Results 11 to 20 of about 241,381 (266)
Journal of Mathematical Physics, 2007 This paper presents the solution to the following optimization problem: What is the shape of the two-dimensional region that minimizes the average Lp distance between all pairs of points if the area of this region is held fixed? Variational techniques are used to show that the boundary curve of the optimal region satisfies a nonlinear integral equation.
Bender, Carl M., Bender, Michael A.
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A Linear View on Shape Optimization
SIAM Journal on Control and Optimization, 2023 Shapes do not define a linear space. This paper explores the linear structure of deformations as a representation of shapes. This transforms shape optimization to a variant of optimal control. The numerical challenges of this point of view are highlighted and a novel linear version of the second shape derivative is proposed leading to particular ...
Stephan Schmidt 0003, Volker H. Schulz
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Optimal shapes of compact strings [PDF]
Nature, 2000 Optimal geometrical arrangements, such as the stacking of atoms, are of relevance in diverse disciplines. A classic problem is the determination of the optimal arrangement of spheres in three dimensions in order to achieve the highest packing fraction; only recently has it been proved that the answer for infinite systems is a face-centred-cubic lattice.
MARITAN, AMOS +3 more
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Multiphase Shape Optimization Problems [PDF]
SIAM Journal on Control and Optimization, 2014 This paper is devoted to the analysis of multiphase shape optimization problems, which can formally be written as $\min\Big\{{g}(F_1(Ω_1),\dots,F_h(Ω_h))+ m\vert\,\bigcup_{i=1}^hΩ_i\vert :\ Ω_i\subset D,\ Ω_i\cap Ω_j =\emptyset\Big\},$ where $D\subset\mathcal{R}^d$ is a given bounded open set, $\vertΩ_i\vert$ is the Lebesgue measure of $Ω_i$ and $m$ is
Bucur D., Velichkov B.
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On Convergence in Elliptic Shape Optimization [PDF]
SIAM Journal on Control and Optimization, 2007 This paper is aimed at analyzing the existence and convergence of approximate solutions in shape optimization. Two questions arise when one applies a Ritz-Galerkin discretization to solve the necessary condition: does there exists an approximate solution and how good does it approximate the solution of the original infinite dimensional problem?
Harbrecht, Helmut +2 more
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Blade Structure Design Based on Topology Optimization and Shape Optimization
Hangkong gongcheng jinzhan, 2020 The blade cross-section design of the helicopter rotor is the basis for studying the rotor dynamics design. A two-stage optimization design method combining joint topology optimization and shape optimization is proposed, which can be used for the design ...
ZHOU Cheng, LIN Jie, LIU Yong
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SHAPE OPTIMIZATION AND REARRANGEMENTS
Far East Journal of Dynamical Systems, 2007 In this note we consider a shape optimization problem with a weighted volume constraint. Using Burton’s theory of rearrangements of functions we transfer the problem into a rearrangement optimization problem. Existence, uniqueness and convexity of optimal shapes are addressed.
Allison, David, Emamizadeh, Behrouz
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Shape Optimization by Pursuing Diffeomorphisms [PDF]
Computational Methods in Applied Mathematics, 2015 Abstract We consider PDE constrained shape optimization in the framework of finite element discretization of the underlying boundary value problem. We present an algorithm tailored to preserve and exploit the approximation properties of the finite element method, and that allows for arbitrarily high resolution of shapes. It employs (i) B-
Ralf Hiptmair, Alberto Paganini
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An active contour model for texture image segmentation using Rényi divergence measure
Mathematical Modelling and Analysis, 2022 This paper proposes an efficient method for active unsupervised texture segmentation. A new descriptor for texture features extractions based on Gaussian and mean curvature is constructed.
Sidi Yassine Idrissi
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Physical Review Letters, 2012 We present filling as a type of spatial subdivision problem similar to covering and packing. Filling addresses the optimal placement of overlapping objects lying entirely inside an arbitrary shape so as to cover the most interior volume. In n-dimensional space, if the objects are polydisperse n-balls, we show that solutions correspond to sets of ...
Phillips, Carolyn L. +3 more
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