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Packing ellipsoids with overlap [article]

Caroline Uhler, Stephen J. Wright
2012 arXiv   pre-print
The problem of packing ellipsoids of different sizes and shapes into an ellipsoidal container so as to minimize a measure of overlap between ellipsoids is considered.  ...  A bilevel optimization formulation is given, together with an algorithm for the general case and a simpler algorithm for the special case in which all ellipsoids are in fact spheres.  ...  We solve the resulting formulation using a combination of Algorithm 1 for sphere packing with Algorithm 4.4 for ellipsoid packing.  ... 
arXiv:1204.0235v1 fatcat:dbtvuoonxnan5huxkcfgsmgwti

Packing Ellipsoids with Overlap

Caroline Uhler, Stephen J. Wright
2013 SIAM Review  
The problem of packing ellipsoids of different sizes and shapes into an ellipsoidal container so as to minimize a measure of overlap between ellipsoids is considered.  ...  A bilevel optimization formulation is given, together with an algorithm for the general case and a simpler algorithm for the special case in which all ellipsoids are in fact spheres.  ...  We solve the resulting formulation using a combination of Algorithm 1 for sphere packing with Algorithm 4.4 for ellipsoid packing.  ... 
doi:10.1137/120872309 fatcat:6c7235rf5nfopfvp756vbly62q

A nonlinear programming model with implicit variables for packing ellipsoids

E. G. Birgin, R. D. Lobato, J. M. Martínez
2016 Journal of Global Optimization  
The reason is that the number of variables and constraints of ellipsoids' packing models is associated with the requirement that every pair of ellipsoids must not overlap.  ...  Usually, the computational effort associated with numerical optimization methods devoted to packing ellipsoids grows quadratically with respect to the number of ellipsoids being packed.  ...  pack a given set of identical ellipsoids; and (e) finding the cuboid with minimum volume that can pack a given set of identical ellipsoids.  ... 
doi:10.1007/s10898-016-0483-8 fatcat:azehg47drfgrvlzd25n4o6k4ja

PACKING OF ELLIPSOIDS IN A CONVEX CONTAINER

Yu. Ye. Pankratova, O. M. Khlud, V. M. Patsuk
2018 Системи управління навігації та зв'язку Збірник наукових праць  
We consider the problem of optimal packing of a given collection of unequal ellipsoids into an arbitrary convex container of minimal sizes.  ...  We provide computational results illustrated with figures.  ...  Instances with up to 100 ellipsoids.  ... 
doi:10.26906/sunz.2018.1.080 fatcat:bqbwx3rmpndptng35zbr77z7je

Optimizing Packing Fraction in Granular Media Composed of Overlapping Spheres [article]

Leah K. Roth, Heinrich M. Jaeger
2015 arXiv   pre-print
Direct experimental comparison with 3D-printed aspherical ellipsoids demonstrates that the triangular particles pack exceedingly well not only in the limit of large system size but also when confined to  ...  We validate the simulations with experiments using 3D-printed copies of the simplest member of the family, a planar particle consisting of three overlapping spheres with identical radius.  ...  All particle images were generated with Ovito (http://ovito.org/). 45 This work was supported by the National Science Foundation through CBET-1334426.  ... 
arXiv:1510.05718v1 fatcat:eqtxcdkx7fdfpnddwc7bhijt24

Optimizing packing fraction in granular media composed of overlapping spheres

Leah K. Roth, Heinrich M. Jaeger
2016 Soft Matter  
Direct experimental comparison with 3D-printed aspherical ellipsoids demonstrates that the triangular particles pack exceedingly well not only in the limit of large system size but also when confined to  ...  We validate the simulations with experiments using 3D-printed copies of the simplest member of the family, a planar particle consisting of three overlapping spheres with identical radius.  ...  All particle images were generated with Ovito (http://ovito.org/). 45 This work was supported by the National Science Foundation through CBET-1334426.  ... 
doi:10.1039/c5sm02335a pmid:26592541 fatcat:6fnqdwesxvhgvcodlaj7od5cna

Development of the mathematical model and the method to solve a problem on the optimization of packing the ellipsoids into a convex container

Olha Khlud, Olexander Pankratov, Olexander Pankratov, Tetyana Romanova, Tetyana Romanova
2018 Eastern-European Journal of Enterprise Technologies  
In order to make sure that the ellipsoids do not overlap with each other, the separating hyperplanes are constructed.  ...  of the ratio of the non-overlapping of ellipsoids.  ... 
doi:10.15587/1729-4061.2018.140722 fatcat:2ooabss4bbbtflrsuub26a3v4u

A Discrete Element Method to simulate the mechanical behavior of ellipsoidal particles for a fusion breeding blanket

M. Moscardini, Y. Gan, R.K. Annabattula, M. Kamlah
2017 Fusion engineering and design  
Sensitivity studies were carried out with different packing factors of the assembly and several aspect ratios of the particles.  ...  The multi-sphere approach was implemented to generate the ellipsoidal particles while the existing random close packing algorithm was modified to create the assemblies.  ...  Stress-strain curves for compressive load concerning assemblies (a) of 5000 ellipsoidal particles with ar ∼ 1.12 equal-packed and (b) of 5000 spheres with R = 0.25 mm.  ... 
doi:10.1016/j.fusengdes.2017.05.110 fatcat:tpimaltq45g2zmas4cvglh2rvu

Neighbor list collision-driven molecular dynamics simulation for nonspherical hard particles

Aleksandar Donev, Salvatore Torquato, Frank H. Stillinger
2005 Journal of Computational Physics  
The high precision of the event-driven approach enables us to reach previously unavailable high densities and to produce tightly jammed ellipsoid packings with several thousand particles, even for relatively  ...  We first give some introductory material, and then discuss several overlap (contact) functions for ellipsoids, based on the work of Perram and Wertheim [30] .  ...  Fig. 5 shows one of our ellipsoid packings with an unusually high density. The properties of this computer-generated packing compare very well to actual experimental data.  ... 
doi:10.1016/j.jcp.2004.08.025 fatcat:75loegu6fbg4hnxrjjz2nsmbya

Packing ellipsoids into volume-minimizing rectangular boxes

Josef Kallrath
2015 Journal of Global Optimization  
Separating hyperplanes are constructed to ensure that the ellipsoids do not overlap with each other. For up to 100 ellipsoids we compute feasible points with the global solvers available in GAMS.  ...  A set of tri-axial ellipsoids, with given semi-axes, is to be packed into a rectangular box; its widths, lengths and height are subject to lower and upper bounds.  ...  Siegfried Jetzke (Ostfalia Hochschule, Salzgitter, Germany) for his interest in this work, comments on the manuscript and discussion about the usefulness of ellipses and ellipsoids in real world problems  ... 
doi:10.1007/s10898-015-0348-6 fatcat:g4hzf43jjzfv7iw36tzt33klxm

Packing ellipsoids by nonlinear optimization

E. G. Birgin, R. D. Lobato, J. M. Martínez
2015 Journal of Global Optimization  
Two different models for the non-overlapping and models for the inclusion of ellipsoids within half-spaces and ellipsoids are presented.  ...  The problem consists in minimizing a measure of the total overlap of a given set of ellipsoids arranged within a given ellipsoidal container.  ...  the cuboid with minimum volume that can pack a given set of identical ellipsoids.  ... 
doi:10.1007/s10898-015-0395-z fatcat:7qjst77yazht7ir6mxfxcvgwzi

Microstructural modelling of cement-based materials via random packing of three-dimensional ellipsoidal particles

Wenxiang Xu, Huisu Chen
2012 Procedia Engineering  
The accuracy and reliability of the algorithm were verified by a visualization of the random packing of monodispersed ellipsoidal particles with rigid boundary conditions.  ...  Finally, applied stereological tools and serial sectioning analysis technique, microstructure of cement pastes, composed of ellipsoidal cement particles, was characterized and compared with that of spherical  ...  For an ellipsoidal particles packing system in the cubic model structure with rigid boundary conditions, particles were not allowed to traverse through the cubic model structure walls and overlap with  ... 
doi:10.1016/j.proeng.2011.12.460 fatcat:yjwezixz25aull72y56athqyoa

Generalized Formula of the Fraction of Interphase for Polydisperse Non-Spherical Particles: Theoretical and Numerical Models

Zhigang Zhu, Wenxiang Xu
2019 International Conference on Computational & Experimental Engineering and Sciences  
Then, the fraction of overlapping interphase in each packing structure is statistically obtained.  ...  In addition, the algorithm can be further used to detect the overlap between adjacent ellipsoidal particles (2D ellipses).  ...  Then, the fraction of overlapping interphase in each packing structure is statistically obtained.  ... 
doi:10.32604/icces.2019.04957 fatcat:acqqqnmtu5agtlydcuheavobmy

Sequential random packings of spheres and ellipsoids

Pedro G. Lind, Masami Nakagawa, Stefan Luding
2009 AIP Conference Proceedings  
We introduce sequential random procedures to pack polydisperse spheres and ellipsoids.  ...  For ellipsoids, we show how to use variational methods to determine both translations and rotations for packing them sequentially.  ...  One starts with an ellipsoid E 0 (solid contour) in contact with another ellipsoid E 2 and overlapping E 1 .  ... 
doi:10.1063/1.3179897 fatcat:43xrkny4encenjux6mxhna5wp4

Random packing of elliptical disks

G. Delaney, D. Weaire, S. Hutzler *, S. Murphy
2005 Philosophical Magazine Letters  
[Science 303 990 (2004)], recently reported for the random packing of ellipsoids in three dimensions. 90 G. Delaney et al.  ...  We have studied two-dimensional random packings of ellipses. When the aspect ratio is varied, a maximum packing fraction of 0.895 is found.  ...  Furthermore, computer simulations of packings of ellipsoids with principal axes having three different values, lead to random packings with packing fractions close to that of fcc/hcp.  ... 
doi:10.1080/09500830500080763 fatcat:a3admz7wcjekhdwixlxdovmcqu
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