Detection and characterization of transport barriers in complex flows via ridge extraction of the finite time Lyapunov exponent field

International Journal for Numerical Methods in Engineering

Volumn 86, Issue 9, 2011, Pages 1163-1174

  Senatore, Carmine ^a   Ross, Shane D ^a  

^a State University   (United States)

Author keywords

Dynamical barrier; Geophysical flow; Image processing; Phase space transport; Ridge detection; Ridge strength

Indexed keywords

DYNAMICAL BARRIER; GEOPHYSICAL FLOW; PHASE SPACE TRANSPORT; RIDGE DETECTION; RIDGE STRENGTH;

ALGORITHMS; DIFFERENTIAL EQUATIONS; GEOPHYSICS; IMAGE PROCESSING; IMAGING SYSTEMS; LYAPUNOV FUNCTIONS; LYAPUNOV METHODS; MATHEMATICAL MODELS; STRUCTURAL GEOLOGY; THREE DIMENSIONAL;

DYNAMICAL SYSTEMS;

EID: 79954622488     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.3101     Document Type: Article

References (39)

1. Haller G, Yuan G. Lagrangian coherent structures and mixing in two-dimensional turbulence. Physica D 2000; 147:352-370.
2. Haller G. Finding finite-time invariant manifolds in two-dimensional velocity fields. Chaos 2000; 10:99-108.
3. Haller G. Distinguished material surfaces and coherent structures in 3D fluid flows. Physica D 2001; 149:248-277.
4. Haller G. Lagrangian structures and the rate of strain in a partition of two-dimensional turbulence. Physics of Fluids 2001; 13:3365-3385.
5. Haller G. Lagrangian coherent structures from approximate velocity data. Physics of Fluids 2002; 13:3365.
6. Shadden SC, Lekien F, Marsden JE. Definition and properties of Lagrangian coherent structures: mixing and transport in two-dimensional aperiodic flows. Physica D 2005; 212:271-304.
7. Lekien F, Coulliette C, Mariano AJ, Ryan EH, Shay LK, Haller G, Marsden JE. Pollution release tied to invariant manifolds: a case study for the coast of Florida. Physica D 2005; 210:1-20.
8. Lekien F, Shadden SC, Marsden JE. Lagrangian coherent structures in n-dimensional systems. Journal of Mathematical Physics 2007; 48:065404.
9. Shadden SC, Taylor CA. Characterization of coherent structures in the cardiovascular system. Annals of Biomedical Engineering 2008; 36:1152-1162.
10. Senatore C, Ross SD. Fuel-efficient navigation in complex flows. Proceedings of 2008 American Control Conference, Seattle, WA, 2008; 1244-1248.
11. Tallapragada P, Ross SD. Particle segregation by Stokes number for small neutrally buoyant spheres in a fluid. Physical Review E 2008; 78:036308.
12. Gawlik ES, Marsden JE, Du Toit PC, Campagnola S. Lagrangian coherent structures in the planar elliptic restricted three-body problem. Celestial Mechanics and Dynamical Astronomy 2009; 103(3):227-249.
13. Tanaka ML, Ross SD. Separatrices and basins of stability from time series data: an application to biodynamics. Nonlinear Dynamics 2009; 58(1-2):1-21.
14. Lekien F, Ross SD. The computation of finite-time Lyapunov exponents on unstructured meshes and for non-Euclidean manifolds. Chaos 2010; 20:017505.
15. Mathur M, Haller G, Peacock T, Ruppert-Felsot JE, Swinney HL. Uncovering the Lagrangian skeleton of turbulence. Physical Review Letters 2007; 98:144502.
16. O'Gorman L, Nickerson JV. An approach to fingerprint filter design. Pattern Recognition 1989; 22(1):29-38.
17. Maio D, Maltoni D. Direct gray-scale minutiae detection in fingerprints. IEEE Transactions on Pattern Analysis and Machine Intelligence 1997; 19(1):27-40.
18. Zhu E, Yin J, Hu C, Zhang G. A systematic method for fingerprint ridge orientation estimation and image segmentation. Pattern Recognition 2006; 39:1452-1472.
19. Jiang X, Yau WY, Ser W. Detecting the fingerprint minutiae by adaptive tracing the gray-level ridge. Pattern Recognition 2001; 34:999-1013.
20. Xiao Q, Raafat H. Fingerprint image postprocessing: a combined statistical and structural approach. Pattern Recognition 1991; 24(10):985-992.
21. Farina A, Kovács-Vajna ZM, Leone A. Fingerprint minutiae extraction from skeletonized binary images. Pattern Recognition 1999; 32:877-889.
22. He Y, Tian J, Li L, Chen H, Yang X. Fingerprint matching based on global comprehensive similarity. IEEE Transactions on Pattern Analysis and Machine Intelligence 2006; 28(6):850-862.
23. Garth C, Gerhardt F, Tricoche X, Hagen H. Efficient computation and visualization of coherent structures in fluid flow applications. IEEE Transactions on Visualization and Computer Graphics 2007; 13(6):1464-1471.
24. Sadlo F, Peikert R. Efficient visualization of Lagrangian coherent structures by filtered AMR ridge extraction. IEEE Transactions on Visualization and Computer Graphics 2007; 13(6):1456-1463.
25. Sahner J, Weinkauf T, Teuber N, Hege H. Vortex and strain skeletons in Eulerian and Lagrangian frames. IEEE Transactions on Visualization and Computer Graphics 2007; 13(5):980-990.
26. Shi K, Theisel H, Weinkauf T, Hege H, Seidel H. Finite time transport structures of flow fields. IEEE Pacific Visualization Symposium, Kyoto, Japan, 4-7 March 2008.
27. Peikert R, Sadlo F. Height ridge computation and filtering for visualization. IEEE Pacific Visualization Symposium, Kyoto, Japan, 4-7 March 2008.
28. Eberly D. Ridges in Image and Data Analysis. Kluwer Academic Publishers: Dordrecht, 1996.
29. Florack L. Image Structure. Kluwer Academic Publishers: Dordrecht, 1997.
30. Lindeberg T. Scale-space theory: A basic tool for analysing structures at different scales. Journal of Applied Statistics 21:225-270.
31. Lindeberg T. Edge detection and ridge detection with automatic scale selection. International Journal of Computer Vision 1998; 30(2):117-156.
32. Subirana-Vilanova JB, Sung KK. Multi-scale vector-ridge-detection for perceptual organization without edges. Technical Report, Massachussets Institute of Technology, 1992.
33. Shadden SC. A dynamical systems approach to unsteady systems. Ph.D. Thesis, California Institute of Technology, 2003.
34. National Oceanic and Atmospheric Administration. Nomads Data Access, 12km North American Mesoscale (nam) dataset. Available from: Available from: [June 2009].
35. Aylor DE. Spread of plant disease on a continental scale: role of aerial dispersal of pathogens. Ecology 2003; 84:1989-1997.
36. Isard SA, Gage SH, Comtois P, Russo JH. Principles of the atmospheric pathway for invasive species applied to soybean rust. BioScience 2005; 55(10):851-861.
37. Schmale DG, Shields EJ, Bergstrom GC. Night-time spore deposition of the Fusarium head blight pathogen gibberella zeae. Canadian Journal Plant Pathology 2006; 28:100-108.
38. Newton PK, Ross SD. Chaotic advection in the restricted four-vortex problem on a sphere. Physica D 2006; 223:36-53.
39. Boehm MT, Aylor DE. Lagrangian stochastic modeling of heavy particle transport in the convective boundary layer. Atmospheric Environment 2005; 39:4841-4850.