{"id":204186,"date":"2025-01-21T10:26:17","date_gmt":"2025-01-21T16:26:17","guid":{"rendered":"https:\/\/lifeboat.com\/blog\/2025\/01\/capturing-the-mathematics-of-complex-evolving-systems"},"modified":"2025-01-21T10:26:17","modified_gmt":"2025-01-21T16:26:17","slug":"capturing-the-mathematics-of-complex-evolving-systems","status":"publish","type":"post","link":"https:\/\/lifeboat.com\/blog\/2025\/01\/capturing-the-mathematics-of-complex-evolving-systems","title":{"rendered":"Capturing the mathematics of complex, evolving systems"},"content":{"rendered":"<p><a class=\"aligncenter blog-photo\" href=\"https:\/\/lifeboat.com\/blog.images\/capturing-the-mathematics-of-complex-evolving-systems.jpg\"><\/a><\/p>\n<p>The challenge for researchers is to develop the often complicated series of equations that are needed to describe these phenomena and ensure that they can be solved to recover information on the location of the objects over time. Often the systems of equations needed to describe such phenomena are based on partial differential equations: the series of equations that describe the location and time-evolution of a system are known as a distributed parameter system.<\/p>\n<blockquote><p>Mathematical models can help us not just understand historical behaviour but predict where the smoke particles will spread next.<\/p><\/blockquote>\n<p>Professor Francisco Jurado at the Tecnol\u00f3gico Nacional de M\u00e9xico has been working on approaches to solve the problem of distributed parameter systems to describe diffusion\u2013convection systems. He has recently developed an approach using a combination of approaches, including the Sturm-Liouville differential operator and the regulator problem, to develop a model for diffusion\u2013convection behaviour that is sufficiently stable and free of external disturbances. Importantly, this approach allows us to yield meaningful information for real systems.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The challenge for researchers is to develop the often complicated series of equations that are needed to describe these phenomena and ensure that they can be solved to recover information on the location of the objects over time. Often the systems of equations needed to describe such phenomena are based on partial differential equations: the [\u2026]<\/p>\n","protected":false},"author":662,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[385,41,2229,48],"tags":[],"class_list":["post-204186","post","type-post","status-publish","format-standard","hentry","category-evolution","category-information-science","category-mathematics","category-particle-physics"],"_links":{"self":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts\/204186","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/users\/662"}],"replies":[{"embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/comments?post=204186"}],"version-history":[{"count":0,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts\/204186\/revisions"}],"wp:attachment":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/media?parent=204186"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/categories?post=204186"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/tags?post=204186"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}