Numerical simulation and pattern characterization of nonlinear spatiotemporal dynamics on fractal surfaces for the whole-heart modeling applications
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...
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| Vydané v: | The European physical journal. B, Condensed matter physics Ročník 89; číslo 8; s. 1 - 16 |
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| Hlavní autori: | , |
| Médium: | Journal Article |
| Jazyk: | English |
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Berlin/Heidelberg
Springer Berlin Heidelberg
01.08.2016
Springer Springer Nature B.V |
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| ISSN: | 1434-6028, 1434-6036 |
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| 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. |
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| AbstractList | 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. Engineered and natural systems often involve irregular and self-similar geometric forms,which is called fractal geometry. For instance, precision machining produces a visuallyflat surface, while which looks like a rough mountain in the nanometer scale under themicroscope. Human heart consists of a fractal network of muscle cells, Purkinje fibers,arteries and veins. Cardiac electrical activity exhibits highly nonlinear and fractalbehaviors. Although space-time dynamics occur on the fractal geometry, e.g., chemicaletching on the surface of machined parts and electrical conduction in the heart, most ofexisting works modeled space-time dynamics (e.g., reaction, diffusion and propagation) onthe Euclidean geometry (e.g., flat planes and rectangular volumes). This brings inaccurateapproximation of real-world dynamics, due to sensitive dependence of nonlinear dynamicalsystems on initial conditions. In this paper, we developed novel methods and tools for thenumerical simulation and pattern recognition of spatiotemporal dynamics on fractalsurfaces of complex systems, which include (1) characterization and modeling of fractalgeometry, (2) fractal-based simulation and modeling of spatiotemporal dynamics, (3)recognizing and quantifying spatiotemporal patterns. Experimental results show that theproposed methods outperform traditional modeling approaches based on the Euclideangeometry, and provide effective tools to model and characterize space-time dynamics onfractal surfaces of complex systems. |
| ArticleNumber | 181 |
| Audience | Academic |
| Author | Chen, Yun Yang, Hui |
| Author_xml | – sequence: 1 givenname: Yun surname: Chen fullname: Chen, Yun organization: School of Mechanical Engineering, Jiangsu University of Science and Technology – sequence: 2 givenname: Hui surname: Yang fullname: Yang, Hui email: huy25@psu.edu organization: Complex Systems Monitoring, Modeling and Control Laboratory, Pennsylvania State University |
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| SubjectTerms | Cardiology Complex Systems Condensed Matter Physics Electric properties Electrical conduction Euclidean geometry Fluid- and Aerodynamics Fractal geometry Initial conditions Modelling Nonlinear dynamics Numerical analysis Pattern recognition Physics Physics and Astronomy Precision machining Regular Article Self-similarity Solid State Physics |
| Title | Numerical simulation and pattern characterization of nonlinear spatiotemporal dynamics on fractal surfaces for the whole-heart modeling applications |
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