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The double bubble conjecture
 FOCUS, Math. Assn. Amer
, 1995
"... We prove that the standard double bubble provides the leastarea way to enclose and separate two regions of prescribed volume in R 3. 1. ..."
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Cited by 20 (1 self)
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We prove that the standard double bubble provides the leastarea way to enclose and separate two regions of prescribed volume in R 3. 1.
Capturing the Behavior of Bubbles and Drops Using the Variational Level Set Approach
, 1998
"... this article we shall develop a class of algorithms to capture the behavior of multiphase b ubbles and drops in two and three space dimensions. We include some very interesting and recently analyzed steady state casese.g. [8], where "double bubbles minimize." This general class of problems has r ..."
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Cited by 17 (7 self)
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this article we shall develop a class of algorithms to capture the behavior of multiphase b ubbles and drops in two and three space dimensions. We include some very interesting and recently analyzed steady state casese.g. [8], where "double bubbles minimize." This general class of problems has recently received a lot of attention [19]. 1 Research supported by ARPA/ONR N0001492J1890, NSF DMS9404942, and ARO DAAH049510155 2 H. K. Zhao is currently at: Mathematics Department, Stanford University, Stanford, CA 943052125. 495 00219991/98 $25.00 Cop yright c 1998 by Academic Press All rights of reproduction in any form reserved. 496 ZHAO ET AL. W e shall use the level set method, first developed in [15], which has been successfully applied to a variety of problems, in order to capture the evolution of complex interf aces in fluid dynamics and elsewhere (see, e.g., [13, 14] and the references therein). Topological changes and the development of singularities pose no difficulties for this method. As initially designed in [15], the levelset method applied naturally to problems in which there is a clear distinction between "inside" and "outside" of a (possibly multiply connected) re gion. Two phase flow problems coupling the motion to the full NavierStokes of Euler equations [2, 21] or to heat release [3], as well as unstable vortex sheet motion [5] and other unstable fronts [6], were recently solved using this method, extending its utility beyond the geometrydri
Interval Computations as an Important Part of Granular Computing: An Introduction
"... This chapter provides a general introduction to interval computations, especially to interval computations as an important part of granular computing. ..."
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Cited by 1 (0 self)
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This chapter provides a general introduction to interval computations, especially to interval computations as an important part of granular computing.
© Hindawi Publishing Corp. THE DOUBLE BUBBLE PROBLEM IN SPHERICAL AND HYPERBOLIC SPACE
, 2002
"... We prove that the standard double bubble is the leastarea way to enclose and separate two regions of equal volume in H 3, and in S 3 when the exterior is at least ten percent of S 3. 2000 Mathematics Subject Classification: 49Q10, 53A10. 1. Introduction. The ..."
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We prove that the standard double bubble is the leastarea way to enclose and separate two regions of equal volume in H 3, and in S 3 when the exterior is at least ten percent of S 3. 2000 Mathematics Subject Classification: 49Q10, 53A10. 1. Introduction. The