A Literature Review on Circle and Sphere Packing Problems: Models and Methodologies

Hifi, Mhand; M’Hallah, Rym

doi:10.1155/2009/150624

Cited by 170 publications

(112 citation statements)

References 56 publications

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“…Consequently, control over their structure enables control over their optical properties, with implications for cloaking (23), chemical sensing (24), imaging (25), nonlinear optics (26), and the creation of so-called metafluids (27)(28)(29), among a host of other applications (30). Recent work on plasmonic nanoclusters of faceted particles including nanocubes (31), nanoprisms (32), and nanooctahedra (33) introduces an additional means by which to tailor optical response.While some theoretical studies have addressed the confinement of anisotropic particles in one or two dimensions (34-38), a majority have focused on the confinement of spherical particles in one, two, and three dimensions (8,19,(39)(40)(41)(42)(43)(44)(45)(46)(47)(48)(49)(50). There have also been studies of 2D packings of circles, ellipses, and convex polygons (9, 51-55).…”

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“…While some theoretical studies have addressed the confinement of anisotropic particles in one or two dimensions (34-38), a majority have focused on the confinement of spherical particles in one, two, and three dimensions (8,19,(39)(40)(41)(42)(43)(44)(45)(46)(47)(48)(49)(50). There have also been studies of 2D packings of circles, ellipses, and convex polygons (9, 51-55).…”

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confidence: 99%

“…clusters | confinement | packing | colloids | nanoparticles P henomena as diverse as crowding in the cell (1,2), DNA packaging in cell nuclei and virus capsids (3,4), the growth of cellular aggregates (5), biological pattern formation (6), blood clotting (7), efficient manufacturing and transport, the planning and design of cellular networks (8), and efficient food and pharmaceutical packaging and transport (9) are related to the optimization problem of packing objects of a specified shape as densely as possible within a confining geometry, or packing in confinement. Packing in confinement is also a laboratory technique used to produce particle aggregates with consistent structure.…”

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Clusters of polyhedra in spherical confinement

Teich

Anders

Klotsa

et al. 2016

Proc. Natl. Acad. Sci. U.S.A.

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Dense particle packing in a confining volume remains a rich, largely unexplored problem, despite applications in blood clotting, plasmonics, industrial packaging and transport, colloidal molecule design, and information storage. Here, we report densest found clusters of the Platonic solids in spherical confinement, for up to N = 60 constituent polyhedral particles. We examine the interplay between anisotropic particle shape and isotropic 3D confinement. Densest clusters exhibit a wide variety of symmetry point groups and form in up to three layers at higher N. For many N values, icosahedra and dodecahedra form clusters that resemble sphere clusters. These common structures are layers of optimal spherical codes in most cases, a surprising fact given the significant faceting of the icosahedron and dodecahedron. We also investigate cluster density as a function of N for each particle shape. We find that, in contrast to what happens in bulk, polyhedra often pack less densely than spheres. We also find especially dense clusters at so-called magic numbers of constituent particles. Our results showcase the structural diversity and experimental utility of families of solutions to the packing in confinement problem.clusters | confinement | packing | colloids | nanoparticles P henomena as diverse as crowding in the cell (1, 2), DNA packaging in cell nuclei and virus capsids (3, 4), the growth of cellular aggregates (5), biological pattern formation (6), blood clotting (7), efficient manufacturing and transport, the planning and design of cellular networks (8), and efficient food and pharmaceutical packaging and transport (9) are related to the optimization problem of packing objects of a specified shape as densely as possible within a confining geometry, or packing in confinement. Packing in confinement is also a laboratory technique used to produce particle aggregates with consistent structure. These aggregates may serve as building blocks (or "colloidal molecules") in hierarchical structures (10, 11), information storage units (12), or drug delivery capsules (13). Experiments concerning cluster formation via spherical droplet confinement (13-20) are of special interest here. Droplets are typically either oil-in-water or water-inoil emulsions, and particle aggregation is induced via the evaporation of the droplet solvent. Clusters may be hollow [in which case they are termed "colloidosomes" (13)] or filled, depending on the formation protocol, and may contain a few (15) to a few billion (14) particles. Clusters of several metallic nanoparticles are especially intriguing given their ability to support surface plasmon modes over a range of frequencies (21). The subwavelength scale of these clusters means that their optical response is highly dependent on their specific geometry (22). Consequently, control over their structure enables control over their optical properties, with implications for cloaking (23), chemical sensing (24), imaging (25), nonlinear optics (26), and the creation of so-called metafluids (27)(28)(29), a...

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Clusters of polyhedra in spherical confinement

Teich

Anders

Klotsa

et al. 2016

Proc. Natl. Acad. Sci. U.S.A.

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“…Finally, we refer interested readers to (Wäscher et al, 2007;Castillo et al, 2008;Hifi and M'Hallah, 2009) for more comprehensive reviews about the C&P problems.…”

Section: Related Literaturementioning

confidence: 99%

Iterated tabu search for the circular open dimension problem

Huang

2013

European Journal of Operational Research

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This paper mainly investigates the circular open dimension problem (CODP), which consists of packing a set of circles of known radii into a strip of fixed width and unlimited length without overlapping. The objective is to minimize the length of the strip. An iterated tabu search approach, named ITS, is proposed. ITS starts from a randomly generated solution and attempts to gain improvements by a tabu search procedure. After that, if the obtained solution is not feasible, a perturbation operator is subsequently employed to reconstruct the incumbent solution and an acceptance criterion is implemented to determine whether or not accept the perturbed solution. This process is repeated until a feasible solution has been found or the allowed computation time has been elapsed. Computational experiments based on well-known benchmark instances show that ITS produces quite competitive results with respect to the best known results. For 18 representative CODP instances taken from the literature, ITS succeeds in improving 13 best known results within reasonable time. In addition, for another challenging related variant: the problem of packing arbitrary sized circles into a circular container, ITS also succeeds in improving many best known results. Supplementary experiments are also provided to analyze the influence of the perturbation operator, as well as the acceptance criterion.

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“…Hifi & M'Hallah [3] have classified CPPs as 'NP hard' optimisation problems. An NP hard problem is defined by Mathworld as follows: "A problem is NP-hard if an algorithm for solving it can be translated into one for solving any NP-problem (nondeterministic polynomial time).…”

Section: Introduction To the Circle Packing Problemmentioning

confidence: 99%

An Operations Research and Simulation�based Study on Improving the Efficiency of a Slurry Drying Tower

Jongh

Botha

2013

sajie

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This paper relates to a company that produces washing powders. The focus is on improving the efficiency of gas usage (per unit of powder produced) in the furnace that produces hot air. This hot air is an integral part of washing powder production: it dries the viscous slurry and transforms it into the base powder used in all washing powders. The cost of gas is the factory's largest expense. This paper attempts to increase the productivity and profitability of the operations by applying operations research using MATLAB and the non-linear optimiser called SNOPT (sparse non-linear optimiser). Using these techniques, a proposed solution that aims to balance the amount of open space between spraying slurry, as well as the overlap of spraying slurry within the furnace, is obtained. This is achieved by optimising the positioning of the top layer of 24 lances. The placement of the bottom layer of lances is done by positioning them in the areas of biggest overlap. These improvements result in a positive impact on the amount of gas burnt within the furnace to dry slurry to powder. OPSOMMINGHierdie navorsing handel oor 'n aangeleentheid wat verband hou met die aktiwiteite van 'n onderneming wat waspoeiers vervaardig. Daar word gepoog om die rendement van 'n verhittingsoond wat lug verhit vir die droging van poeier te verbeter. Die drogingsproses vind plaas deur viskeuse bry te droog tot poeier, wat gebruik kan word as bestanddeel van gewone waspoeier. Hierdie artikel beoog om produktiwiteit en wins van die proses te verhoog deur 'n operasionele navorsingsbenadering toe te pas wat gebruik maak van 'n boeket van toepaslike programmatuur soos o.a. SNOPT ("sparse non-linear optimizer") en Matlab. 'n voorgestelde oplossing is verkry deur van die bogenoemde metodes gebruik te maak, die oplossing beoog om die hoeveelheid oop spasies tussen die viskeuse bry en ook die oorvleueling van die viskeuse bry in die verhittingsoond te balanseer. Dit word bereik deur die optimale posisies te verkry vir die boonste 24 lansiere. Die onderste laag lansiere word geposisioneer in die areas waar die grootste oorvleueling plaasvind. Hierdie verbeterings het 'n positiewe impak op die hoeveelheid gas wat in die verhittingsoond gebrand word. a aa a a a aa a a a a a 1

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A Literature Review on Circle and Sphere Packing Problems: Models and Methodologies

Cited by 170 publications

References 56 publications

Clusters of polyhedra in spherical confinement

Clusters of polyhedra in spherical confinement

Iterated tabu search for the circular open dimension problem

An Operations Research and Simulation�based Study on Improving the Efficiency of a Slurry Drying Tower

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