{"id":431360,"date":"2022-04-14T00:13:41","date_gmt":"2022-04-13T21:13:41","guid":{"rendered":"https:\/\/en.buradabiliyorum.com\/tear-free-brushing-all-you-need-is-math\/"},"modified":"2022-04-14T00:13:41","modified_gmt":"2022-04-13T21:13:41","slug":"tear-free-brushing-all-you-need-is-math","status":"publish","type":"post","link":"https:\/\/buradabiliyorum.com\/en\/tear-free-brushing-all-you-need-is-math\/","title":{"rendered":"#Tear-free brushing? All you need is math"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_84 counter-hierarchy ez-toc-counter ez-toc-custom ez-toc-container-direction\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<label for=\"ez-toc-cssicon-toggle-item-6a22a881a2b4e\" class=\"ez-toc-cssicon-toggle-label\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #dd3333;color:#dd3333\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #dd3333;color:#dd3333\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/label><input type=\"checkbox\"  id=\"ez-toc-cssicon-toggle-item-6a22a881a2b4e\" checked aria-label=\"Toggle\" \/><nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-1'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/buradabiliyorum.com\/en\/tear-free-brushing-all-you-need-is-math\/#%E2%80%9CTear-free_brushing_All_you_need_is_math%E2%80%9D\" >&#8220;Tear-free brushing? All you need is math&#8221;<\/a><\/li><\/ul><\/nav><\/div>\n<h1><span class=\"ez-toc-section\" id=\"%E2%80%9CTear-free_brushing_All_you_need_is_math%E2%80%9D\"><\/span>&#8220;Tear-free brushing? All you need is math&#8221;<span class=\"ez-toc-section-end\"><\/span><\/h1>\n<div>\n<div class=\"article-gallery lightGallery\">\n<div data-thumb=\"https:\/\/scx1.b-cdn.net\/csz\/news\/tmb\/2022\/tear-free-brushing-all.jpg\" data-src=\"https:\/\/scx2.b-cdn.net\/gfx\/news\/hires\/2022\/tear-free-brushing-all.jpg\" data-sub-html=\"Experiments and simulations show the tine moving along the double helix from the clamped end towards the free end. Credit: Harvard SEAS\">\n<figure class=\"article-img\">\n            <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/scx1.b-cdn.net\/csz\/news\/800a\/2022\/tear-free-brushing-all.jpg\" alt=\"Tear-free brushing? All you need is math\" title=\"Experiments and simulations show the tine moving along the double helix from the clamped end towards the free end. Credit: Harvard SEAS\" width=\"800\" height=\"530\"\/><figcaption class=\"text-darken text-low-up text-truncate-js text-truncate mt-3\">\n                Experiments and simulations show the tine moving along the double helix from the clamped end towards the free end. Credit: Harvard SEAS<br \/>\n            <\/figcaption><\/figure>\n<\/p><\/div>\n<\/div>\n<p>As anyone who has ever had to brush long hair knows, knots are a nightmare. But with enough experience, most learn the tricks of detangling with the least amount of pain\u2014start at the bottom, work your way up to the scalp with short, gentle brushes, and <a href=\"https:\/\/buradabiliyorum.com\/en\/category\/download-scripts-themes-apps\/\" data-internallinksmanager029f6b8e52c=\"9\" title=\"Download Scripts &amp; Themes &amp; Apps\" target=\"_blank\" rel=\"noopener\">app<\/a>ly detangler when necessary.<\/p>\n<section class=\"article-banner first-banner ads-336x280\">\n         <!-- \/4988204\/Phys_Story_InText_Box --><\/p>\n<\/section>\n<p>L. Mahadevan, the Lola England de Valpine Professor of Applied Mathematics, of Organismic and Evolutionary Biology, and of Physics, learned the mechanics of combing years ago while brushing his young daughter&#8217;s hair.<\/p>\n<p>&#8220;I recall that detangling spray seemed to work sometimes, but I still had to be careful to comb gently, by starting from the free ends,&#8221; said Mahadevan. &#8220;But I was soon fired from the job as I was not very patient.&#8221;<\/p>\n<p>While Mahadevan lost his role as hairdresser, he was still a scientist and the topology, geometry and mechanics of detangling posed interesting mathematical questions that are relevant to a range of applications including textile manufacturing and chemical processes such as polymer processing.<\/p>\n<p>In a new paper, published in the journal <i>Soft Matter,<\/i> Mahadevan and co-authors Thomas Plumb Reyes and Nicholas Charles, explore the mathematics of combing and explain why the brushing technique used by so many is the most effective method to detangle a bundle of fibers.<\/p>\n<p>To simplify the problem, the researchers simulated two helically entwined filaments, rather than a whole head of hair.<\/p>\n<p>&#8220;Using this minimal model, we study the detangling of the double helix via a single stiff tine that moves along it, leaving two untangled filaments in its wake,&#8221; said Plumb-Reyes, a graduate student at SEAS. &#8220;We measured the forces and deformations associated with combing and then simulated it numerically.&#8221;  <\/p>\n<p>&#8220;Short strokes that start at the free end and move towards the clamped end remove tangles by creating a flow of a mathematical quantity called the &#8216;link density&#8217; that characterizes the amount that hair strands that are braided with each other, consistent with simulations of the process,&#8221; said Nicholas Charles, a graduate student at SEAS.<\/p>\n<p>The researchers also identified the optimal minimum length for each stroke\u2014any smaller and it would take forever to comb out all the tangles and any longer and it would be too painful.<\/p>\n<p>The mathematical principles of brushing developed by Plumb-Reyes, Charles and Mahadevan were recently used by Professor Daniela Rus and her team at MIT to design algorithms for brushing hair by a robot.<\/p>\n<p>Next, the team aims to study the mechanics of brushing curlier hair and how it responds to humidity and temperature, which may lead to a mathematical understanding of a fact every person with curly hair knows: never brush dry hair.<\/p>\n<hr\/>\n<div class=\"article-main__explore my-4 d-print-none\">\n<p>                                            <a rel=\"nofollow noopener\" target=\"_blank\" class=\"text-medium text-info mt-2 d-inline-block\" href=\"https:\/\/techxplore.com\/news\/2021-05-untangle-hair-robots.html\">Untangle your hair with help from robots<\/a>\n                                        <\/div>\n<hr class=\"mb-4\"\/>\n<div class=\"article-main__more p-4\">\n                                                                                                <strong>More information:<\/strong><br \/>\n                                                Thomas B. Plumb-Reyes et al, Combing a double helix, <i>Soft Matter<\/i> (2022).  <a rel=\"nofollow noopener\" target=\"_blank\" data-doi=\"1\" href=\"https:\/\/dx.doi.org\/10.1039\/D1SM01533H\">DOI: 10.1039\/D1SM01533H<\/a><\/p><\/div>\n<div class=\"d-inline-block text-medium my-4\">\n                                                Provided by<br \/>\n                                                                                                    Harvard John A. Paulson School of Engineering and Applied <a href=\"https:\/\/buradabiliyorum.com\/en\/category\/sciencee\/\" data-internallinksmanager029f6b8e52c=\"5\" title=\"Science\" target=\"_blank\" rel=\"noopener\">Science<\/a>s<br \/>\n                                                                                                        <a rel=\"nofollow noopener\" target=\"_blank\" class=\"icon_open\" href=\"https:\/\/www.seas.harvard.edu\"><br \/>\n                                                        <svg>\n                                                            <use href=\"https:\/\/phys.b-cdn.net\/tmpl\/v6\/img\/svg\/sprite.svg#icon_open\" x=\"0\" y=\"0\"\/>\n                                                        <\/svg><br \/>\n                                                    <\/a><\/p><\/div>\n<p>                                        <!-- print only --><\/p>\n<div class=\"d-none d-print-block\">\n<p>                                                 <strong>Citation<\/strong>:<br \/>\n                                                 Tear-free brushing? All you need is math (2022, April 13)<br \/>\n                                                 retrieved 13 April 2022<br \/>\n                                                 from https:\/\/phys.org\/<a href=\"https:\/\/buradabiliyorum.com\/en\/category\/news\/\" data-internallinksmanager029f6b8e52c=\"2\" title=\"News\" target=\"_blank\" rel=\"noopener\">news<\/a>\/2022-04-tear-free-math.html<\/p>\n<p>                                            This document is subject to copyright. Apart from any fair dealing for the purpose of private study or research, no<br \/>\n                                            part may be reproduced without the written permission. The content is provided for information purposes only.<\/p><\/div>\n<\/p><\/div>\n<p><script id=\"facebook-jssdk\" async=\"\" src=\"https:\/\/connect.facebook.net\/en_US\/sdk.js\"><\/script><\/p>\n<blockquote><p><strong><span style=\"color: #ff6600;\">If you liked the article, do not forget to share it with your friends. 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All you need is math&#8221; Experiments and simulations show the tine moving along the double helix from the clamped end towards the free end. Credit: Harvard SEAS As anyone who has ever had to brush long hair knows, knots are a nightmare. But with enough experience, most learn the tricks of detangling with&#8230;<\/p>\n","protected":false},"author":1,"featured_media":431361,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"https:\/\/scx2.b-cdn.net\/gfx\/news\/hires\/2022\/tear-free-brushing-all.jpg","fifu_image_alt":"","footnotes":""},"categories":[16],"tags":[],"class_list":["post-431360","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-sciencee"],"_links":{"self":[{"href":"https:\/\/buradabiliyorum.com\/en\/wp-json\/wp\/v2\/posts\/431360","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/buradabiliyorum.com\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/buradabiliyorum.com\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/buradabiliyorum.com\/en\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/buradabiliyorum.com\/en\/wp-json\/wp\/v2\/comments?post=431360"}],"version-history":[{"count":0,"href":"https:\/\/buradabiliyorum.com\/en\/wp-json\/wp\/v2\/posts\/431360\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/buradabiliyorum.com\/en\/wp-json\/wp\/v2\/media\/431361"}],"wp:attachment":[{"href":"https:\/\/buradabiliyorum.com\/en\/wp-json\/wp\/v2\/media?parent=431360"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/buradabiliyorum.com\/en\/wp-json\/wp\/v2\/categories?post=431360"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/buradabiliyorum.com\/en\/wp-json\/wp\/v2\/tags?post=431360"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}