Structural complexity (applied mathematics): Difference between revisions

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Structural complexity emerges from all systems that display morphological organization.{{sfn | Nicolis | 1989 | p=}} Filamentary structures, for instance, are an example of [[Lagrangian coherent structures|coherent structures]] that emerge, interact and evolve in many physical and biological systems, such as mass distribution in the [[Shape of the universe|Universe]], [[Vortex |vortex filaments]] in turbulent flows, [[neural networks]] in our brain and genetic material (such as [[DNA]]) in a cell. In general information on the degree of morphological [[Order and disorder (physics)|disorder]] present in the system tells us something important about fundamental physical or biological processes.
 
Structural complexity methods are based on applications of [[differential geometry]] and [[topology]] (and in particular [[knot theory]]) to interpret physical properties of [[dynamical systems]].{{sfn | Abraham |Shaw| 1992 | p=}}{{sfn | Ricca | 2009 | p=}} such as relations between [[kinetic energy]] and tangles of vortex filaments in a turbulent flow or [[magnetic energy]] and braiding of magnetic fields in the solar corona, including aspects of [[topological fluid dynamics]].
 
==Literature==
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* {{cite book | last=Nicolis | first=G | author-link= Grégoire Nicolis|title=Exploring complexity : an introduction | publisher=W.H. Freeman | ___location=New York | year=1989 | isbn=978-0-7167-1859-8 | oclc=18989681}}
*{{cite book|last=Ricca|first=R.L.|author-link=Renzo_L._Ricca |year=2005|chapter=Structural complexity|title=Encyclopedia of Nonlinear Science|editor= A. Scott|pages= 885–887|publisher=Routledge, New York and London|isbn=9781579583859}}
*{{cite book|authorlast=Ricca, |first=R.L.|year=2009|chapter=Detecting structural complexity: from visiometrics to genomics and brain research|url=https://www.springer.com/mathematics/applications/book/978-88-470-1121-2|title=Mathknow|editor= M. Emmer & A. Quarteroni|pages=167–181|publisher=Springer-Verlag|isbn=9788847011212}}
 
==References==