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Academic literature on the topic 'Soap Bubble Theorem'

Author: Grafiati
Published: 10 March 2023

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Journal articles on the topic "Soap Bubble Theorem"

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Magnanini, Rolando, and Giorgio Poggesi. "On the stability for Alexandrov’s Soap Bubble theorem." Journal d'Analyse Mathématique 139, no. 1 (October 2019): 179–205. http://dx.doi.org/10.1007/s11854-019-0058-y.

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Colasuonno, Francesca, and Fausto Ferrari. "The Soap Bubble Theorem and a $ p $-Laplacian overdetermined problem." Communications on Pure & Applied Analysis 19, no. 2 (2020): 983–1000. http://dx.doi.org/10.3934/cpaa.2020045.

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Magnanini, Rolando, and Giorgio Poggesi. "Serrin's problem and Alexandrov's Soap Bubble Theorem: enhanced stability via integral identities." Indiana University Mathematics Journal 69, no. 4 (2020): 1181–205. http://dx.doi.org/10.1512/iumj.2020.69.7925.

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Magnanini, Rolando, and Giorgio Poggesi. "Interpolating estimates with applications to some quantitative symmetry results." Mathematics in Engineering 5, no. 1 (2022): 1–21. http://dx.doi.org/10.3934/mine.2023002.

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<abstract><p>We prove interpolating estimates providing a bound for the oscillation of a function in terms of two $ L^p $ norms of its gradient. They are based on a pointwise bound of a function on cones in terms of the Riesz potential of its gradient. The estimates hold for a general class of domains, including, e.g., Lipschitz domains. All the constants involved can be explicitly computed. As an application, we show how to use these estimates to obtain stability for Alexandrov's Soap Bubble Theorem and Serrin's overdetermined boundary value problem. The new approach results in several novelties and benefits for these problems.</p></abstract>
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Santilli, Mario. "Normal bundle and Almgren’s geometric inequality for singular varieties of bounded mean curvature." Bulletin of Mathematical Sciences 10, no. 01 (April 2020): 2050008. http://dx.doi.org/10.1142/s1664360720500083.

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In this paper we deal with a class of varieties of bounded mean curvature in the viscosity sense that has the remarkable property to contain the blow up sets of all sequences of varifolds whose mean curvatures are uniformly bounded and whose boundaries are uniformly bounded on compact sets. We investigate the second-order properties of these varieties, obtaining results that are new also in the varifold’s setting. In particular we prove that the generalized normal bundle of these varieties satisfies a natural Lusin (N) condition, a property that allows to prove a Coarea-type formula for their generalized Gauss map. Then we use this formula to extend a sharp geometric inequality of Almgren and the associated soap bubble theorem. As a consequence of the geometric inequality we obtain sufficient conditions to conclude that the area-blow-up set is empty for sequences of varifolds whose first variation is controlled.
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FENG, Y., H. J. RUSKIN, and B. ZHU. "PERSISTENCE MEASURES FOR 2D SOAP FROTH." International Journal of Modern Physics C 14, no. 09 (November 2003): 1163–70. http://dx.doi.org/10.1142/s0129183103005285.

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Soap froths as typical disordered cellular structures, exhibiting spatial and temporal evolution, have been studied through their distributions and topological properties. Recently, persistence measures, which permit representation of the froth as a two-phase system, have been introduced to study froth dynamics at different length scales. Several aspects of the dynamics may be considered and cluster persistence has been observed through froth experiment. Using a direct simulation method, we have investigated persistent properties in 2D froth both by monitoring the persistence of survivor cells, a topologically independent measure, and in terms of cluster persistence. It appears that the area fraction behavior for both survivor and cluster persistence is similar for Voronoi froth and uniform froth (with defects). Survivor and cluster persistent fractions are also similar for a uniform froth, particularly when geometries are constrained, but differences observed for the Voronoi case appear to be attributable to the strong topological dependency inherent in cluster persistence. Survivor persistence, on the other hand, depends on the number rather than size and position of remaining bubbles and does not exhibit the characteristic decay to zero.
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Thien, Vo Minh. "A bubble-enhanced quadrilateral finite element for estimation bearing capacity factors of strip footing." Journal of Science and Technology in Civil Engineering (STCE) - NUCE 15, no. 2 (April 27, 2021): 77–89. http://dx.doi.org/10.31814/stce.nuce2021-15(2)-07.

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In this paper, a computational approach using a combination of the upper bound theorem and the bubble-enhanced quadrilateral finite element (FEM-Qi6) is proposed to evaluate bearing capacity factors of strip footing in cohesive-frictional soil. The new element is built based on the quadrilateral element (Q4) by adding a pair of internal nodes to solve the volumetric locking phenomenon. In the upper bound finite element limit analysis, the soil behaviour is described as a perfectly plastic material and obeys associated plastic flow rule following the Mohr-Coulomb failure criterion. The discrete limit analysis problem can be formulated in the form of the well-known second-order cone programming to utilize the interior-point method efficiently. The bearing capacity factors of strip footing and failure mechanisms in both rough and smooth interfaces are obtained directly from solving the optimization problems and presented in design tables and charts for engineers to use. To demonstrate the accuracy of the proposed method, the results of bearing capacity factors using FEM-Qi6 were compared with those available in the literature. Keywords: limit analysis; bearing capacity factors; strip footing; SOCP; FEM-Qi6.
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Zhang, Dongliang. "Swarm Intelligence Based Structure Emergence for Parallel Processing: A Simulation of Mechanical Principle of Soap Bubbles." Journal of Information and Computational Science 10, no. 16 (November 1, 2013): 5409–19. http://dx.doi.org/10.12733/jics20103242.

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9

"On the geometry of composite bubbles." Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences 434, no. 1891 (August 8, 1991): 441–47. http://dx.doi.org/10.1098/rspa.1991.0103.

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Clusters of three and four soap bubbles in which all surfaces are spherical are analysed. A simple geometrical theorem pertaining to the collinearity of centres of various soap film surfaces in the three-bubble problem is restated in terms of projective configurations, and expressions for various distances and radii in this system are derived. An extension of the analysis to the four-bubble problem is explored.
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10

Gálvez, José A., Pablo Mira, and Marcos P. Tassi. "A quasiconformal Hopf soap bubble theorem." Calculus of Variations and Partial Differential Equations 61, no. 4 (May 5, 2022). http://dx.doi.org/10.1007/s00526-022-02222-7.

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AbstractWe show that any compact surface of genus zero in $${\mathbb {R}}^3$$ R 3 that satisfies a quasiconformal inequality between its principal curvatures is a round sphere. This solves an old open problem by H. Hopf, and gives a spherical version of Simon’s quasiconformal Bernstein theorem. The result generalizes, among others, Hopf’s theorem for constant mean curvature spheres, the classification of round spheres as the only compact elliptic Weingarten surfaces of genus zero, and the uniqueness theorem for ovaloids by Han, Nadirashvili and Yuan. The proof relies on the Bers-Nirenberg representation of solutions to linear elliptic equations with discontinuous coefficients.
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Dissertations / Theses on the topic "Soap Bubble Theorem"

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Ghaderi, Hazhar. "The Phase-Integral Method, The Bohr-Sommerfeld Condition and The Restricted Soap Bubble : with a proposition concerning the associated Legendre equation." Thesis, Uppsala universitet, Institutionen för fysik och astronomi, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-169572.

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After giving a brief background on the subject we introduce in section two the Phase-Integral Method of Fröman & Fröman in terms of the platform function of Yngve and Thidé. In section three we derive a different form of the radial Bohr-Sommerfeld condition in terms of the apsidal angle of the corresponding classical motion. Using the derived expression, we then show how easily one can calculate the exact energy eigenvalues of the hydrogen atom and the isotropic three-dimensional harmonic oscillator, we also derive an expression for higher order quantization condition. In section four we derive an expression for the angular frequencies of a restricted (0≤φ≤β) soap bubble and also give a proposition concerning the parameters l and m of the associated Legendre differential equation.
Vi använder Fröman & Frömans Fas-Integral Metod tillsammans med Yngve & Thidés plattformfunktion för att härleda kvantiseringsvilkoret för högre ordningar. I sektion tre skriver vi Bohr-Sommerfelds kvantiseringsvillkor på ett annorlunda sätt med hjälp av den så kallade apsidvinkeln (definierad i samma sektion) för motsvarande klassiska rörelse, vi visar också hur mycket detta underlättar beräkningar av energiegenvärden för väteatomen och den isotropa tredimensionella harmoniska oscillatorn. I sektion fyra tittar vi på en såpbubbla begränsad till området 0≤φ≤β för vilket vi härleder ett uttryck för dess (vinkel)egenfrekvenser. Här ger vi också en proposition angående parametrarna l och m tillhörande den associerade Legendreekvationen.
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2

Poggesi, Giorgio. "The Soap Bubble Theorem and Serrin's problem: quantitative symmetry." Doctoral thesis, 2019. http://hdl.handle.net/2158/1151383.

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Book chapters on the topic "Soap Bubble Theorem"

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Guckenheimer, Jean. "Singularities in Soap-Bubble-Like and Soap-Film-Like Surfaces." In Geometric Measure Theory and Minimal Surfaces, 155–71. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-10970-6_4.

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Morgan, Frank. "Soap Bubble Clusters." In Geometric Measure Theory, 121–38. Elsevier, 1995. http://dx.doi.org/10.1016/b978-0-12-506857-4.50017-5.

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Morgan, Frank. "Soap Bubble Clusters." In Geometric Measure Theory, 121–39. Elsevier, 2000. http://dx.doi.org/10.1016/b978-012506851-2/50013-3.

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Morgan, Frank. "Soap Bubble Clusters." In Geometric Measure Theory, 121–41. Elsevier, 2016. http://dx.doi.org/10.1016/b978-0-12-804489-6.50013-6.

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