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Academic literature on the topic 'Minimal surface equation'

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Published: 9 March 2023

Last updated: 10 March 2023

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Journal articles on the topic "Minimal surface equation"

1

Fouladgar, K., and Leon Simon. "The symmetric minimal surface equation." Indiana University Mathematics Journal 69, no. 1 (2020): 331–66. http://dx.doi.org/10.1512/iumj.2020.69.8412.

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SHAVOKHINA, N. S. "FEDOROV UNIVERSAL EQUATIONS IN THE STRING AND MEMBRANE THEORIES." International Journal of Modern Physics B 04, no. 01 (January 1990): 93–111. http://dx.doi.org/10.1142/s0217979290000048.

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It is shown that the equation of minimal hypersurface in the Euclidean (or pseudo-Euclidean) space can be written as the universal Fedorov matrix equation with first-order partial derivatives. Time-like minimal surfaces in the pseudo-Euclidean Minkowski space describe the free motion of relativistic strings and membranes, whereas space-like minimal surfaces describe the potential in the nonlinear Born electrostatic. All of them are imaginary images of minimal surface of the Euclidean space. Spherically symmetric surfaces are found to be all the three types, the hypercatenoid of any dimensionality and its imaginary images. The Fedorov equations provide rich information on the minimal surfaces.

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Simon, Leon. "Entire solutions of the minimal surface equation." Journal of Differential Geometry 30, no. 3 (1989): 643–88. http://dx.doi.org/10.4310/jdg/1214443827.

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ALÍAS, LUIS J., and BENNETT PALMER. "A duality result between the minimal surface equation and the maximal surface equation." Anais da Academia Brasileira de Ciências 73, no. 2 (June 2001): 161–64. http://dx.doi.org/10.1590/s0001-37652001000200002.

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In this note we show how classical Bernstein's theorem on minimal surfaces in the Euclidean space can be seen as a consequence of Calabi-Bernstein's theorem on maximal surfaces in the Lorentz-Minkowski space (and viceversa). This follows from a simple but nice duality between solutions to their corresponding differential equations.

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Bellettini, Giovanni, Matteo Novaga, and Giandomenico Orlandi. "Eventual regularity for the parabolic minimal surface equation." Discrete and Continuous Dynamical Systems 35, no. 12 (May 2015): 5711–23. http://dx.doi.org/10.3934/dcds.2015.35.5711.

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Grundland, Alfred, and Alexander Hariton. "Algebraic Aspects of the Supersymmetric Minimal Surface Equation." Symmetry 9, no. 12 (December 18, 2017): 318. http://dx.doi.org/10.3390/sym9120318.

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Hwang, Jenn-Fang. "Phragmen-Lindelof Theorem for the Minimal Surface Equation." Proceedings of the American Mathematical Society 104, no. 3 (November 1988): 825. http://dx.doi.org/10.2307/2046800.

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Dierkes, Ulrich, and Nico Groh. "Symmetric solutions of the singular minimal surface equation." Annals of Global Analysis and Geometry 60, no. 2 (June 21, 2021): 431–53. http://dx.doi.org/10.1007/s10455-021-09785-2.

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AbstractWe classify all rotational symmetric solutions of the singular minimal surface equation in both cases $$\alpha <0$$ α < 0 and $$\alpha >0$$ α > 0 . In addition, we discuss further geometric and analytic properties of the solutions, in particular stability, minimizing properties and Bernstein-type results.

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Ziemer, William. "The nonhomogeneous minimal surface equation involving a measure." Pacific Journal of Mathematics 167, no. 1 (January 1, 1995): 183–200. http://dx.doi.org/10.2140/pjm.1995.167.183.

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Hwang, Jenn-Fang. "A uniqueness theorem for the minimal surface equation." Pacific Journal of Mathematics 176, no. 2 (December 1, 1996): 357–64. http://dx.doi.org/10.2140/pjm.1996.176.357.

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Dissertations / Theses on the topic "Minimal surface equation"

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Krust, Romain. "Le problème de Dirichlet pour l' équation des surfaces minimales." Paris 7, 2005. http://www.theses.fr/1992PA077323.

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Melin, Jaron Patric. "Examples of discontinuity for the variational solution of the minimal surface equation with Dirichlet data on a domain with a nonconvex corner and locally negative mean curvature." Thesis, Wichita State University, 2013. http://hdl.handle.net/10057/10639.

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The purpose of this thesis is to investigate the role of smoothness, specifically the smoothness of the boundary ∂Ω, in the behavior of the variational solution f on a domain Ω to the Dirichlet problem for the Minimal Surface Equation at a point O ∈ ∂Ω when the (generalized) curvature of ∂Ω has a negative upper bound in a neighborhood of O. We give examples which show that the assumption of boundary-regularity which Simon made in [12] or at least some weaker boundary-regularity assumption which excludes nonconvex corners in the boundary of the domain is necessary in order to guarantee that the variational solution of the Dirichlet problem for the Minimal Surface Equation is continuous in the closure of the domain for every Lipschitz-continuous boundary-data function ϕ : ∂Ω → R. This is independent of whether or not f equals ϕ on ∂Ω. Furthermore, these examples give credence to the Concus-Finn Conjecture, which still awaits to be proven in the case that the contact-angle is 0 or π at nonconvex corners.
Thesis (M.S.)--Wichita State University, College of Liberal Arts and Sciences, Dept. of Mathematics, Statistics, and Physics

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COLOMBO, GIULIO. "GLOBAL GRADIENT BOUNDS FOR SOLUTIONS OF PRESCRIBED MEAN CURVATURE EQUATIONS ON RIEMANNIAN MANIFOLDS." Doctoral thesis, Università degli Studi di Milano, 2021. http://hdl.handle.net/2434/813095.

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This thesis is concerned with the study of qualitative properties of solutions of the minimal surface equation and of a class of prescribed mean curvature equations on complete Riemannian manifolds. We derive global gradient bounds for non-negative solutions of such equations on manifolds satisfying a uniform Ricci lower bound and we obtain Liouville-type theorems and other rigidity results on Riemannian manifolds with non-negative Ricci curvature. The proof of the aforementioned global gradient bounds for non-negative solutions u is based on the application of the maximum principle to an elliptic differential inequality satisfied by a suitable auxiliary function z=f(u,|Du|), in the spirit of Bernstein’s method of a priori estimates for nonlinear PDEs and of Yau’s proof of global gradient bounds for harmonic functions on complete Riemannian manifolds. The particular choice of the auxiliary function z parallels the one in Korevaar’s proof of a priori gradient estimates for the prescribed mean curvature equation in Euclidean space. The rigidity results obtained in the last part of the thesis include a Liouville theorem for positive solutions of the minimal surface equation on complete Riemannian manifolds with non-negative Ricci curvature, a splitting theorem for complete parabolic manifolds of non-negative sectional curvature supporting non-constant solutions with linear growth of the minimal surface equation, and a splitting theorem for domains of complete parabolic manifolds with non-negative Ricci curvature supporting non-constant solutions of overdetermined problems involving the mean curvature operator.

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Pagliardini, Dayana. "Fractional minimal surfaces and Allen-Cahn equations." Doctoral thesis, Scuola Normale Superiore, 2018. http://hdl.handle.net/11384/85738.

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In recent years fractional operators have received considerable attention both in pure and applied mathematics. They appear in biological observations, finance, crystal dislocation, digital image reconstruction and minimal surfaces. In this thesis we study nonlocal minimal surfaces which are boundaries of sets minimizing certain integral norms and can be interpreted as a non-infinitesimal version of classical minimal surfaces. In particular, we consider critical points, with or withouth constraints, of suitable functionals, or approximations through diffuse models as the Allen-Cahn’s. In the first part of the thesis we prove an existence and multiplicity result for critical points of the fractional analogue of the Allen-Cahn equation in bounded domains. We bound the functional using a standard nonlocal tool: we split the domain in two regions and we analyze the three significative interactions. Then, the proof becomes an application of a classical Krasnoselskii’s genus result. Then, we consider a fractional mesoscopic model of phase transition i.e. the fractional Allen-Cahn equation with the addition of a mesoscopic term changing the ‘pure phases’ ±1 in periodic functions. We investigate geometric properties of the interface of the associated minimal solutions. Then we construct minimal interfaces lying to a strip of prescribed direction and universal width. We provide a geometric and variational technique adapted to deal with nonlocal interactions. In the last part of the thesis, we study functionals involving the fractional perimeter. In particular, first we study the localization of sets with constant nonlocal mean curvature and small prescribed volume in an open bounded domain, proving that these sets are ‘sufficiently close’ to critical points of a suitable potential. The proof is an application of the Lyupanov-Schmidt reduction to the fractional perimeter. Finally, we consider the fractional perimeter in a half-space. We prove the existence of a minimal set with fixed volume and some of its properties as intersection with the hyperplane {xN = 0}, symmetry, to be a graph in the xN-direction and smoothness.

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Bäck, Per. "Bäcklund transformations for minimal surfaces." Thesis, Linköpings universitet, Matematik och tillämpad matematik, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-119914.

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In this thesis, we study a Bäcklund transformation for minimal surfaces - surfaces with vanishing mean curvature - transforming a given minimal surface into a possible infinity of new ones. The transformation, also carrying with it mappings between solutions to the elliptic Liouville equation, is first derived by using geometrical concepts, and then by using algebraic methods alone - the latter we have not been able to find elsewhere. We end by exploiting the transformation in an example, transforming the catenoid into a family of new minimal surfaces.

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Mazet, Laurent. "Construction de surfaces minimales par résolution du problème de Dirichlet." Phd thesis, Université Paul Sabatier - Toulouse III, 2004. http://tel.archives-ouvertes.fr/tel-00007780.

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Le cadre de cette thèse est la théorie des surfaces minimales. En 2001, C. Cosin et A. Ros démontrent que, si un polygone borde un disque immergé, ce polygone est le polygone de flux d'un r-noide Alexandrov-plongé symétrique de genre 0. Leur démonstration se fonde sur l'étude de l'espace de ces surfaces minimales. Notre travail présente une démonstration plus constructive de leur résultat. Notre méthode repose sur la résolution du problème de Dirichlet pour l'équation des surfaces minimales. A cette fin, nous étudions la convergence de suites de solutions de cette équation. Nous définissons la notion de lignes de divergence de la suite qui sont les points ou la suite des gradients est non-bornées. L'étude de ces lignes permet de conclure sur la convergence d'une suite. Les r-noides sont alors construits comme les surfaces conjuguées aux graphes de solutions du problème de Dirichlet sur des domaines fixés par les polygones. Dans une seconde partie, nous montrons que, sous l'hypothèse de border un disque immergé, un polygone est aussi le polygone de flux d'un r-noide Alexandrov-plongé symétrique de genre $1$. La démonstration repose sur une amélioration des idées de celle du premier résultat, elle nécessite entre autre la résolution d'un problème de période. Cette résolution passe par l'étude du comportement limite de certaines suites de surfaces minimales.

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Rodiac, Rémy. "Méthodes variationnelles pour des problèmes sous contrainte de degrés prescrits au bord." Thesis, Paris Est, 2015. http://www.theses.fr/2015PESC1108/document.

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Cette thèse est dédiée à l'analyse mathématique de quelques problèmes variationnels motivés par le modèle de Ginzburg-Landau en théorie de la supraconductivité. Dans la première partie on étudie l'existence de solutions pour les équations de Ginzburg-Landau sans champ magnétique et avec données au bord de type semi-rigides. Ces données consistent à prescrire le module de la fonction sur le bord du domaine ainsi que son degré topologique. C'est un cas particulier de problèmes à bord libre, ou la donnée complète de la fonction sur le bord est une inconnue du problème. L'existence de solutions à ce problème n'est pas assurée. En effet la méthode directe du calcul des variations ne peut pas s'appliquer car le degré sur le bord n'est pas continu pour la convergence faible dans l'espace de Sobolev adapté. On dit que c'est un problème sans compacité. En étudiant le phénomène de "bubbling" qui apparaît dans l'étude de tels problèmes on donne des résultats d'existence et de non existence de solutions. Dans le Chapitre 1 on étudie des conditions qui permettent d'affirmer que la différence entre deux niveaux d'énergie est strictement optimale. Pour cela on adapte une technique due à Brezis-Coron. Ceci nous permet de redémontrer un résultat (précédemment obtenu par Berlaynd Rybalko et Dos Santos) d'existence de solutions stables pour les équations de Ginzburg-Landau dans des domaines multiplement connexes. Dans le Chapitre 2 on considère les applications harmoniques a valeurs dans $R^2$ avec des conditions au bord de type degrés prescrits sur un anneau. On fait un lien entre ce problème et la théorie des surfaces minimales dans $R^3$ grâce à la différentielle quadratique de Hopf. Ceci nous conduit à l'étude des surfaces minimales bordées par deux cercles dans des plans parallèles. On prouve l'existence de telles surfaces qui ne sont pas des catenoides grâce a un résultat de bifurcation. On utilise alors les résultats obtenus pour déduire des théorèmes d'existence et de non existence de minimiseurs de l'énergie de Ginzburg-Landau à degrés prescrits dans un anneau. Dans ce troisième Chapitre on obtient des résultats pour une valeur du paramètre " grand. Le Chapitre 4 a pour objet l'étude des problèmes a degrés prescrits en dimension n3. On y montre la non existence des minimiseurs de la n-énergie de Ginzburg-Landau a degrés prescrits dans un domaine simplement connexe. On étudie ensuite des points critiques de type min-max pour une énergie perturbée. La deuxième partie est consacrée a l'analyse asymptotique des solutions des équations deGinzburg-Landau lorsque " tend vers zero. Sandier et Serfaty ont étudié le comportement asymptotique des mesures de vorticité associées aux équations. Ils ont notamment trouvé des conditions critiques sur les mesures limites dans le cas des équations avec et sans champ magnétique. Nous nous intéressons alors à ces conditions critiques dans le cas sans champ magnétique. Le problème de la régularité locale des mesures limites se ramène ainsi a l'étude de la régularité des fonctions stationnaires harmoniques dont le Laplacien est une mesure. Nous montrons que localement de telles mesures sont supportées par une union de lignes appartenant à l'ensemble des zéros d'une fonction harmonique
This thesis is devoted to the mathematical analysis of some variational problems. These problem sare motivated by the Ginzburg-Landau model related to the super conductivity. In the first part we study existence of solutions of the Ginzburg-Landau equations without magnetic eld but with semi-sti boundary conditions. These conditions are obtained by prescribing the modulus of the function on the boundary of the domain along with its topological degree. This is a particular case of free boundary problems, where the function on the boundary is an unknown of the problem. Existence of solutions of that problem does not necessary hold. Indeed we can not apply the direct method of the calculus of variations since the degree on the boundaryis not continuous with respect to the weak convergence in an appropriated Sobolev space. This is problem with loss of compactness. By studying the bublling" phenomenon which come upin such problems we obtain some existence and non existence results .In Chapter 1 we study conditions under which the dierence between two energy levels is strictly optimal. In order to do that we adapt a technique due to Brezis-Coron. This allow us to recover known existence results (previously obtained by Berlyand and Rybalko and DosSantos) for stable solutions of the Ginzburg-Landau equations in multiply connected domains. In Chapter 2 we are interested in harmonic maps with values in $R^2$ with prescribed degree boundary condition in an annulus. We make a link between this problem and the minimal surface theory in $R^3$ thanks to the so-called Hopf quadratic differential. This leads us to study immersed minimal surfaces bounded by two circles in parallel planes. We prove the existence of such surfaces die rent from catenoids by using a bifurcation argument. We then apply the results obtained to deduce existence and non existence results for minimizers of the Ginzburg-Landau energy with prescribed degrees. This is done in Chapter 3 where the results are obtained for large ".Chapter 4 is devoted to prescribed degree problems in dimension n3 . We prove the non existence of minimizers of the Ginzburg-Landau energy in simply connected domains. We then study min-max critical points of a perturbed energy. The second part is devoted to the asymptotic analysis of solutions of the Ginzburg-Landau equations when "goes to zero. Sandier and Serfaty studied the asymptotic behavior of the vorticity measures associated to these equations. They derived critical conditions on the limiting measures both with and without magnetic Field. We are interested by these conditions when there is no magnetic Field. The problem of the local regularity of the limiting measures is then equivalent to the study of regularity of stationary harmonic functions whose Laplacianis a measure. We show that locally such measures are concentrated on a union of lines which belong to the zero set of an harmonic function

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Melo, Marcos Ferreira de. "ImersÃes isomÃtricas em grupos de Lie nilpotentes e solÃveis." Universidade Federal do CearÃ, 2008. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=5541.

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CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel Superior
Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico
Neste trabalho, demonstramos teoremas estabelecendo condiÃÃes suficientes para a existÃncia de imersÃes isomÃtricas com curvatura extrÃnseca prescrita em grupos de Lie nilpotentes e solÃveis. Obtemos assim uma generalizaÃÃo do Teorema Fundamental da Teoria de Subvariedades em Rn e, em particular, obtemos resultados de imersÃo em todos os grupos tipo-Heisenberg e em todos os espaÃos de Damek-Ricci.
In this paper, we prove theorems establishing sufficient conditions to existence for isometric immersions with prescribed extrinsic curvature in two-step nilpotent Lie groups and solvmanifolds. We obtain a generalization of the Fundamental Theorem of Submanifold Theory in Rn and, in particular, we one has immersion results in the generally Heisenberg type groups and Damek-Ricci spaces.

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Wuttke, Sebastian. "Some aspects of the Wilson loop." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät I, 2015. http://dx.doi.org/10.18452/17225.

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Diese Arbeit wird durch die AdS/CFT Korrespondenz, sowie durch die Dualität zwischen lichtartigen, polygonalen Wilsonschleifen und Gluonenstreuamplituden in N=4 Super-Yang-Mills-Theorie motiviert. Bei starker Kopplung haben lichtartige, polygonale Wilsonschleifen und Gluonenstreuamplituden eine Beschreibung über raumartige Minimalflächen in AdS5. Wir benutzen eine Pohlmeyerreduktion, um eine Klassifikation aller raumartigen Minimalflächen in AdS3xS3 mit flachen Projektionen herzuleiten. Diese Klassifikation enthält neun verschiedene Klassen von Flächen. Dabei treten raumartige, zeitartige und degenerierte AdS3-Projektionen auf. Bei denjenigen Lösungen, die einen geschlossenen, polygonalen und lichtartigen Rand besitzen, berechnen wir den regularisierten Flächeninhalt. Bei schwacher Kopplung erfüllen lichtartige, polygonale Wilsonschleifen und Gluonenstreuamplituden den um eine Remainderfunktion korrigierten BDS-Ansatz. Wir präsentieren eine Technik, die auf einer Renormierungsgruppengleichung für selbstschneidende Wilsonschleifen beruht, mit der wir die Divergenzen der Remainderfunktion in diesem Limes berechnen können. Mittels dieser Technik analysieren wir zwei Arten des Selbstschnittes. Im Falle des Selbstschnittes zwischen zwei Ecken berechnen wir die führenden Divergenzen bis zur vierten Schleifenordnung. Beim Selbstschnitt zwischen zwei Kanten berechnen wir die führenden und nächstfolgenden Divergenzen bis zur vierten Schleifenordnung und präsentieren eine analytische Fortsetzung in die Region der Euklidischen Wilsonschleifen und sagen bestimmte Terme vorher, die in dem unbekannten analytischen Ausdruck für die Remainderfunktion enthalten sein müssen.
This thesis is motivated by the AdS/CFT correspondence and the duality between gluon scattering amplitudes and light-like polygonal Wilson loops in N=4 super Yang-Mills theory. At strong coupling light-like polygonal Wilson loops and gluon scattering amplitudes have a description in terms of space-like minimal surfaces in AdS5. We use a Pohlmeyer reduction to derive a classification of all space-like minimal surfaces in AdS3xS3 that have flat projections. The classification consists of nine different classes and contains space-like, time-like and degenerated AdS3 projections. For solutions that admit a closed light-like polygonal boundary we calculate the regularized area. At weak coupling light-like polygonal Wilson loops and gluon scattering amplitudes obey the BDS Ansatz corrected by a remainder function. We present a renormalisation group equation technique using self-crossing Wilson loops to extract the divergences of the remainder function in this limit. Using this technique we analyse two different types of self-crossing. We present the leading and sub-leading divergences up to four loops for a crossing between two edges and the leading divergences for a crossing between two vertices. For a crossing between two edges we present an analytic continuation to the euclidean regime to predict certain terms that have to occur in the unknown analytic expression of the remainder function.

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Li, Jin Chuan, and 李金川. "Some uniqueness theorems for the minimal surface equation on an unbounded domain in R2." Thesis, 1995. http://ndltd.ncl.edu.tw/handle/83646109159180482059.

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Books on the topic "Minimal surface equation"

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1931-, Colares A. Gervasio, ed. Minimal surfaces in IR³. Berlin: Springer-Verlag, 1986.

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P, Minicozzi William, ed. A course in minimal surfaces. Providence, R.I: American Mathematical Society, 2011.

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Hitchin, N. J. Monopoles, minimal surfaces, and algebraic curves. Montréal, Québec, Canada: Presses de l'Université de Montréal, 1987.

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Stefan, Hildebrandt, and Tromba Anthony, eds. Global analysis of minimal surfaces. 2nd ed. Heidelberg: Springer, 2010.

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Paul, Krée, ed. Ennio de Giorgi Colloquium. Boston: Pitman Advanced Pub. Program, 1985.

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Conference on Multigrid Methods (2nd 1985 Cologne, Germany). Multigrid methods II: Proceedings of the 2nd European Conference on Multigrid Methods, held at Cologne, October 1-4, 1985. Berlin: Springer-Verlag, 1986.

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1966-, Pérez Joaquín, and Galvez José A. 1972-, eds. Geometric analysis: Partial differential equations and surfaces : UIMP-RSME Santaló Summer School geometric analysis, June 28-July 2, 2010, University of Granada, Granada, Spain. Providence, R.I: American Mathematical Society, 2012.

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author, Tkachev Vladimir 1963, and Vlăduț, S. G. (Serge G.), 1954- author, eds. Nonlinear elliptic equations and nonassociative algebras. Providence, Rhode Island: American Mathematical Society, 2014.

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Southeast Geometry Seminar (15th 2009 University of Alabama at Birmingham). Geometric analysis, mathematical relativity, and nonlinear partial differential equations: Southeast Geometry Seminars Emory University, Georgia Institute of Technology, University of Alabama, Birmingham, and the University of Tennessee, 2009-2011. Edited by Ghomi Mohammad 1969-. Providence, Rhode Island: American Mathematical Society, 2013.

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Mann, Peter. Constrained Lagrangian Mechanics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0008.

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This chapter builds on the previous two chapters to tackle constrained systems, using Lagrangian mechanics and constrained variations. The first section deals with holonomic constraint equations using Lagrange multipliers; these can be used to reduce the number of coordinates until a linearly independent minimal set is obtained that describes a constraint surface within configuration space, so that Lagrange equations can be set up and solved. Motion is understood to be confined to a constraint submanifold. The variational formulation of non-holonomic constraints is then discussed to derive the vakonomic formulation. These erroneous equations are then compared to the central Lagrange equation, and the precise nature of the variations used in each formulation is investigated. The vakonomic equations are then presented in their Suslov form (Suslov–vakonomic form) in an attempt to reconcile the two approaches. In addition, the structure of biological membranes is framed as a constrained optimisation problem.

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Book chapters on the topic "Minimal surface equation"

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Rønquist, Einar M., and Øystein Tråsdahl. "Minimal Surface Equation." In Encyclopedia of Applied and Computational Mathematics, 920–23. Berlin, Heidelberg: Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-540-70529-1_377.

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Simon, Leon. "The Minimal Surface Equation." In Geometry V, 239–66. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/978-3-662-03484-2_5.

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Nirenberg, Louis. "I.4. Minimal Surface Equation." In James Serrin. Selected Papers, 241–82. Basel: Springer Basel, 2014. http://dx.doi.org/10.1007/978-3-0348-0845-3_4.

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Tomter, Per. "On Dynamical Systems and the Minimal Surface Equation." In From Topology to Computation: Proceedings of the Smalefest, 259–69. New York, NY: Springer US, 1993. http://dx.doi.org/10.1007/978-1-4612-2740-3_26.

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Heinonen, Esko. "Survey on the Asymptotic Dirichlet Problem for the Minimal Surface Equation." In Minimal Surfaces: Integrable Systems and Visualisation, 111–29. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-68541-6_7.

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Dierkes, Ulrich. "Singular Minimal Surfaces." In Geometric Analysis and Nonlinear Partial Differential Equations, 177–93. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-642-55627-2_11.

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López, Rafael. "The Translating Soliton Equation." In Minimal Surfaces: Integrable Systems and Visualisation, 187–216. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-68541-6_11.

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Heinz, Erhard. "On quasi-minimal surfaces." In Calculus of Variations and Partial Differential Equations, 139–45. Berlin, Heidelberg: Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/bfb0082892.

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Wang, Guangyin. "Minimal Surfaces in Riemannian Manifolds." In Partial Differential Equations in China, 104–10. Dordrecht: Springer Netherlands, 1994. http://dx.doi.org/10.1007/978-94-011-1198-0_8.

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Polthier, Konrad. "Unstable Periodic Discrete Minimal Surfaces." In Geometric Analysis and Nonlinear Partial Differential Equations, 129–45. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-642-55627-2_9.

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Conference papers on the topic "Minimal surface equation"

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Foust, Henry, and Malay Ghosehajra. "Design Curves Utilized for Production Levels Associated With an Ultrafiltration Process." In ASME 2009 Fluids Engineering Division Summer Meeting. ASMEDC, 2009. http://dx.doi.org/10.1115/fedsm2009-78029.

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In this paper, an equation for permeate rates associated with dead-end filtration is shown to be applicable to a pilot scale study of an ultrafiltration process being designed and built at the Hanford Department of Energy facility. This permeate rate equation was utilized in mass balance equations for mass of solids and sodium within the system, and forms the basis for design curves to determine the minimal membrane surface area for a prescribed treatment time and other conditions.

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Zakharov, Vladimir, Donald Resio, and Andrei Pushkarev. "On the Tuning-Free Statistical Model of Ocean Surface Waves." In ASME 2018 37th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/omae2018-78417.

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Absence of mathematically justified criteria during development of the wind energy input and wave breaking energy dissipation source terms in Hasselmann equation (HE), used as the framework of modern operational wave forecasting models, lead to creation of plethora of parameterizations, having enormous scatter, disconnected from the physical background and obeying dozens of tuning parameters to adjust the HE model to the specific situation. We show that it’s possible, based on analytical analysis and experimental observation data, to create the new set of source terms, reproducing experimental observations with minimal number of tuning parameters. We also numerically analyze six historically developed and new wind input source terms for their ability to hold specific invariants, related to HE self-similar nature. The degree of preservation of those invariants could be used as their selection tool. We hope that this research is the step toward the creation of physically justified tuning-free operational models.

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Shen, Cai, Chia-fon F. Lee, and Way L. Cheng. "Estimation of the Occurrence of Micro-Explosion for the Diesel-Biofuel Multi-Components Droplets." In ASME 2012 Internal Combustion Engine Division Fall Technical Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/icef2012-92175.

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A numerical study of micro-explosion in multi-component bio-fuel droplets is presented. The onset of micro-explosion is characterized by the normalized onset radius (NOR). Bubble expansion is described by a modified Rayleigh equation. The final breakup is modeled from a surface energy approach by determining the minimal surface energy (MSE). After the breakup, the Sauter mean radius (SMR) for initially small size droplets can be estimated from a look-up table generated from the current breakup model. There exists an optimal droplet size for the onset of micro-explosion. The MSE approach reaches the same conclusion as previous model determining atomization by aerodynamic disturbances. The SMR of secondary droplets can be estimated by the possible void fraction, ε, at breakup and the corresponding surface Weber number, Wes, at the minimal surface energy ratio (MSER). Biodiesel can enhance micro-explosion in the fuel blends of ethanol and diesel (which is represented by a single composition tetradecane). The simulation results show that the secondary atomization of bio-fuel and diesel blends can be achieved by micro-explosion under typical diesel engine operation conditions.

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Ratkus, Andris, and Toms Torims. "Mathematical Model of the Influence of Process Parameters on Geometrical Values and Shape in MIG/MAG Multi-Track Cladding." In ASME 2014 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/imece2014-37479.

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The cladding process in the present case contributes to a repair technology, in which a new layer of material is created by using Metal Inert Gas/Metal Active Gas technology on inner cylindrical surfaces, e.g. bucket bores or hydro cylinders. The cladded layer is subsequently subjected to mechanical processing. Although cladding technology itself is well known, its results are hardly ever predicted with regard to inner surface renewal. In this paper, we explore the influence of cladding technological process parameters on geometrical values: the thickness, cross-section areas and shape of the newly cladded layer are established. Current research provided significant information which enabled mathematical models to be developed for inner surface cladding. Polynomial regression was used to create a mathematical model, where coefficients established with the SYSTAT software and their adequacy was checked using the analysis of variance technique. Thus an equation was obtained to help identify the effects of parameters on the final result. The most significant factor identified in cladding geometry is the amount of material that is supplied to the melting pool, followed by the process speed and heat input. The obtained coefficient describing the amount of material is presented, together with equations for calculating minimal thickness, efficient thickness and the multi-track cladding shape.

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Chiang, Ting-Lung, and George S. Dulikravich. "Inverse Design of Composite Turbine Blade Circular Coolant Flow Passages." In ASME 1986 International Gas Turbine Conference and Exhibit. American Society of Mechanical Engineers, 1986. http://dx.doi.org/10.1115/86-gt-190.

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An inverse design and optimization method is developed to determine the proper size and location of the circular shaped holes (coolant flow passages) in a composite turbine blade. The temperature distributions specified on the outer blade surface and on the surfaces of the inner holes can be prescribed a priori. In addition, heat flux distribution on the outer blade surface can be prescribed and iteratively enforced using optimization procedures. The prescribed heat flux distribution on the outer surface is iteratively approached by using the Sequential Unconstrained Minimization Technique (SUMT) to adjust the sizes and locations of the initially guessed circular holes. During each optimization iteration, a two-dimensional heat conduction equation is solved using direct Boundary Element Method (BEM) with linear temperature singularity distribution. For manufacturing purposes the additional constraints are enforced assuring the minimal prescribed blade wall thickness and spacing between the walls of two neighboring holes. The method is applicable to both single material (homogeneous) and coated (composite) turbine blades. Three different cases were tested to prove the feasibility and the accuracy of the method.

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Alkhamis, Nawaf, Ali Anqi, Dennis E. Oztekin, Abdulmohsen Alsaiari, and Alparslan Oztekin. "Gas Separation Using a Membrane." In ASME 2013 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/imece2013-62764.

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Computational fluid dynamics simulation will be conducted for multicomponent fluid flows in a channel containing spacers. The Navier-Stokes equation and the species transport equations are solved for various values of Reynolds numbers. The membrane will be modeled as a functional surface, where the membrane fluxes of each component will be determined based on the local partial pressures of each species, the permeability and the selectivity of the membrane. Laminar flow modeling is employed for the flow inside the channel without the spacers; while k-ω turbulent modeling is used to simulate the flow inside the channel with the spacer, for Re = 100, 150 and 200. The spacers are placed in an inline arrangement. The presence of spacers in the channel improves the membrane performance at Re = 200. The effects of the spacer on the separation process at low flow speeds (Re = 100 and 150) are negligible. The performance of the system will be measured by the maximum mass separation with minimal friction losses.

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Lyathakula, Karthik Reddy, Sevki Cesmeci, Mohammad Fuad Hassan, Hanping Xu, and Jing Tang. "A Proof-of-Concept Study of a Novel Elasto-Hydrodynamic Seal for CO2." In ASME 2022 Power Conference. American Society of Mechanical Engineers, 2022. http://dx.doi.org/10.1115/power2022-86607.

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Abstract This paper deals with numerical studies of a novel Elasto-Hydrodynamic Seal (EHD), which has been developed for supercritical CO2 (sCO2) turbomachinery applications. Current sCO2 turbomachinery suffer from high leakage rates, which is creating a major roadblock for the full realization of sCO2 power technology. The high leakage rates not only penalize the efficiencies but also create environmental concerns due to greenhouse effects caused by increased CO2 discharge to the atmosphere. The proposed novel EHD seal needs to work at elevated pressures (12–35 MPa) and temperatures (350–700 °C) with low leakage and minimal wear. The unique mechanism of such a EHD seal provides a self-regulated constriction effect to restrict the flow without substantial material contact, thereby minimizing the leakage and wear. This work utilizes a physics-based modeling approach. The flow through the gradually narrowing seal clearance is modeled by the well-known Reynolds equation in EHD lubrication theory. Whereas the deformation of the seal is modeled by using the governing equations of three-dimensional solid mechanics. As for the solution methodology, COMSOL’s Thin-Film Flow and Solid Mechanics Modules were employed with their powerful capabilities. The numerical results were presented and discussed. It was observed that the Reynolds equation fully coupled with the surface deformation was able to capture the constriction effect successfully. It was also interesting to observe that the seal leakage followed a quadratic trend with increasing pressure differential, which can become advantageous for high-pressure applications such as sCO2 power generation technology.

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Hegde, Shreyas S., Narendran Ganesan, and N. Gnanasekaran. "Conjugate Heat Transfer in a Hexagonal Micro Channel Using Hybrid Nano Fluids." In ASME 2016 14th International Conference on Nanochannels, Microchannels, and Minichannels collocated with the ASME 2016 Heat Transfer Summer Conference and the ASME 2016 Fluids Engineering Division Summer Meeting. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/icnmm2016-7961.

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Research is being focused on the use of micro channels with nano fluids as the heat sinks. This requires fundamental understanding of the heat transfer phenomenon in micro channels. The objective of this paper is to present results from a numerical study on laminar forced convection in a Hexagonal Micro Channel (HMC) heat sink. In particular, the numerical study is carried out using a single phase model. The fluid considered is Alumina-Copper hybrid Nano fluid. The performance of Al2O3+Cu+water is compared with Al2O3+water nano fluid and pure water with different volume fractions. The solid region of the channel is assumed as aluminum with a hydraulic diameter of 175μm. The solid and fluid regions of the micro channel are discretized using finite volume method by combining Navier Stokes equation and energy equation for conjugate heat transfer. The thermo physical properties for alumina nanoparticles are calculated by considering it as a spherical particle of 45nm diameter. The effect of surface roughness on convective heat transfer coefficient and pressure drop for the case of nano fluids is also considered. The analysis is further extended by adding pulsating input and by varying the velocity sinusoidally. The Brownian motion of nano particles is increased to study the efficiency of the heat sink. This ensures all the nano particles are in suspension and the randomness increases the micro convection in the fluid. Incorporating the pulsating flow increases the dispersion of the heat in the nano fluid at a faster rate and also decreases particle settlement in laminar flow. The combined effect of surface roughness and pulsating flow accounts for the change in the velocity profile and thermal boundary layer of the channel. Also the effect of surface roughness ranging from 0.2–0.6 is attempted and the variations in pressure drop, Nusselt number, and heat transfer coefficient are studied. The influence of hexagonal geometry and its interaction with alumina nano fluids is intensively studied by evaluating a three dimensional conjugate heat transfer model. The effect of side wall angle of 45°, 50° and 55° are computed to relate the velocity function with pressure drop, surface roughness and local heat transfer coefficient. The variation of Nusselt number with very low volume fraction of nano particles with a minimal amount of pressure drop is also presented.

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Jugeau, F. "Quark-antiquark bound state equation in the Wilson loop approach with minimal surfaces." In QCD@WORK 2005: International Workshop on Quantum Chromodynamics: Theory and Experiment. AIP, 2006. http://dx.doi.org/10.1063/1.2163769.

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Strömberg, Niclas. "Automatic Postprocessing of Topology Optimization Solutions by Using Support Vector Machines." In ASME 2018 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/detc2018-85051.

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The postprocessing step from the density result in topology optimization to a parametric CAD model is typically most time consuming and usually involves several hands on maneuvers by an engineer. In this paper we propose an approach in order to automate this step by using soft non-linear support vector machines (SVM). Our idea is to generate the boundaries separating regions of material (elements with densities equal to one) and no material (elements with densities equal zero) obtained from topology optimization automatically by using SVM. The hyper-surface of the SVM can then in the long run be explicitly implemented in any CAD software. In this work we generate these hypersurfaces by solving the dual formulation of the SVM with soft penalization and nonlinear kernel functions using quadratic programming or the sequential minimal optimization approach. The proposed SVM-based postprocessing approach is studied on topology optimization results of orthotropic elastic design domains with mortar contact conditions studied most recently in a previous work. The potential energy of several bodies with nonmatching meshes is maximized. In such manner no extra adjoint equation is needed. Intermediate density values are penalized using SIMP or RAMP, and the regularization is obtained by applying sensitivity or density filters following the approaches of Sigmund and Bourdin. The study demonstrates that the SVM-based postprocessing approach automatically generates proper hypersurfaces which can be used efficiently in the CAD modelling.

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Reports on the topic "Minimal surface equation"

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Wu, Yingjie, Selim Gunay, and Khalid Mosalam. Hybrid Simulations for the Seismic Evaluation of Resilient Highway Bridge Systems. Pacific Earthquake Engineering Research Center, University of California, Berkeley, CA, November 2020. http://dx.doi.org/10.55461/ytgv8834.

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Bridges often serve as key links in local and national transportation networks. Bridge closures can result in severe costs, not only in the form of repair or replacement, but also in the form of economic losses related to medium- and long-term interruption of businesses and disruption to surrounding communities. In addition, continuous functionality of bridges is very important after any seismic event for emergency response and recovery purposes. Considering the importance of these structures, the associated structural design philosophy is shifting from collapse prevention to maintaining functionality in the aftermath of moderate to strong earthquakes, referred to as “resiliency” in earthquake engineering research. Moreover, the associated construction philosophy is being modernized with the utilization of accelerated bridge construction (ABC) techniques, which strive to reduce the impact of construction on traffic, society, economy and on-site safety. This report presents two bridge systems that target the aforementioned issues. A study that combined numerical and experimental research was undertaken to characterize the seismic performance of these bridge systems. The first part of the study focuses on the structural system-level response of highway bridges that incorporate a class of innovative connecting devices called the “V-connector,”, which can be used to connect two components in a structural system, e.g., the column and the bridge deck, or the column and its foundation. This device, designed by ACII, Inc., results in an isolation surface at the connection plane via a connector rod placed in a V-shaped tube that is embedded into the concrete. Energy dissipation is provided by friction between a special washer located around the V-shaped tube and a top plate. Because of the period elongation due to the isolation layer and the limited amount of force transferred by the relatively flexible connector rod, bridge columns are protected from experiencing damage, thus leading to improved seismic behavior. The V-connector system also facilitates the ABC by allowing on-site assembly of prefabricated structural parts including those of the V-connector. A single-column, two-span highway bridge located in Northern California was used for the proof-of-concept of the proposed V-connector protective system. The V-connector was designed to result in an elastic bridge response based on nonlinear dynamic analyses of the bridge model with the V-connector. Accordingly, a one-third scale V-connector was fabricated based on a set of selected design parameters. A quasi-static cyclic test was first conducted to characterize the force-displacement relationship of the V-connector, followed by a hybrid simulation (HS) test in the longitudinal direction of the bridge to verify the intended linear elastic response of the bridge system. In the HS test, all bridge components were analytically modeled except for the V-connector, which was simulated as the experimental substructure in a specially designed and constructed test setup. Linear elastic bridge response was confirmed according to the HS results. The response of the bridge with the V-connector was compared against that of the as-built bridge without the V-connector, which experienced significant column damage. These results justified the effectiveness of this innovative device. The second part of the study presents the HS test conducted on a one-third scale two-column bridge bent with self-centering columns (broadly defined as “resilient columns” in this study) to reduce (or ultimately eliminate) any residual drifts. The comparison of the HS test with a previously conducted shaking table test on an identical bridge bent is one of the highlights of this study. The concept of resiliency was incorporated in the design of the bridge bent columns characterized by a well-balanced combination of self-centering, rocking, and energy-dissipating mechanisms. This combination is expected to lead to minimum damage and low levels of residual drifts. The ABC is achieved by utilizing precast columns and end members (cap beam and foundation) through an innovative socket connection. In order to conduct the HS test, a new hybrid simulation system (HSS) was developed, utilizing commonly available software and hardware components in most structural laboratories including: a computational platform using Matlab/Simulink [MathWorks 2015], an interface hardware/software platform dSPACE [2017], and MTS controllers and data acquisition (DAQ) system for the utilized actuators and sensors. Proper operation of the HSS was verified using a trial run without the test specimen before the actual HS test. In the conducted HS test, the two-column bridge bent was simulated as the experimental substructure while modeling the horizontal and vertical inertia masses and corresponding mass proportional damping in the computer. The same ground motions from the shaking table test, consisting of one horizontal component and the vertical component, were applied as input excitations to the equations of motion in the HS. Good matching was obtained between the shaking table and the HS test results, demonstrating the appropriateness of the defined governing equations of motion and the employed damping model, in addition to the reliability of the developed HSS with minimum simulation errors. The small residual drifts and the minimum level of structural damage at large peak drift levels demonstrated the superior seismic response of the innovative design of the bridge bent with self-centering columns. The reliability of the developed HS approach motivated performing a follow-up HS study focusing on the transverse direction of the bridge, where the entire two-span bridge deck and its abutments represented the computational substructure, while the two-column bridge bent was the physical substructure. This investigation was effective in shedding light on the system-level performance of the entire bridge system that incorporated innovative bridge bent design beyond what can be achieved via shaking table tests, which are usually limited by large-scale bridge system testing capacities.

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A SURROGATE MODEL TO ESTIMATE THE AXIAL COMPRESSIVE CAPACITY OF COLD-FORMED STEEL OPEN BUILT-UP SECTIONS. The Hong Kong Institute of Steel Construction, August 2022. http://dx.doi.org/10.18057/icass2020.p.316.

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This paper proposed a surrogate model to simplify the process of estimating the axial compressive capacity of cold-formed steel (CFS) open built-up sections composed of lipped channels with different section sizes, thickness, length, and connector spacing. The surrogate model was developed based on the current design methods, i.e., the Effective Width Method (EWM) and Direct Strength Method (DSM), which are codified in the North American Specification AISI S100-16. This new model features two surface regression equations with a boundary inequality criteria, anchored on two important parameters, i.e., modified slenderness ratio, (KL/r)m and minimum thickness-to-width ratio (t/w)min of the built-up sections. The model was validated with 1089 sets of the experimental results data collected from previous research tested on the axial capacity of CFS open built-up sections with the different design configurations. The proposed surrogate model is aimed to simplify the design process among practising engineers for a quick preliminary calculation of the axial compressive capacity of these new CFS open built-up sections.

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