{"id":86955,"date":"2021-09-01T16:28:11","date_gmt":"2021-09-01T15:28:11","guid":{"rendered":"https:\/\/datascientest.com\/?p=86955"},"modified":"2023-11-09T14:06:43","modified_gmt":"2023-11-09T14:06:43","slug":"mouvement-brownien-definition","status":"publish","type":"post","link":"https:\/\/datascientest.com\/mouvement-brownien-definition","title":{"rendered":"Le mouvement Brownien : principe et utilisations pratiques"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"86955\" class=\"elementor elementor-86955\" data-elementor-post-type=\"post\">\n\t\t\t\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-1785de1 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"1785de1\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-75cfd7e\" data-id=\"75cfd7e\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-b5c0706 elementor-widget elementor-widget-text-editor\" data-id=\"b5c0706\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.15.0 - 02-08-2023 *\/\n.elementor-widget-text-editor.elementor-drop-cap-view-stacked .elementor-drop-cap{background-color:#69727d;color:#fff}.elementor-widget-text-editor.elementor-drop-cap-view-framed .elementor-drop-cap{color:#69727d;border:3px solid;background-color:transparent}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap{margin-top:8px}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap-letter{width:1em;height:1em}.elementor-widget-text-editor .elementor-drop-cap{float:left;text-align:center;line-height:1;font-size:50px}.elementor-widget-text-editor .elementor-drop-cap-letter{display:inline-block}<\/style>\t\t\t\t<h2><strong>Prenons une particule de taille microm\u00e9trique qui baigne dans une fluide. Cette particule va poss\u00e9der un mouvement al\u00e9atoire d\u00fb aux chocs d\u2019autres petites particules sur cette \u00ab grosse \u00bb particule. C\u2019est le principe du mouvement brownien \u00e9galement appel\u00e9 processus de Wiener.<\/strong><\/h2>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-9f80dfb elementor-widget elementor-widget-text-editor\" data-id=\"9f80dfb\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><span style=\"color: #000000;\"><span style=\"font-weight: 400;\">Historiquement, c\u2019est en 1827 que le <\/span><span style=\"font-weight: 400;\">botaniste Robert Brown<\/span><span style=\"font-weight: 400;\"> d\u00e9couvrit le mouvement brownien. Il observa le mouvement chaotique de <\/span><span style=\"font-weight: 400;\">grains de pollen<\/span><span style=\"font-weight: 400;\"> dans l\u2019eau.\u00a0<\/span><\/span><\/p><p><span style=\"color: #000000;\"><span style=\"font-weight: 400;\">\u00c0 partir de 1857, le travail de Robert Brown commence \u00e0 susciter un grand int\u00e9r\u00eat et plusieurs scientifiques d\u00e9finissent les\u00a0<\/span><span style=\"font-weight: 400;\">propri\u00e9t\u00e9s du mouvement brownien.<\/span><span style=\"font-weight: 400;\">\u00a0\u00a0<\/span><\/span><\/p><p><span style=\"color: #000000;\">Il faut attendre <\/span><b>Albert Einstein en 1905<\/b><span style=\"color: #000000;\"> qui va d\u00e9crire de fa\u00e7on quantitative le mouvement brownien. Il relie notamment la moyenne quadratique de la distance parcourue \u00e0 la dur\u00e9e de l\u2019observation. <span style=\"font-weight: 400;\">Ses calculs seront valid\u00e9s exp\u00e9rimentalement par <\/span><a href=\"https:\/\/www.cnrs.fr\/fr\/personne\/jean-perrin\">Jean Perrin<\/a><span style=\"font-weight: 400;\">. Les exp\u00e9riences de ce dernier permettront \u00e9galement de d\u00e9terminer <\/span><a href=\"https:\/\/culturesciences.chimie.ens.fr\/thematiques\/chimie-analytique\/analyse-quantitative\/avogadro-sa-constante-entre-mythe-et-realite\">laconstante d\u2019Avogadro<\/a><span style=\"font-weight: 400;\">.\u00a0<\/span><\/span><\/p><p><span style=\"font-weight: 400; color: #000000;\">Le mouvement brownien poss\u00e8de des applications dans diff\u00e9rents domaines. Dans le domaine de la physique, il est notamment utilis\u00e9 pour <\/span><b>d\u00e9terminer le mouvement de petites particules<\/b><span style=\"font-weight: 400; color: #000000;\"> tels que les a\u00e9rosols dans l\u2019air par exemple. Une force al\u00e9atoire est prise en compte (notamment dans les \u00e9quations de Langevin).\u00a0<\/span><\/p><p><span style=\"font-weight: 400; color: #000000;\">Le mouvement brownien poss\u00e8de \u00e9galement des applications math\u00e9matiques avec des <\/span><b>processus stochastiques<\/b> <span style=\"font-weight: 400; color: #000000;\">: des mod\u00e8les probabilistes qui permettent d\u2019\u00e9tudier un ph\u00e9nom\u00e8ne al\u00e9atoire au cours du temps. Cela est tr\u00e8s utilis\u00e9 en <\/span><b>probabilit\u00e9s<\/b><span style=\"font-weight: 400; color: #000000;\">, et il y existe plusieurs applications dans le domaine de la finance.\u00a0<\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-c0d3003 elementor-align-center button-principale elementor-widget elementor-widget-button\" data-id=\"c0d3003\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm elementor-animation-grow\" href=\"https:\/\/datascientest.com\/formation-aws\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">D\u00e9couvrir nos formations<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-8514196 elementor-widget elementor-widget-heading\" data-id=\"8514196\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.15.0 - 02-08-2023 *\/\n.elementor-heading-title{padding:0;margin:0;line-height:1}.elementor-widget-heading .elementor-heading-title[class*=elementor-size-]>a{color:inherit;font-size:inherit;line-height:inherit}.elementor-widget-heading .elementor-heading-title.elementor-size-small{font-size:15px}.elementor-widget-heading .elementor-heading-title.elementor-size-medium{font-size:19px}.elementor-widget-heading .elementor-heading-title.elementor-size-large{font-size:29px}.elementor-widget-heading .elementor-heading-title.elementor-size-xl{font-size:39px}.elementor-widget-heading .elementor-heading-title.elementor-size-xxl{font-size:59px}<\/style><h3 class=\"elementor-heading-title elementor-size-default\">L\u2019application du mouvement brownien dans les micromanipulations de mol\u00e9cules d\u2019ADN<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-3539939 elementor-widget elementor-widget-heading\" data-id=\"3539939\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">1. Le principe<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-fdd60d5 elementor-widget elementor-widget-text-editor\" data-id=\"fdd60d5\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><span style=\"font-weight: 400; color: #000000;\">A titre d&rsquo;exemple, nous allons nous int\u00e9resser \u00e0 une des applications physiques du mouvement brownien qui est\u00a0<\/span><span style=\"font-weight: 400;\"><b>la micromanipulation de la mol\u00e9cule d\u2019ADN<\/b><\/span><span style=\"font-weight: 400; color: #000000;\"><span style=\"color: #6e4bec;\">.<\/span> Il est possible de micromanipuler des mol\u00e9cules d\u2019ADN gr\u00e2ce \u00e0 divers outils comme des pinces optiques ou des pinces magn\u00e9tiques.<\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-2e24197 elementor-widget elementor-widget-image\" data-id=\"2e24197\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.15.0 - 02-08-2023 *\/\n.elementor-widget-image{text-align:center}.elementor-widget-image a{display:inline-block}.elementor-widget-image a img[src$=\".svg\"]{width:48px}.elementor-widget-image img{vertical-align:middle;display:inline-block}<\/style>\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t\t<a href=\"https:\/\/www.researchgate.net\/figure\/Principe-de-la-micromanipulation-dune-molecule-dADN-Les-molecules-dADN-sont_fig36_28612296\">\n\t\t\t\t\t\t\t<img decoding=\"async\" width=\"800\" height=\"439\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2021\/08\/illu_schema_brownien-36-1-1024x562.jpg\" class=\"attachment-large size-large wp-image-94169\" alt=\"mouvement brownien\" srcset=\"https:\/\/datascientest.com\/wp-content\/uploads\/2021\/08\/illu_schema_brownien-36-1-1024x562.jpg 1024w, https:\/\/datascientest.com\/wp-content\/uploads\/2021\/08\/illu_schema_brownien-36-1-300x165.jpg 300w, https:\/\/datascientest.com\/wp-content\/uploads\/2021\/08\/illu_schema_brownien-36-1-768x422.jpg 768w, https:\/\/datascientest.com\/wp-content\/uploads\/2021\/08\/illu_schema_brownien-36-1-1536x844.jpg 1536w, https:\/\/datascientest.com\/wp-content\/uploads\/2021\/08\/illu_schema_brownien-36-1-2048x1125.jpg 2048w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/>\t\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">Principe de la micromanipulation d'une mol\u00e9cule d'ADN.<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-8b4e6f7 elementor-widget elementor-widget-text-editor\" data-id=\"8b4e6f7\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><span style=\"color: #000000;\"><span style=\"font-weight: 400;\">Le <\/span><\/span><b>principe de micromanipulation<\/b> <span style=\"color: #000000;\"><span style=\"font-weight: 400;\">est le suivant\u00a0:<\/span><\/span><\/p><ul><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400; color: #000000;\">On fixe une extr\u00e9mit\u00e9 de la mol\u00e9cule d\u2019ADN sur un capillaire en verre.\u00a0<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400; color: #000000;\">Sur l\u2019autre extr\u00e9mit\u00e9, on fixe une bille magn\u00e9tique. Cette bille sera plac\u00e9e dans le champ d\u2019un aimant.\u00a0<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400; color: #000000;\">Le d\u00e9placement des aimants va permettre de tirer la mol\u00e9cule d\u2019ADN ou la faire tourner sur elle-m\u00eame afin de cr\u00e9er des torsades.<\/span><\/li><\/ul>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-f17c0b6 elementor-widget elementor-widget-heading\" data-id=\"f17c0b6\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">2. L\u2019int\u00e9r\u00eat du mouvement brownien<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1e57dad elementor-widget elementor-widget-text-editor\" data-id=\"1e57dad\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><span style=\"font-weight: 400; color: #000000;\">Une fois ce contexte mis en place, on peut se demander o\u00f9 est-ce que le mouvement brownien intervient ?<\/span><\/p><p><span style=\"font-weight: 400; color: #000000;\">La force n\u00e9cessaire pour \u00e9tirer la mol\u00e9cule d\u2019ADN donne des informations assez importantes sur notre macromol\u00e9cule.<\/span><\/p><p><span style=\"color: #000000;\"><span style=\"font-weight: 400;\">Cette force est tr\u00e8s faible (ordre du piconewton c\u2019est-\u00e0-dire 10<sup>-12<\/sup><\/span><span style=\"font-weight: 400;\">\u00a0<\/span><span style=\"font-weight: 400;\">Newton). \u00c9tant faible, elle n\u2019est pas facilement mesurable \u00e0 partir d\u2019appareils de mesure classiques qui sont limit\u00e9s par <\/span><span style=\"font-weight: 400;\">l\u2019agitation thermique<\/span><span style=\"font-weight: 400;\">.\u00a0\u00a0<\/span><\/span><\/p><p><span style=\"color: #000000;\"><span style=\"font-weight: 400;\">Cependant, le mouvement brownien va permettre de mesurer la force. En effet, l\u2019agitation thermique va cr\u00e9er une force al\u00e9atoire qui \u00e9cartera la bille de sa position d\u2019\u00e9quilibre.<\/span><span style=\"font-weight: 400;\"> Des calculs permettent de d\u00e9montrer que la force d\u2019\u00e9tirement de la mol\u00e9cule d\u2019ADN est directement reli\u00e9e aux fluctuations quadratiques moyennes.\u00a0<br \/><\/span><\/span><\/p><p><span style=\"font-weight: 400; color: #000000;\">Maintenant il nous reste \u00e0 d\u00e9terminer les fluctuations quadratiques moyennes. Pour ce faire, il faut s\u2019inspirer de l\u2019exp\u00e9rience de Jean Perrin.\u00a0<\/span><\/p><ul><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"color: #000000;\"><span style=\"font-weight: 400;\">Une premi\u00e8re \u00e9tape est d\u2019<\/span><\/span><b>enregistrer les mouvements de la <\/b><b>particule sph\u00e9rique<\/b><span style=\"color: #000000;\"><span style=\"font-weight: 400;\">plac\u00e9e \u00e0 l\u2019extr\u00e9mit\u00e9 de la mol\u00e9cule d\u2019ADN \u00e0 l\u2019aide d\u2019une cam\u00e9ra reli\u00e9e \u00e0 un microscope.\u00a0<\/span><\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"color: #000000;\"><span style=\"font-weight: 400;\">Dans un deuxi\u00e8me temps, des<\/span><\/span><b> logiciels de reconnaissance vid\u00e9o<\/b><span style=\"color: #000000;\"><span style=\"font-weight: 400;\"> permettent d\u2019acc\u00e9der aux coordonn\u00e9es de la bille \u00e0 chaque instant. Puis les coordonn\u00e9es permettent de calculer les fluctuations browniennes.<\/span><\/span><\/li><\/ul>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-7dbf7ba elementor-widget elementor-widget-heading\" data-id=\"7dbf7ba\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">3. L\u2019utilisation de Python pour acc\u00e9der aux coordonn\u00e9es de la bille<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-6d39922 elementor-widget elementor-widget-text-editor\" data-id=\"6d39922\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><span style=\"font-weight: 400; color: #000000;\">\u00c0 partir de la vid\u00e9o, on peut acc\u00e9der aux coordonn\u00e9es de la bille de mani\u00e8re beaucoup plus complexe gr\u00e2ce \u00e0 Python.<\/span><\/p><p><span style=\"color: #000000;\"><span style=\"font-weight: 400;\">En effet, une fois que la vid\u00e9o est convertie en succession d\u2019images. On utilise <a href=\"https:\/\/pypi.org\/project\/imageio\/\">la <\/a><\/span><a href=\"https:\/\/pypi.org\/project\/imageio\/\">biblioth\u00e8que imageio<\/a><span style=\"font-weight: 400;\"><a href=\"https:\/\/pypi.org\/project\/imageio\/\">\u00a0de Python<\/a>. <\/span><span style=\"font-weight: 400;\">Elle permet de travailler avec les images en les pr\u00e9sentant comme des tableaux de 3 dimensions. Les deux premi\u00e8res dimensions permettent de d\u00e9terminer la position d\u2019un pixel et la troisi\u00e8me dimension nous renseigne sur l\u2019intensit\u00e9 de couleur (ce qui nous donnera la couleur du pixel).<\/span><span style=\"font-weight: 400;\"> Une fois que les images sont converties en nuances de gris, on peut se ramener \u00e0 un tableau \u00e0 deux dimensions vu que les valeurs de la troisi\u00e8me dimension seront toutes \u00e9gales (car l\u2019image est en nuances de gris). Il suffit alors de cr\u00e9er des fonctions qui permettent, par <\/span><\/span><b>une m\u00e9thode barycentrique<\/b><span style=\"font-weight: 400;\">, <strong>de<\/strong><\/span><b> d\u00e9terminer les coordonn\u00e9es du pixel d\u2019intensit\u00e9 maximale<\/b><span style=\"color: #000000;\"><span style=\"font-weight: 400;\"><span style=\"color: #6e4bec;\">.<\/span> En r\u00e9it\u00e9rant ce processus sur la succession d\u2019images, nous obtenons \u00e0 la fin nos coordonn\u00e9es de la bille \u00e0 chaque instant.<\/span><\/span><\/p><p><span style=\"font-weight: 400; color: #000000;\">L\u2019acc\u00e8s aux coordonn\u00e9es permet d\u2019acc\u00e9der aux fluctuations browniennes, puis \u00e0 la force d\u2019\u00e9tirement de la mol\u00e9cule d\u2019ADN.<\/span><\/p><p><span style=\"font-weight: 400; color: #000000;\">Ainsi, le mouvement brownien est tr\u00e8s utile dans la micromanipulation de la mol\u00e9cule d\u2019ADN. Le travail sur l\u2019analyse de la vid\u00e9o est \u00e9galement un \u00e9l\u00e9ment tr\u00e8s important. Comme nous l\u2019avons vu, ce processus peut se faire \u00e0 l&rsquo;aide de <\/span><span style=\"color: #000000;\"><a href=\"https:\/\/datascientest.com\/python-tout-savoir\">Python<\/a><\/span><span style=\"font-weight: 400; color: #000000;\">.\u00a0\u00a0<\/span><\/p><p><span style=\"font-weight: 400; color: #000000;\">Les formations propos\u00e9es par DataScientest permettent de maitriser Python, un outil indispensable en data science. Nous proposons \u00e9galement <\/span><b>un module sur le traitement d\u2019image<\/b><span style=\"font-weight: 400; color: #000000;\"> :\u00a0 Introduction \u00e0 la computer Vision avec OpenCV<\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-25d2fdb elementor-align-center button-principale elementor-widget elementor-widget-button\" data-id=\"25d2fdb\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm elementor-animation-grow\" href=\"https:\/\/datascientest.com\/formations-data\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">En savoir plus sur nos formations en data science<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-626b365 elementor-widget elementor-widget-heading\" data-id=\"626b365\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">\u00c0 propos de l'auteur... <\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-9818155 elementor-widget elementor-widget-testimonial\" data-id=\"9818155\" data-element_type=\"widget\" data-widget_type=\"testimonial.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.15.0 - 02-08-2023 *\/\n.elementor-testimonial-wrapper{overflow:hidden;text-align:center}.elementor-testimonial-wrapper .elementor-testimonial-content{font-size:1.3em;margin-bottom:20px}.elementor-testimonial-wrapper .elementor-testimonial-name{line-height:1.5;display:block}.elementor-testimonial-wrapper .elementor-testimonial-job{font-size:.85em;display:block}.elementor-testimonial-wrapper .elementor-testimonial-meta{width:100%;line-height:1}.elementor-testimonial-wrapper .elementor-testimonial-meta-inner{display:inline-block}.elementor-testimonial-wrapper .elementor-testimonial-meta .elementor-testimonial-details,.elementor-testimonial-wrapper .elementor-testimonial-meta .elementor-testimonial-image{display:table-cell;vertical-align:middle}.elementor-testimonial-wrapper .elementor-testimonial-meta .elementor-testimonial-image img{width:60px;height:60px;border-radius:50%;-o-object-fit:cover;object-fit:cover;max-width:none}.elementor-testimonial-wrapper .elementor-testimonial-meta.elementor-testimonial-image-position-aside .elementor-testimonial-image{padding-right:15px}.elementor-testimonial-wrapper .elementor-testimonial-meta.elementor-testimonial-image-position-aside .elementor-testimonial-details{text-align:left}.elementor-testimonial-wrapper .elementor-testimonial-meta.elementor-testimonial-image-position-top .elementor-testimonial-details,.elementor-testimonial-wrapper .elementor-testimonial-meta.elementor-testimonial-image-position-top .elementor-testimonial-image{display:block}.elementor-testimonial-wrapper .elementor-testimonial-meta.elementor-testimonial-image-position-top .elementor-testimonial-image{margin-bottom:20px}<\/style>\t\t<div class=\"elementor-testimonial-wrapper\">\n\t\t\t\t\t\t\t<div class=\"elementor-testimonial-content\">\u00c9tudiant en \u00e9cole d'ing\u00e9nieur ainsi qu'\u00e0 l'universit\u00e9 de Paris-Saclay, se sp\u00e9cialise dans le domaine des math\u00e9matiques appliqu\u00e9es en Data Science ainsi qu'en intelligence artificielle.<\/div>\n\t\t\t\n\t\t\t\t\t\t<div class=\"elementor-testimonial-meta elementor-has-image elementor-testimonial-image-position-aside\">\n\t\t\t\t<div class=\"elementor-testimonial-meta-inner\">\n\t\t\t\t\t\t\t\t\t\t\t<div class=\"elementor-testimonial-image\">\n\t\t\t\t\t\t\t<img decoding=\"async\" width=\"2560\" height=\"3062\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2021\/09\/image.png\" class=\"attachment-full size-full wp-image-96640\" alt=\"Avraham rosenberg\" srcset=\"https:\/\/datascientest.com\/wp-content\/uploads\/2021\/09\/image.png 2560w, https:\/\/datascientest.com\/wp-content\/uploads\/2021\/09\/image-251x300.png 251w, https:\/\/datascientest.com\/wp-content\/uploads\/2021\/09\/image-856x1024.png 856w, https:\/\/datascientest.com\/wp-content\/uploads\/2021\/09\/image-768x919.png 768w, https:\/\/datascientest.com\/wp-content\/uploads\/2021\/09\/image-1284x1536.png 1284w, https:\/\/datascientest.com\/wp-content\/uploads\/2021\/09\/image-1712x2048.png 1712w\" sizes=\"(max-width: 2560px) 100vw, 2560px\" \/>\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t<div class=\"elementor-testimonial-details\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"elementor-testimonial-name\">Avraham Rosenberg<\/div>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t<div class=\"elementor-element elementor-element-e72dfe1 e-flex e-con-boxed e-con\" data-id=\"e72dfe1\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-71decfe elementor-widget elementor-widget-html\" data-id=\"71decfe\" data-element_type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<script type=\"application\/ld+json\">\r\n{\r\n  \"@context\": \"https:\/\/schema.org\",\r\n  \"@type\": \"FAQPage\",\r\n  \"mainEntity\": {\r\n    \"@type\": \"Question\",\r\n    \"name\": \"Comment fonctionne l\u2019application du mouvement brownien ?\",\r\n    \"acceptedAnswer\": {\r\n      \"@type\": \"Answer\",\r\n      \"text\": \"A titre d'exemple, nous allons nous int\u00e9resser \u00e0 une des applications physiques du mouvement brownien qui est la micromanipulation de la mol\u00e9cule d\u2019ADN. Il est possible de micromanipuler des mol\u00e9cules d\u2019ADN gr\u00e2ce \u00e0 divers outils comme des pinces optiques ou des pinces magn\u00e9tiques.\"\r\n    }\r\n  }\r\n}\r\n<\/script>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Prenons une particule de taille microm\u00e9trique qui baigne dans une fluide. Cette particule va poss\u00e9der un mouvement al\u00e9atoire d\u00fb aux chocs d\u2019autres petites particules sur cette \u00ab grosse \u00bb particule. C\u2019est le principe du mouvement brownien \u00e9galement appel\u00e9 processus de Wiener. Historiquement, c\u2019est en 1827 que le botaniste Robert Brown d\u00e9couvrit le mouvement brownien. Il [&hellip;]<\/p>\n","protected":false},"author":77,"featured_media":92330,"comment_status":"open","ping_status":"open","sticky":false,"template":"elementor_theme","format":"standard","meta":{"content-type":"","inline_featured_image":false},"categories":[2497],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v21.7 (Yoast SEO v21.7) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Le mouvement Brownien : principe et utilisations pratiques<\/title>\n<meta name=\"description\" content=\"Prenons une particule de taille microm\u00e9trique qui baigne dans une fluide. Cette particule va poss\u00e9der un mouvement al\u00e9atoire d\u00fb aux chocs d\u2019autres petites particules sur cette \u00ab grosse \u00bb particule. C\u2019est le principe du mouvement brownien \u00e9galement appel\u00e9 processus de Wiener.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/datascientest.com\/mouvement-brownien-definition\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Le mouvement Brownien : principe et utilisations pratiques\" \/>\n<meta property=\"og:url\" content=\"https:\/\/datascientest.com\/mouvement-brownien-definition\" \/>\n<meta property=\"og:site_name\" content=\"Formation Data Science | DataScientest.com\" \/>\n<meta property=\"article:published_time\" content=\"2021-09-01T15:28:11+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2023-11-09T14:06:43+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/datascientest.com\/wp-content\/uploads\/2021\/08\/illu_brownien-32.png\" \/>\n\t<meta property=\"og:image:width\" content=\"1024\" \/>\n\t<meta property=\"og:image:height\" content=\"562\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/png\" \/>\n<meta name=\"author\" content=\"Raphael Kassel\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u00c9crit par\" \/>\n\t<meta name=\"twitter:data1\" content=\"Raphael Kassel\" \/>\n\t<meta name=\"twitter:label2\" content=\"Dur\u00e9e de lecture estim\u00e9e\" \/>\n\t<meta name=\"twitter:data2\" content=\"5 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/datascientest.com\/mouvement-brownien-definition\",\"url\":\"https:\/\/datascientest.com\/mouvement-brownien-definition\",\"name\":\"Le mouvement Brownien : principe et utilisations pratiques\",\"isPartOf\":{\"@id\":\"https:\/\/datascientest.com\/#website\"},\"datePublished\":\"2021-09-01T15:28:11+00:00\",\"dateModified\":\"2023-11-09T14:06:43+00:00\",\"author\":{\"@id\":\"https:\/\/datascientest.com\/#\/schema\/person\/6eca16f63daaafcbc96e15549b9d4ee1\"},\"description\":\"Prenons une particule de taille microm\u00e9trique qui baigne dans une fluide. 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