{"id":11876,"date":"2025-04-11T21:27:08","date_gmt":"2025-04-11T21:27:08","guid":{"rendered":"https:\/\/www.europesays.com\/uk\/11876\/"},"modified":"2025-04-11T21:27:08","modified_gmt":"2025-04-11T21:27:08","slug":"this-is-something-we-did-not-see-coming-new-physics-from-odd-shapes-predicts-what-appears-as-random-motion","status":"publish","type":"post","link":"https:\/\/www.europesays.com\/uk\/11876\/","title":{"rendered":"“This is Something We Did Not See Coming.” New Physics from Odd Shapes Predicts what Appears as Random Motion"},"content":{"rendered":"

Conventional physics<\/a> quickly gets messy in an irregular world, according to Harvard<\/a> scientists who found a few new surprises while tackling an old problem: what happens when a ball rolls downhill.<\/p>\n

L. Mahadevan, a professor at the Harvard<\/a> John A. Paulson School of Engineering and Applied Sciences (SEAS)<\/a>, led the team as they peered into the complex physics<\/a> of imperfect objects. Their work moved from simulation<\/a> to real-world work, with surprising results that replayed some mathematical<\/a> oldies but provided new insights into fundamental physics<\/a>.<\/p>\n

\u201cWe go about the world seeing just about what everyone else sees,\u201d Mahadevan said<\/a>. \u201cBut if we choose to pause and wonder even as we wander, we learn about the world, and perhaps even about ourselves. Drawing connections between different fields of mathematics and physics by exploring this simple problem was fun \u2013 who knows, it might even turn out to be useful one day.\u201d<\/p>\n

Simulating the Plane<\/p>\n

The Harvard team began with computer simulations in which they rolled slightly irregular spheres and cylinders down ramps set at differing degrees of incline. From their first simulations, the team saw that while perfectly round objects continually roll along, irregular ones stammer as they descend. Steeper ramps exhibited a higher propensity for the object to roll, with objects more likely to falter on a flatter plane. Mahadevan\u2019s team found the most intriguing physics at the liminal point, the angle at which motion ceased.<\/p>\n

\u201cIndeed the behavior of the object near the transition angle, or a critical point, has the features of a phase transition, or bifurcation, which separates two qualitatively distinct states \u2013 rolling and not rolling,\u201d first author Daoyuan Qian said.<\/p>\n

The team measured entropy to better understand this behavior by observing each object\u2019s terminal rolling speed just before it stopped. Their analysis revealed that inertia and object dimensions significantly influenced rolling behavior. They found that as an object resolves into a stable rolling motion, the time it can roll without stopping theoretically diverges to infinity. Interestingly, spheres behaved differently from cylinders due to their ability to roll across their entire surface in multiple directions.<\/p>\n

While the simulations revealed fascinating behavior, the team used real-world experiments to validate their data. Using irregular cylinders and spheres on ramps of varying inclines, their laboratory results largely aligned with their simulations, though not without a few surprises.<\/p>\n

At first glance, the lurching motion of a rolling sphere appeared random. But as the team mapped out its movement, a pattern emerged. Once a steady state was reached, the sphere repeated periodic motions, rolling over twice during each period before returning to its original orientation.<\/p>\n

Explaining the Physics<\/p>\n

\u201cThis was something we did not see coming at all,\u201d Qian said.<\/p>\n

Despite their surprise, the team found mathematical theorems that explained the phenomena. One was the Hairy Ball Theorem, which Mahadevan described using the metaphor, \u201cYou cannot comb the hair on a sphere without a cowlick.\u201d Another was Dirac\u2019s Plate Trick, which states that an object with attached strings must rotate twice to return to its original state\u2014a concept mirrored in the sphere\u2019s jerky, doubled rolling motion.<\/p>\n

Phase transitions can be either continuous\u2014like a magnet slowly demagnetizing with heat\u2014or discontinuous, such as the abrupt shift from water to ice. There is no in-between.<\/p>\n

\u201cIn the rolling study, we see both \u2013 when there is no inertia, the rolling speed can be very very small close to the critical ramp angle (average speed continuously increasing from 0), but under inertia effects the object accelerates once it starts rolling, so the final speed changes from 0 to some large number discontinuously at the transition,\u201d Qian explained to The Debrief.<\/p>\n

Next Steps<\/p>\n

\u201cIt\u2019s quite interesting how we can see these kinds of abstract mathematics made visible with this simple experiment,\u201d said co-author and postdoctoral fellow Yeonsu Jung.\u00a0 \u201cAnd then the question could be, \u2018What else can we do?\u2019\u2026 Maybe we could explore something that hasn\u2019t been studied by mathematicians yet.\u201d<\/p>\n

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The work has practical applications in nanoscale cellular transport and robotics, and Qian explained to The Debrief how the knowledge could be applied to many real-life scenarios, including bowling.<\/p>\n

\u201cOne of the most surprising things we found is that the rolling motion of an irregular object is actually regular, so if you know the shape really well, then you can indeed predict how it rolls, Qian said. \u201cThis contrasts with what is commonly known as a random walk, where one would not be able to perform this prediction.\u201d<\/p>\n

\u201cThe most interesting part of the research (to me) is in demonstrating the possibility of simplifying a very complex problem by thinking about it in a different way,\u201d Qian concluded.<\/p>\n

The paper \u201cPhase Transitions in the Rolling of Irregular Cylinders and Spheres<\/a>\u201d appeared on March 25, 2025, in Proceedings of the National Academy of Sciences.<\/p>\n

Ryan Whalen covers science and technology for The Debrief. He holds an MA in History and a Master of Library and Information Science with a certificate in Data Science. He can be contacted at\u00a0<\/b>ryan@thedebrief.org<\/b><\/a>, and follow him on Twitter <\/b>@mdntwvlf<\/b><\/a>.<\/b><\/p>\n","protected":false},"excerpt":{"rendered":"Conventional physics quickly gets messy in an irregular world, according to Harvard scientists who found a few new…\n","protected":false},"author":2,"featured_media":11877,"comment_status":"","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3845],"tags":[401,8132,8133,74,70,464,16,15],"class_list":{"0":"post-11876","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-physics","8":"tag-harvard","9":"tag-harvard-john-a-paulson-school-of-engineering-and-applied-sciences","10":"tag-inertia","11":"tag-physics","12":"tag-science","13":"tag-simulation","14":"tag-uk","15":"tag-united-kingdom"},"share_on_mastodon":{"url":"https:\/\/pubeurope.com\/@uk\/114321453397036682","error":""},"_links":{"self":[{"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/posts\/11876","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/comments?post=11876"}],"version-history":[{"count":0,"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/posts\/11876\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/media\/11877"}],"wp:attachment":[{"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/media?parent=11876"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/categories?post=11876"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.europesays.com\/uk\/wp-json\/wp\/v2\/tags?post=11876"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}