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:''This{{About|the page is about structural complexityarea in applied mathematics.|the For structural complexity theoryarea in [[computational complexity theory]] of [[computer science]] see [[structural|Structural complexity theory]].''}}
'''Structural complexity''' is a science of [[applied mathematics]], that aims atto relatingrelate fundamental physical or biological aspects of a [[complex system]] with the mathematical description of the morphological complexity that the system exhibits, by establishing rigorous relations between mathematical and physical properties of such system.{{sfn | (Ricca | 2005). | p=}}
Structural complexity emerges from all systems that display morphological organization.{{sfn | (Nicolis & Prigogine| 1989). | p=}} Filamentary structures, for instance, are an example of [[Lagrangian_coherent_structuresLagrangian coherent structures|coherent structures]] that emerge, interact and evolve in many physical and biological systems, such as mass distribution in the [[Shape_of_the_UniverseShape 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_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]].
==ReferencesLiterature==
* {{cite book | last1=Abraham | first1=Ralph |authorlink1=Ralph Abraham (mathematician)|first2=C.D.|last2=Shaw|authorlink2=Robert_Shaw_(Physicist)#Illustrations | title=Dynamics--the geometry of behavior | publisher=Addison-Wesley, Advanced Book Program | ___location=Redwood City, Calif | year=1992 | isbn=978-0-201-56717-5 | oclc=24374484}}
* {{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 , in ''|title=Encyclopedia of Nonlinear Science '' (ed.|editor= A. Scott ), pp. 885-887.|pages= 885–887|publisher=Routledge, New York and London . ISBN |isbn=9781579583859 }}▼* {{cite book|last=Ricca , |first=R.L. (|year=2009 ) |chapter=Detecting structural complexity: from visiometrics to genomics and brain research , in [http|url=https://www.springer.com/mathematics/applications/book/978-88-470-1121-2 ''|title=Mathknow ''], (ed.|editor= M. Emmer & A. Quarteroni ), pp. 167-181. |pages=167–181|publisher=Springer-Verlag . ISBN |isbn=9788847011212 }}▼
==References==
*[[Ralph_Abraham |Abraham, R.H.]] & [[Robert_Shaw_(Physicist)#Illustrations |Shaw, C.D.]] (1992) ''Dynamics - the Geometry of Behavior''. Addison-Wesley. ISBN 978-0201567175
{{reflist}}
*Nicolis, G. & [[Ilya_Prigogine |Prigogine, I.]] (1989) ''Exploring Complexity''. W.H. Freeman & Co., New York. ISBN 9780716718598
▲*Ricca, R.L. (2005) Structural complexity, in ''Encyclopedia of Nonlinear Science'' (ed. A. Scott), pp. 885-887. Routledge, New York and London. ISBN 9781579583859
▲*Ricca, R.L. (2009) Detecting structural complexity: from visiometrics to genomics and brain research, in [http://www.springer.com/mathematics/applications/book/978-88-470-1121-2 ''Mathknow''], (ed. M. Emmer & A. Quarteroni), pp. 167-181. Springer-Verlag. ISBN 9788847011212
[[Category:Applied mathematics]]
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