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A method how to determine parameters arising in a smoldering evolution equation by image segmentation for experiment's movies
1. | Faculty of Engineering, Yamagata University, 4-3-16 Jonan, Yonezawa-shi, Yamagata 992-8510, Japan |
2. | Graduate School of Science and Technology, Meiji University, 1-1-1 Higashi-Mita, Tama-ku, Kawasaki-shi, Kanagawa 214-8571, Japan |
3. | School of Science and Technology, Meiji University, 1-1-1 Higashi-Mita, Tama-ku, Kawasaki-shi, Kanagawa 214-8571, Japan |
We propose a simple and accurate procedure how to extract the values of model parameters in a flame/smoldering evolution equation from 2D movie images of real experiments. The procedure includes a novel method of image segmentation, which can detect an expanding smoldering front as a plane polygonal curve. The evolution equation is equivalent to the so-called Kuramoto-Sivashinsky (KS) equation in a certain scale. Our results suggest a valid range of parameters in the KS equation as well as the validity of the KS equation itself.
References:
[1] |
M. Beneš, M. Kimura, P. Pauš, D. Ševčovič, T. Tsujikawa and S. Yazaki,
Application of a curvature adjusted method in image segmentation, Bulletin of the Institute of Mathematics, Academia Sinica New Series, 3 (2008), 509-523.
|
[2] |
C. L. Epstein and M. Gage,
The curve shortening flow, Wave Motion: Theory, Modelling, and Computation (Berkeley, Calif., 1986) Mathematical Sciences Research Institute Publications, Springer, New York, 7 (1987), 15-59.
doi: 10.1007/978-1-4613-9583-6_2. |
[3] |
M. L. Frankel and G. I. Sivashinsky,
On the nonlinear thermal diffusive theory of curved flames, Journal de Physique, 48 (1987), 25-28.
doi: 10.1051/jphys:0198700480102500. |
[4] |
M. Goto, K. Kuwana and S. Yazaki,
A simple and fast numerical method for solving flame/smoldering evolution equations, JSIAM Letter, 10 (2018), 49-52.
doi: 10.14495/jsiaml.10.49. |
[5] |
M. Goto, K. Kuwana, G. Kushida and S. Yazaki,
Experimental and theoretical study on near-floor flame spread along a thin solid, Proceedings of the Combustion Institute, 37 (2019), 3783-3791.
doi: 10.1016/j.proci.2018.06.001. |
[6] |
M. Kass, A. Witkin and D. Terzopulos,
Snakes: Active contour models, Int. J. Computer Vision, 1 (1988), 321-331.
doi: 10.1007/BF00133570. |
[7] |
Y. Kuramoto and T. Tsuzuki,
Persistent propagation of concentration waves in dissipative media far from thermal equilibrium, Progress of Theoretical Physics, 55 (1976), 356-369.
doi: 10.1143/PTP.55.356. |
[8] |
K. Mikula and D. Ševčovič,
A direct method for solving an anisotropic mean curvature flow of plane curves with an external force, Math. Methods Appl. Sci., 27 (2004), 1545-1565.
doi: 10.1002/mma.514. |
[9] |
K. Mikula and D. Ševčovič,
Computational and qualitative aspects of evolution of curves driven by curvature and external force, Comput. Vis. Sci., 6 (2004), 211-225.
doi: 10.1007/s00791-004-0131-6. |
[10] |
D. Ševčovič and S. Yazaki,
Evolution of plane curves with a curvature adjusted tangential velocity, Japan J. Indust. Appl. Math., 28 (2011), 413-442.
doi: 10.1007/s13160-011-0046-9. |
[11] |
D. Ševčovič and S. Yazaki,
On a gradient flow of plane curves minimizing the anisoperimetric ratio, IAENG International J. Appl. Math., 43 (2013), 160-171.
|
[12] |
G. I. Sivashinsky,
Nonlinear analysis of hydrodynamic instability in laminar flames. I. Derivation of basic equations, Acta Astronautica, 4 (1977), 1177-1206.
doi: 10.1016/0094-5765(77)90096-0. |
[13] |
N. M. Zaitoun and M. J. Aqel,
Survey on image segmentation techniques, Procedia Computer Science, 65 (2015), 797-806.
doi: 10.1016/j.procs.2015.09.027. |
show all references
References:
[1] |
M. Beneš, M. Kimura, P. Pauš, D. Ševčovič, T. Tsujikawa and S. Yazaki,
Application of a curvature adjusted method in image segmentation, Bulletin of the Institute of Mathematics, Academia Sinica New Series, 3 (2008), 509-523.
|
[2] |
C. L. Epstein and M. Gage,
The curve shortening flow, Wave Motion: Theory, Modelling, and Computation (Berkeley, Calif., 1986) Mathematical Sciences Research Institute Publications, Springer, New York, 7 (1987), 15-59.
doi: 10.1007/978-1-4613-9583-6_2. |
[3] |
M. L. Frankel and G. I. Sivashinsky,
On the nonlinear thermal diffusive theory of curved flames, Journal de Physique, 48 (1987), 25-28.
doi: 10.1051/jphys:0198700480102500. |
[4] |
M. Goto, K. Kuwana and S. Yazaki,
A simple and fast numerical method for solving flame/smoldering evolution equations, JSIAM Letter, 10 (2018), 49-52.
doi: 10.14495/jsiaml.10.49. |
[5] |
M. Goto, K. Kuwana, G. Kushida and S. Yazaki,
Experimental and theoretical study on near-floor flame spread along a thin solid, Proceedings of the Combustion Institute, 37 (2019), 3783-3791.
doi: 10.1016/j.proci.2018.06.001. |
[6] |
M. Kass, A. Witkin and D. Terzopulos,
Snakes: Active contour models, Int. J. Computer Vision, 1 (1988), 321-331.
doi: 10.1007/BF00133570. |
[7] |
Y. Kuramoto and T. Tsuzuki,
Persistent propagation of concentration waves in dissipative media far from thermal equilibrium, Progress of Theoretical Physics, 55 (1976), 356-369.
doi: 10.1143/PTP.55.356. |
[8] |
K. Mikula and D. Ševčovič,
A direct method for solving an anisotropic mean curvature flow of plane curves with an external force, Math. Methods Appl. Sci., 27 (2004), 1545-1565.
doi: 10.1002/mma.514. |
[9] |
K. Mikula and D. Ševčovič,
Computational and qualitative aspects of evolution of curves driven by curvature and external force, Comput. Vis. Sci., 6 (2004), 211-225.
doi: 10.1007/s00791-004-0131-6. |
[10] |
D. Ševčovič and S. Yazaki,
Evolution of plane curves with a curvature adjusted tangential velocity, Japan J. Indust. Appl. Math., 28 (2011), 413-442.
doi: 10.1007/s13160-011-0046-9. |
[11] |
D. Ševčovič and S. Yazaki,
On a gradient flow of plane curves minimizing the anisoperimetric ratio, IAENG International J. Appl. Math., 43 (2013), 160-171.
|
[12] |
G. I. Sivashinsky,
Nonlinear analysis of hydrodynamic instability in laminar flames. I. Derivation of basic equations, Acta Astronautica, 4 (1977), 1177-1206.
doi: 10.1016/0094-5765(77)90096-0. |
[13] |
N. M. Zaitoun and M. J. Aqel,
Survey on image segmentation techniques, Procedia Computer Science, 65 (2015), 797-806.
doi: 10.1016/j.procs.2015.09.027. |



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