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Titlebook: Non-Local Cell Adhesion Models; Symmetries and Bifur Andreas Buttenschön,Thomas Hillen Book 2021 The Editor(s) (if applicable) and The Auth

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发表于 2025-3-21 19:23:44 | 显示全部楼层 |阅读模式
书目名称Non-Local Cell Adhesion Models
副标题Symmetries and Bifur
编辑Andreas Buttenschön,Thomas Hillen
视频videohttp://file.papertrans.cn/667/666964/666964.mp4
概述Presents the first ever application of abstract bifurcation theory to a non-local problem.Includes leading research on pattern formation of non-local models.Describes in detail the development of basi
丛书名称CMS/CAIMS Books in Mathematics
图书封面Titlebook: Non-Local Cell Adhesion Models; Symmetries and Bifur Andreas Buttenschön,Thomas Hillen Book 2021 The Editor(s) (if applicable) and The Auth
描述.This monograph considers the mathematical modeling of cellular adhesion, a key interaction force in cell biology. While deeply grounded in the biological application of cell adhesion and tissue formation, this monograph focuses on the mathematical analysis of non-local adhesion models. The novel aspect is the non-local term (an integral operator), which accounts for forces generated by long ranged cell interactions. The analysis of non-local models has started only recently, and it has become a vibrant area of applied mathematics. This monograph contributes a systematic analysis of steady states and their bifurcation structure, combining global bifurcation results pioneered by Rabinowitz, equivariant bifurcation theory, and the symmetries of the non-local term. These methods allow readers to analyze and understand cell adhesion on a deep level..
出版日期Book 2021
关键词non-local equation; cell adhesion; symmetries; global bifurcation; non-local boundary conditions; non-loc
版次1
doihttps://doi.org/10.1007/978-3-030-67111-2
isbn_softcover978-3-030-67113-6
isbn_ebook978-3-030-67111-2Series ISSN 2730-650X Series E-ISSN 2730-6518
issn_series 2730-650X
copyrightThe Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl
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发表于 2025-3-21 23:15:37 | 显示全部楼层
978-3-030-67113-6The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl
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发表于 2025-3-22 02:19:12 | 显示全部楼层
Non-Local Cell Adhesion Models978-3-030-67111-2Series ISSN 2730-650X Series E-ISSN 2730-6518
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发表于 2025-3-22 05:36:48 | 显示全部楼层
CMS/CAIMS Books in Mathematicshttp://image.papertrans.cn/n/image/666964.jpg
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发表于 2025-3-22 15:14:45 | 显示全部楼层
IntroductionCellular adhesion is one of the most important interaction forces in tissues. Cells adhere to each other, to other cells, and to the extracellular matrix (ECM). Cell adhesion is responsible for the formation of tissues, membranes, vasculature, muscle tissue, as well as cell movement and cancer spread.
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发表于 2025-3-22 19:25:30 | 显示全部楼层
PreliminariesIn this section, we present some basic results that are needed later. We give a summary of the derivation of the non-local adhesion model from biological principles as presented.
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发表于 2025-3-22 22:41:36 | 显示全部楼层
Local BifurcationThe success of the Armstrong–Painter–Sherratt adhesion model (.) is that it can replicate the complicated patterns observed in cell sorting experiments.
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发表于 2025-3-23 04:46:12 | 显示全部楼层
Global BifurcationFor each ., we found local bifurcations at . with non-trivial eigenfunctions .. of . in . be given by . where ..(.) are the Fourier sine coefficients of . (see .).
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