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Numerical simulation and pattern characterization of nonlinear spatiotemporal dynamics on fractal surfaces for the whole-heart modeling applications

Author

Listed:
  • Yun Chen

    (School of Mechanical Engineering, Jiangsu University of Science and Technology)

  • Hui Yang

    (Complex Systems Monitoring, Modeling and Control Laboratory, Pennsylvania State University)

Abstract

Engineered and natural systems often involve irregular and self-similar geometric forms, which is called fractal geometry. For instance, precision machining produces a visually flat surface, while which looks like a rough mountain in the nanometer scale under the microscope. Human heart consists of a fractal network of muscle cells, Purkinje fibers, arteries and veins. Cardiac electrical activity exhibits highly nonlinear and fractal behaviors. Although space-time dynamics occur on the fractal geometry, e.g., chemical etching on the surface of machined parts and electrical conduction in the heart, most of existing works modeled space-time dynamics (e.g., reaction, diffusion and propagation) on the Euclidean geometry (e.g., flat planes and rectangular volumes). This brings inaccurate approximation of real-world dynamics, due to sensitive dependence of nonlinear dynamical systems on initial conditions. In this paper, we developed novel methods and tools for the numerical simulation and pattern recognition of spatiotemporal dynamics on fractal surfaces of complex systems, which include (1) characterization and modeling of fractal geometry, (2) fractal-based simulation and modeling of spatiotemporal dynamics, (3) recognizing and quantifying spatiotemporal patterns. Experimental results show that the proposed methods outperform traditional modeling approaches based on the Euclidean geometry, and provide effective tools to model and characterize space-time dynamics on fractal surfaces of complex systems.

Suggested Citation

  • Yun Chen & Hui Yang, 2016. "Numerical simulation and pattern characterization of nonlinear spatiotemporal dynamics on fractal surfaces for the whole-heart modeling applications," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 89(8), pages 1-16, August.
  • Handle: RePEc:spr:eurphb:v:89:y:2016:i:8:d:10.1140_epjb_e2016-60960-6
    DOI: 10.1140/epjb/e2016-60960-6
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    Cited by:

    1. Patricio Venegas-Aravena, 2024. "Past large earthquakes influence future strong ground motion: Example of the Chilean subduction zone," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 120(12), pages 10669-10685, September.

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    Keywords

    Statistical and Nonlinear Physics;

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