## Particle ClumpingJuly 9, 2014 Since our earliest days, each of us has been concerned with the common human activities of packing and filling. As children, we needed to pack our toys in our toy chest and our clothes in our dresser drawers and closet. We needed to fill our bowl with breakfast cereal without its overflowing, and the same for cups of milk. Not surprisingly, there's a lot of science behind the optimal packing and filling of regularly- and irregularly-shaped items. As I wrote in a previous article (Packing and Filling, May 17, 2012) the optimal packing of circle in a plane occurs when their centers are on an hexagonal lattice. This packing gives an areal density of (π/2√3) = 0.9069 (see figure). Carl Friedrich Gauss proved that this packing was optimum for a lattice arrangement, and László Fejes Tóth showed that this is the optimal packing, lattice or otherwise.[1]
## References:- Weisstein, Eric W. "Circle Packing." From MathWorld--A Wolfram Web Resource.
- Weisstein, Eric W. "Kepler Conjecture." From MathWorld--A Wolfram Web Resource.
- Steven Schultz, "Sweet science: Common candies yield physics discovery," Princeton University Press Release, February 12, 2004.
- Aleksandar Donev, Ibrahim Cisse, David Sachs, Evan A. Variano, Frank H. Stillinger, Robert Connelly, Salvatore Torquato and P. M. Chaikin, "Improving the Density of Jammed Disordered Packings Using Ellipsoids," Science, vol. 303, no. 5660 (February 13, 2004), pp. 990-993.
- Aleksandar Donev, Frank H. Stillinger, P. M. Chaikin and Salvatore Torquato, "Superdense Crystal Packings of Ellipsoids," arXiv Preprint Server, March 10, 2004.
- S. Torquato, "Reformulation of the Covering and Quantizer Problems as Ground States of Interacting Particles," arXiv Preprint Server, September 8, 2010.
- Salvatore Torquato and Frank H. Stillinger, "Jammed Hard-Particle Packings: From Kepler to Bernal and Beyond," arXiv Preprint Server, August 17, 2010.
- S. Torquato and Y. Jiao, "Exact Constructions of a Family of Dense Periodic Packings of Tetrahedra," arXiv Preprint Server, April 30, 2010.
- Y. Jiao, F. H. Stillinger and S. Torquato, "Novel Features Arising in the Maximally Random Jammed Packings of Superballs," arXiv Preprint Server, January 4, 2010.
- S. Torquato and Y. Jiao, "Dense Packings of Polyhedra: Platonic and Archimedean Solids," arXiv Preprint Server, September 9, 2009.
- S. Torquato and Y. Jiao, "Dense Packings of the Platonic and Archimedean Solids," arXiv Preprint Server, August 27, 2009.
- S. Torquato, T. M. Truskett and P. G. Debenedetti, "Is Random Close Packing of Spheres Well Defined?," arXiv Preprint Server, March 25, 2000.
- Christopher D. Zangmeister, James G. Radney, Lance T. Dockery, Jessica T. Young, Xiaofei Ma, Rian You and Michael R. Zachariah, "Packing density of rigid aggregates is independent of scale," Proc. Natl. Acad. Sci. Early Edition, June 9, 2014, doi:10.1073/pnas.1403768111.
- Supporting information for ref. 13 (PDF File).
- Michael Baum, "Snowballs to Soot: The Clumping Density of Many Things Seems to Be a Standard," NIST Tech Beat, June 10, 2014.
Linked Keywords: Human; child; children; toy; chest; clothing; clothes; lowboy; dresser; drawer; closet; bowl; breakfast cereal; cup; milk; science; circle; plane; center; hexagonal lattice; areal density; Carl Friedrich Gauss; mathematical proof; László Fejes Tóth; penny; pennies; Wikimedia Commons; two-dimensional space; two dimensions; three dimensions; displacement; volume density; computer; phenomenon; phenomena; randomness; random; isosceles triangle; Lubachevsky-Stillinger algorithm; plane; mapping; border; boundary; dimension; sphere; volume; mathematics; sphere packing; packing of identical spheres; round shot; cannonball; greengrocer; fruit; close-packing of equal spheres; Johannes Kepler (1571-1630); conjecture; Carl Friedrich Gauss (1777-1855); equilateral triangle; square; spatial orientation; Thomas Callister Hales; four color theorem; four color conjecture; computer program; Princeton University; Paul Chaikin; New York University; Salvatore Torquato; oblate spheroid; M&M candy; Monte Carlo simulation; ellipse; ChaikinLab Condensed Matter Physics Laboratory; computer simulation; ellipsoid; lenticular; tetrahedron; tetrahedra; icosahedron; icosahedra; dodecahedron; dodecahedra; octahedron; octahedra; physicist; spherical cow; scientific modelling; model; nature; natural; global warming; atmosphere of Earth; atmospheric; soot; carbon; nanometer; scientist; National Institute of Standards and Technology; Gaithersburg, Maryland; University of Maryland (College Park, Maryland); scale invariance; scale invariant; order of magnitude; cosmic dust; interstellar dust clouds; planet; comet; micrometer; microscale; powder; pharmaceutical drug; pharmaceutical; compression; force; initial condition; experiment; high school; college; internship; intern; adhesive; glue; glassware; container; hypothesis; silicon dioxide; silica; ceramic; NASA. |
RSS Feed
## Google Search
Latest Books by Dev Gualtieri
- Soybean Graphene - March 23, 2017
- Income Inequality and Geometrical Frustration - March 20, 2017
- Wireless Power - March 16, 2017
- Trilobite Sex - March 13, 2017
- Freezing, Outside-In - March 9, 2017
- Ammonia Synthesis - March 6, 2017
- High Altitude Radiation - March 2, 2017
- C.N. Yang - February 27, 2017
- VOC Detection with Nanocrystals - February 23, 2017
- Molecular Fountains - February 20, 2017
- Jet Lag - February 16, 2017
- Highly Flexible Conductors - February 13, 2017
- Graphene Friction - February 9, 2017
- Dynamic Range - February 6, 2017
- Robert Boyle's To-Do List for Science - February 2, 2017
- Nanowire Ink - January 30, 2017
- Random Triangles - January 26, 2017
- Torricelli's law - January 23, 2017
- Magnetic Memory - January 19, 2017
- Graphene Putty - January 16, 2017
- Seahorse Genome - January 12, 2017
- Infinite c - January 9, 2017
- 150 Years of Transatlantic Telegraphy - January 5, 2017
- Cold Work on the Nanoscale - January 2, 2017
- Holidays 2016 - December 22, 2016
- Ballistics - December 19, 2016
- Salted Frogs - December 15, 2016
- Negative Thermal Expansion - December 12, 2016
- Verbal Cues and Stereotypes - December 8, 2016
- Capacitance Sensing - December 5, 2016
- Gallium Nitride Tribology - December 1, 2016
- Lunar Origin - November 27, 2016
- Pumpkin Propagation - November 24, 2016
- Math Anxiety - November 21, 2016
- Borophene - November 17, 2016
- Forced Innovation - November 14, 2016
- Combating Glare - November 10, 2016
- Solar Tilt and Planet Nine - November 7, 2016
- The Proton Size Problem - November 3, 2016
- Coffee Acoustics and Espresso Foam - October 31, 2016
- SnIP - An Inorganic Double Helix - October 27, 2016
- Seymour Papert (1928-2016) - October 24, 2016
- Mapping the Milky Way - October 20, 2016
- Electromagnetic Shielding - October 17, 2016
- The Lunacy of the Cows - October 13, 2016
- Random Coprimes and Pi - October 10, 2016
- James Cronin (1931-2016) - October 6, 2016
- The Ubiquitous Helix - October 3, 2016
- The Five-Second Rule - September 29, 2016
- Resistor Networks - September 26, 2016
- Brown Dwarfs - September 22, 2016
- Intrusion Rheology - September 19, 2016
- Falsifiability - September 15, 2016
- Fifth Force - September 12, 2016
- Renal Crystal Growth - September 8, 2016
- The Normality of Pi - September 5, 2016
- Metering Electrical Power - September 1, 2016
### Deep ArchiveDeep Archive 2006-2008
Blog Article Directory on a Single Page |

Copyright © 2017 Tikalon LLC, All Rights Reserved.

Last Update: 03-23-2017