{"id":185847,"date":"2009-09-30T00:00:00","date_gmt":"2011-01-14T20:42:36","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/particle-packing-problems-for-fun-and-profit\/"},"modified":"2016-09-09T10:00:38","modified_gmt":"2016-09-09T17:00:38","slug":"particle-packing-problems-for-fun-and-profit","status":"publish","type":"msr-video","link":"https:\/\/www.microsoft.com\/en-us\/research\/video\/particle-packing-problems-for-fun-and-profit\/","title":{"rendered":"Particle Packing Problems for Fun and Profit"},"content":{"rendered":"<div class=\"asset-content\">\n<p>Packing problems, such as how densely nonoverlapping particles fill d-dimensional Euclidean<br \/>\nspace Rd are ancient and still provide fascinating challenges for scientists and mathematicians<br \/>\n[1,2]. Bernal has remarked that &#8220;heaps&#8221; (particle packings) were the first things that were<br \/>\never measured in the form of basketfuls of grain for the purpose of trading or of collection<br \/>\nof taxes. While maximally dense packings are intimately related to classical ground states<br \/>\nof matter, disordered sphere packings have been employed to model glassy states of matter.<br \/>\nThere has been a resurgence of interest in maximally dense sphere packings in high-dimensional<br \/>\nEuclidean spaces [3,4], which is directly related to the optimal way of sending digital signals<br \/>\nover noisy channels.<br \/>\nI begin by first describing &#8220;order&#8221; maps to classify jammed sphere packings, which enables one<br \/>\nto view a host of packings with varying degrees of disorder as extremal structures. I discuss<br \/>\nwork that provides the putative exponential improvement on a 100-year- old lower bound on<br \/>\nthe maximal packing density due to Minkowski in Rd in the asymptotic limit d ? 8  [4].<br \/>\nOur study suggests that disordered (rather than ordered) sphere packings may be the densest<br \/>\nfor sufficiently large d &#8211; a counterintuitive possibility. Finally, I describe recent work to find<br \/>\nand characterize dense packings of three-dimensional nonspherical shapes of various shapes,<br \/>\nincluding the Platonic and Archimedean solids [5]. We conjecture that the densest packings of<br \/>\nthe Platonic and Archimedean solids with central symmetry are given by their corresponding<br \/>\ndensest lattice packings. This is the analogue of Kepler&#8217;s sphere conjecture for these solids.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Packing problems, such as how densely nonoverlapping particles fill d-dimensional Euclidean space Rd are ancient and still provide fascinating challenges for scientists and mathematicians [1,2]. Bernal has remarked that &#8220;heaps&#8221; (particle packings) were the first things that were ever measured in the form of basketfuls of grain for the purpose of trading or of collection [&hellip;]<\/p>\n","protected":false},"featured_media":290633,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr_hide_image_in_river":0,"footnotes":""},"research-area":[],"msr-video-type":[],"msr-locale":[268875],"msr-post-option":[],"msr-session-type":[],"msr-impact-theme":[],"msr-pillar":[],"msr-episode":[],"msr-research-theme":[],"class_list":["post-185847","msr-video","type-msr-video","status-publish","has-post-thumbnail","hentry","msr-locale-en_us"],"msr_download_urls":"","msr_external_url":"https:\/\/youtu.be\/Wpy9mvzXrLc","msr_secondary_video_url":"","msr_video_file":"","_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/185847","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video"}],"about":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/types\/msr-video"}],"version-history":[{"count":0,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/185847\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media\/290633"}],"wp:attachment":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media?parent=185847"}],"wp:term":[{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=185847"},{"taxonomy":"msr-video-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video-type?post=185847"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=185847"},{"taxonomy":"msr-post-option","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-post-option?post=185847"},{"taxonomy":"msr-session-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-session-type?post=185847"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=185847"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=185847"},{"taxonomy":"msr-episode","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-episode?post=185847"},{"taxonomy":"msr-research-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-theme?post=185847"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}