Workshop. AIP, 2010. http://dx.doi.org/10.1063/1.3460160.

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GUNAYDIN, MURAT. "REALIZATIONS OF EXCEPTIONAL U-DUALITY GROUPS AS CONFORMAL AND QUASI-CONFORMAL GROUPS AND THEIR MINIMAL UNITARY REPRESENTATIONS." In Proceedings of the 3rd International Symposium. WORLD SCIENTIFIC, 2004. http://dx.doi.org/10.1142/9789812702340_0009.

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Taylor, C. M., I. P. Ilyas, K. W. Dalgarno, and J. Gosden. "Manufacture of Production Quality Injection Mold Tools Using SLS and HSM." In ASME 2007 International Manufacturing Science and Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/msec2007-31030.

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The use of a rapid manufacturing method to create injection mould tools offers the opportunity to create conformal cooling channels in the core/cavity inserts. Conformal cooling channels allow for better thermal management of the injection mold tool through the cycle, with the potential to reduce cycle times and/or improve product quality. However, currently available rapid manufacturing methods do not deliver the levels of accuracy and surface finish required to meet typical injection mould tool specifications. This paper reports on a hybrid approach to developing the mold inserts, which uses the rapid manufacturing process of indirect selective laser sintering (SLS), using the 3D Systems LaserForm process, to create a near net shape insert with conformal cooling channels, and then produces the net shape inserts by using high speed machining (HSM) as a finishing process. This approach to injection mold tool development has been tested through three industrial case studies. In each study existing injection mold inserts have been redesigned to give a conformally cooled tool. These have then been manufactured to near net shape in a steel/bronze metal composite through indirect SLS, and finished to production specification using HSM, EDM and polishing. Within the case studies the main aim has been to improve productivity, and the inserts have been evaluated in industrial trials in order to assess their performance in terms of cycle time, energy usage, durability and quality. The results show that significant productivity improvements and energy use reductions in injection molding are possible through the implementation of conformal cooling. Consistency of part quality and material durability have been assessed through extended molding trials, and in some cases there is a clear economic benefit to using the inserts. However, the importance of up front modelling to understand the impact of conformal cooling channels, the need for careful planning in manufacture to ensure that the required internal geometry is created, and the need for multiple representations of the required geometry to inform the different stages of the manufacture process are highlighted.
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To, Son Thanh, Tran Cao Son, and Enrico Pontelli. "A generic approach to planning in the presence of incomplete information: Theory and implementation (Extended Abstract)." In Twenty-Sixth International Joint Conference on Artificial Intelligence. International Joint Conferences on Artificial Intelligence Organization, 2017. http://dx.doi.org/10.24963/ijcai.2017/725.

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This paper proposes a generic approach to planning in the presence of incomplete information. The approach builds on an abstract notion of a belief state representation, along with an associated set of basic operations. These operations facilitate the development of a sound and complete transition function, for reasoning about effects of actions in the presence of incomplete information, and a set of abstract algorithms for planning. The paper demonstrates how the abstract definitions and algorithms can be instantiated in three concrete representations—minimal-DNF, minimal-CNF, and prime implicates—resulting in three highly competitive conformant planners: DNF, CNF, and PIP. The paper relates the notion of a representation to that of ordered binary decision diagrams, a well-known belief state representation employed by many conformant planners, and several target compilation languages that have been presented in the literature.The paper also includes an experimental evaluation of the planners DNF, CNF, and PIP and proposes a new set of conformant planning benchmarks that are challenging for state-of-the-art conformant planners.
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Gantoi, F. Marina, Michael A. Brown, and Ahmed A. Shabana. "ANCF Modeling of the Contact Geometry and Deformation in Biomechanics Applications." In ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/detc2012-70224.

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The purpose of this investigation is to demonstrate the use of the finite element (FE) absolute nodal coordinate formulation (ANCF) and multibody system (MBS) algorithms in modeling both the contact geometry and ligaments deformations in biomechanics applications. Two ANCF approaches can be used to model the rigid contact surface geometry. In the first approach, fully parameterized ANCF volume elements are converted to surface geometry using parametric relationship that reduces the number of independent coordinate lines. This parametric relationship can be defined analytically or using a spline function representation. In the second approach, an ANCF surface that defines a gradient deficient thin plate element is used. This second approach does not require the use of parametric relations or spline function representations. These two geometric approaches shed light on the generality of and the flexibility offered by the ANCF geometry as compared to computational geometry (CG) methods such as B-splines and NURBS (Non-Uniform Rational B-Splines). Furthermore, because B-spline and NURBS representations employ a rigid recurrence structure, they are not suited as general analysis tools that capture different types of joint discontinuities. ANCF finite elements, on the other hand, lend themselves easily to geometric description and can additionally be used effectively in the analysis of ligaments, muscles, and soft tissues (LMST), as demonstrated in this paper using the knee joint as an example. In this study, ANCF finite elements are used to define the femur/tibia rigid body contact surface geometry. The same ANCF finite elements are also used to model the MCL and LCL ligament deformations. Two different contact formulations are used in this investigation to predict the femur/tibia contact forces; the elastic contact formulation where penetrations and separations at the contact points are allowed, and the constraint contact formulation where the non-conformal contact conditions are imposed as constraint equations, and as a consequence, no separations or penetrations at the contact points are allowed. For both formulations, the contact surfaces are described in a parametric form using surface parameters that enter into the ANCF finite element geometric description. A set of nonlinear algebraic equations that depend on the surface parameters is developed and used to determine the location of the contact points. These two contact formulations are implemented in a general MBS algorithm that allows for modeling rigid and flexible body dynamics.
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Feiszli, Matt, and David Mumford. "Shape representation via conformal mapping." In Electronic Imaging 2007, edited by Charles A. Bouman, Eric L. Miller, and Ilya Pollak. SPIE, 2007. http://dx.doi.org/10.1117/12.716028.

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HALLER, STEFAN. "SOME PROPERTIES OF LOCALLY CONFORMAL SYMPLECTIC MANIFOLDS." In Infinite Dimensional Lie Groups in Geometry and Representation Theory. WORLD SCIENTIFIC, 2002. http://dx.doi.org/10.1142/9789812777089_0007.

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BANYAGA, A. "ON THE GEOMETRY OF LOCALLY CONFORMAL SYMPLECTIC MANIFOLDS." In Infinite Dimensional Lie Groups in Geometry and Representation Theory. WORLD SCIENTIFIC, 2002. http://dx.doi.org/10.1142/9789812777089_0006.

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Reports on the topic "Conformal representations"

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Zhang, Yongjie, Wenyan Wang, and Thomas J. Hughes. Conformal Solid T-spline Construction from Boundary T-spline Representations. Defense Technical Information Center, 2012. http://dx.doi.org/10.21236/ada588397.

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Yan, Yujie, and Jerome F. Hajjar. Automated Damage Assessment and Structural Modeling of Bridges with Visual Sensing Technology. Northeastern University, 2021. http://dx.doi.org/10.17760/d20410114.

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Recent advances in visual sensing technology have gained much attention in the field of bridge inspection and management. Coupled with advanced robotic systems, state-of-the-art visual sensors can be used to obtain accurate documentation of bridges without the need for any special equipment or traffic closure. The captured visual sensor data can be post-processed to gather meaningful information for the bridge structures and hence to support bridge inspection and management. However, state-of-the-practice data postprocessing approaches require substantial manual operations, which can be time-consuming and expensive. The main objective of this study is to develop methods and algorithms to automate the post-processing of the visual sensor data towards the extraction of three main categories of information: 1) object information such as object identity, shapes, and spatial relationships - a novel heuristic-based method is proposed to automate the detection and recognition of main structural elements of steel girder bridges in both terrestrial and unmanned aerial vehicle (UAV)-based laser scanning data. Domain knowledge on the geometric and topological constraints of the structural elements is modeled and utilized as heuristics to guide the search as well as to reject erroneous detection results. 2) structural damage information, such as damage locations and quantities - to support the assessment of damage associated with small deformations, an advanced crack assessment method is proposed to enable automated detection and quantification of concrete cracks in critical structural elements based on UAV-based visual sensor data. In terms of damage associated with large deformations, based on the surface normal-based method proposed in Guldur et al. (2014), a new algorithm is developed to enhance the robustness of damage assessment for structural elements with curved surfaces. 3) three-dimensional volumetric models - the object information extracted from the laser scanning data is exploited to create a complete geometric representation for each structural element. In addition, mesh generation algorithms are developed to automatically convert the geometric representations into conformal all-hexahedron finite element meshes, which can be finally assembled to create a finite element model of the entire bridge. To validate the effectiveness of the developed methods and algorithms, several field data collections have been conducted to collect both the visual sensor data and the physical measurements from experimental specimens and in-service bridges. The data were collected using both terrestrial laser scanners combined with images, and laser scanners and cameras mounted to unmanned aerial vehicles.
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