English   español  
Please use this identifier to cite or link to this item: http://hdl.handle.net/10261/173177
Share/Impact:
Statistics
logo share SHARE logo core CORE   Add this article to your Mendeley library MendeleyBASE

Visualizar otros formatos: MARC | Dublin Core | RDF | ORE | MODS | METS | DIDL
Exportar a otros formatos:

Title

Clustering coefficient and periodic orbits in flow networks

AuthorsRodríguez-Méndez, Víctor; Ser-Giacomi, Enrico ; Hernández-García, Emilio
Issue Date2017
PublisherAmerican Institute of Physics
CitationChaos 27(3): 035803 (2017)
AbstractWe show that the clustering coefficient, a standard measure in network theory, when applied to flow networks, i.e., graph representations of fluid flows in which links between nodes represent fluid transport between spatial regions, identifies approximate locations of periodic trajectories in the flow system. This is true for steady flows and for periodic ones in which the time interval τ used to construct the network is the period of the flow or a multiple of it. In other situations, the clustering coefficient still identifies cyclic motion between regions of the fluid. Besides the fluid context, these ideas apply equally well to general dynamical systems. By varying the value of τ used to construct the network, a kind of spectroscopy can be performed so that the observation of high values of mean clustering at a value of τ reveals the presence of periodic orbits of period 3τ , which impact phase space significantly. These results are illustrated with examples of increasing complexity, namely, a steady and a periodically perturbed model two-dimensional fluid flow, the three-dimensional Lorenz system, and the turbulent surface flow obtained from a numerical model of circulation in the Mediterranean sea. The Lagrangian description of fluid dynamics, which focuses on the motion of the fluid particles as they are advected by the flow, provides a useful bridge between the theory of dynamical systems and the analysis of fluid transport and mixing, so that techniques and results can be transferred from one field to the other. Modern network theory has also been brought into contact with fluid dynamics and dynamical systems through the concept of flow networks, in which the motion of fluid particles between different regions is represented by links in a graph. In this paper, we use the flow network framework to show that the clustering coefficient, a standard measure in network theory, identifies periodic orbits, fundamental objects in the theory of dynamical systems, and is also of importance in the context of fluid motion.
Publisher version (URL)https://doi.org/10.1063/1.4971787
URIhttp://hdl.handle.net/10261/173177
DOI10.1063/1.4971787
ISSN1054-1500
E-ISSN1089-7682
Appears in Collections:(IFISC) Artículos
Files in This Item:
File Description SizeFormat 
clustering_coefficient.pdf7,67 MBAdobe PDFThumbnail
View/Open
Show full item record
Review this work
 

Related articles:


WARNING: Items in Digital.CSIC are protected by copyright, with all rights reserved, unless otherwise indicated.