This fragmentation<\/a>, the breakup of one object into many pieces, often follows a rule where shape matters more than material evidence.\u00a0<\/p>\n Villermaux used entropy, a measure of how many outcomes are possible, and he turned that idea into a simple equation.<\/p>\n A vase splitting into four equal pieces is possible, yet the math favors uneven breaks because they outnumber tidy ones.<\/p>\n Fragments and conservation law<\/p>\n The model assumes maximal randomness, where many tiny details average out, so the most probable breakup looks messy. <\/p>\n From that assumption, fragment numbers fall into a power law, which is a pattern where small pieces are far more common.<\/p>\n The steepness of that curve depends on an exponent, a number that controls how quickly big fragments disappear.<\/p>\n In the new law, the exponent comes mainly from dimensionality, whether the object behaves like a line, sheet, or volume.<\/p>\n The equation also relies on a conservation law, a rule that stays true during change, for the pieces as they separate.<\/p>\n In his setup, the summed logarithm, a math scale that turns multiplication into addition, of fragment sizes stays fixed during the internal scramble.<\/p>\n Cracks travel quickly compared with the slow motion of separating chunks, so the object hardly expands before the final pieces exist.<\/p>\n That constraint narrows the possible outcomes, and maximal randomness picks the most likely one without detailing how each crack branched.<\/p>\n Fragment size distribution<\/p>\n For rod-like breaks, the model predicts an exponent near 1.3, while plates trend near 2.4, and solid chunks trend near 3.5.<\/p>\n A larger exponent means big fragments become rarer, and most of the count piles up in the small<\/a> stuff.<\/p>\n The same material can land in different categories because a thin sheet breaks mainly across its surface, not its thickness.<\/p>\n Geometry and randomness matter more than the hammer, drop or explosion, as long as the breakup stays messy.<\/p>\n To test the idea, Villermaux compared the equation with earlier measurements from glass bars, spaghetti, plates, ceramic tubes, ocean plastic, and breaking waves.<\/p>\n In water and air, turbulence \u2013 the chaotic swirling motion in a moving fluid \u2013 can also drive breakup into a wide range of sizes.<\/p>\n Across that mix of settings, the fragment-size distribution kept the same basic shape, even though the materials<\/a> and forces differed widely.<\/p>\n When the rule holds, it offers a shortcut for predicting fragment counts, which can help models run faster and stay realistic.<\/p>\n Sugar cubes and hard floors<\/p>\n He also crushed a sugar cube about 1 inch (2.5 centimeters) across by dropping a weight from different heights onto a hard floor.<\/p>\n \u201cThat was a summer project with my daughters,\u201d said Prof. Villermaux, explaining that the sugar-cube experiment started as family time.<\/p>\n Because impacts have limited energy, the model adds fracture energy, energy needed to create new crack surfaces, which sets a smallest piece.<\/p>\n That limit trims the tiniest fragments, giving the curve a natural cutoff and keeping the total number of pieces finite.<\/p>\n When the rule fails on purpose<\/p>\n One experiment<\/a> on polypropylene found a fragment-mass exponent close to 1.2, placing plastics in a different breakup class.<\/p>\n The authors blamed shear \u2013 the sliding force that makes layers move sideways \u2013 and crack healing, which keep some fragments stuck together.<\/p>\n In a smooth liquid jet, predictable physics sets droplet sizes, so the breakup does not explore many random outcomes.<\/p>\n Even in solids, strong interactions between neighboring pieces can steer the result, so the law works best when fragments separate cleanly.<\/p>\n Implications for mining and hazards<\/p>\n Industries that crush rock for ore depend on fragmentation, because piece size controls how easily material moves through crushers, mills, and screens.<\/p>\n If engineers can predict the full spread of fragment sizes, they can tune energy<\/a> use and avoid over-grinding valuable material.<\/p>\n Rockfalls also break boulders into flying debris, and safety barriers work better when planners know how many medium and small pieces to expect.<\/p>\n A simple law cannot replace site measurements, yet it can provide a starting point when field data are scarce or hard to collect.<\/p>\n Small fragments, big problems<\/p>\n In the ocean, plastics can break into microplastics<\/a>, pieces smaller than about 0.2 inches (0.5 centimeters), which spread far and enter food webs.<\/p>\n Fragment size helps decide whether plastic sinks, floats, or stays suspended, and it also affects which animals can swallow it.<\/p>\n NASA used airburst models<\/a> \u2013 models that track an explosion in the atmosphere before impact \u2013 to track fragment clouds during meteor entries.<\/p>\n Meteor modelers still need chemistry and heat transfer, yet better fragment statistics could help connect shatter experiments in the lab to events in the sky.<\/p>\n Shapes, limits, and better models<\/p>\n Villermaux says that these patterns still leave two important questions unresolved about how shapes vary and what sets the smallest possible fragment.<\/p>\n A 2015 study<\/a> found that many freshly produced rock fragments share similar shape patterns across materials.<\/p>\n The minimum size may depend on crack energy and material structure, and it may also vary with how the impact delivers energy.<\/p>\n Better measurements and broader shatter tests across diverse materials could clarify where this law applies reliably and where other processes may dominate.<\/p>\n The study is published in Physical Review Letters<\/a>.<\/p>\n \u2014\u2013<\/p>\n Like what you read? Subscribe to our newsletter<\/a> for engaging articles, exclusive content, and the latest updates.<\/p>\n Check us out on EarthSnap<\/a>, a free app brought to you by Eric Ralls<\/a> and Earth.com.<\/p>\n \u2014\u2013<\/p>\n","protected":false},"excerpt":{"rendered":"A single equation may predict how many fragments a brittle object makes when it shatters. In Marseille, France,…\n","protected":false},"author":2,"featured_media":362241,"comment_status":"","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2],"tags":[4,450,451,3,79,452,453],"class_list":{"0":"post-362240","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-breaking-news","8":"tag-breaking-news","9":"tag-breakingnews","10":"tag-headlines","11":"tag-news","12":"tag-science","13":"tag-top-stories","14":"tag-topstories"},"_links":{"self":[{"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/posts\/362240","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/comments?post=362240"}],"version-history":[{"count":0,"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/posts\/362240\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/media\/362241"}],"wp:attachment":[{"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/media?parent=362240"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/categories?post=362240"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/tags?post=362240"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
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\n<\/a><\/p>\n