Duality in interaction potentials for curved surface bodies and inside particles

doi:10.1007/s10483-017-2223-9

Applied Mathematics and Mechanics (English Edition) ›› 2017, Vol. 38 ›› Issue (8): 1071-1090.doi: https://doi.org/10.1007/s10483-017-2223-9

Duality in interaction potentials for curved surface bodies and inside particles

Dan WANG¹, Yajun YIN¹, Jiye WU², Zheng ZHONG³

1. Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China;
2. Department of Civil Engineering, Nanjing Tech University, Nanjing 211800, China;
3. Department of Engineering Mechanics, Tongji University, Shanghai 200092, China

收稿日期:2016-11-01 修回日期:2016-12-06 出版日期:2017-08-01 发布日期:2017-08-01
通讯作者: Yajun YIN,E-mail:yinyj@tsinghua.edu.cn E-mail:yinyj@tsinghua.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Nos. 11672150 and 11272175), the Natural Science Foundation of Jiangsu Province (No. BK20130910), and the specialized Research Found for Doctoral Program of Higher Education (No. 2013000211004)

Duality in interaction potentials for curved surface bodies and inside particles

Dan WANG¹, Yajun YIN¹, Jiye WU², Zheng ZHONG³

1. Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China;
2. Department of Civil Engineering, Nanjing Tech University, Nanjing 211800, China;
3. Department of Engineering Mechanics, Tongji University, Shanghai 200092, China

Received:2016-11-01 Revised:2016-12-06 Online:2017-08-01 Published:2017-08-01
Contact: Yajun YIN E-mail:yinyj@tsinghua.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Nos. 11672150 and 11272175), the Natural Science Foundation of Jiangsu Province (No. BK20130910), and the specialized Research Found for Doctoral Program of Higher Education (No. 2013000211004)

摘要/Abstract

摘要：

Based on the viewpoint of duality, this paper studies the interaction between a curved surface body and an inside particle. By convex/concave bodies with geometric duality, interaction potentials of particles located outside and inside the curved surface bodies are shown to have duality. With duality, the curvature-based potential between a curved surface body and an inside particle is derived. Furthermore, the normal and tangential driving forces exerted on the particle are studied and expressed as a function of curvatures and curvature gradients. Numerical experiments are designed to test accuracy of the curvature-based potential.

关键词: transverse crack, saturate crack spacing, damage, stress, curvature gradient, curvature, micro/nano curved surface body, curvature-based potential, driving force, duality

Abstract:

Key words: transverse crack, saturate crack spacing, damage, stress, micro/nano curved surface body, curvature-based potential, curvature, driving force, duality, curvature gradient

中图分类号:

55U30

Dan WANG, Yajun YIN, Jiye WU, Zheng ZHONG. Duality in interaction potentials for curved surface bodies and inside particles[J]. Applied Mathematics and Mechanics (English Edition), 2017, 38(8): 1071-1090.

参考文献

[1] Yin, Y. J., Chen, C., Lü, C. J., and Zheng, Q. S. Shape gradient and classical gradient of curvatures:driving forces on micro/nano curved surfaces. Applied Mathematics and Mechanics (English Edition), 32(5), 533-550(2011) DOI 10.1007/s10483-011-1436-6
[2] Wu, J. Y., Yin, Y. J., Wang, X. G., and Fan, Q. S. Interaction potential between micro/nano curved surface and a particle located inside the surface (I):driving forces induced by curvatures. Science China:Physics Mechanics and Astronomy, 55(6), 1066-1076(2012)
[3] Wu, J. Y., Yin, Y. J., Huang, K., and Fan, Q. S. Interaction potential between micro/nano curved surface and a particle located inside the surface (Ⅱ):numerical experiment and equipotential surfaces. Science China:Physics Mechanics and Astronomy, 55(6), 1077-1082(2012)
[4] Wang, X. G., Yin, Y. J., Wu, J. Y., and Wang, D. Curvature-based interaction potential between an isolated particle and micro/nano space curve. Physica E:Low-Dimensional Systems and Nanostructures, 67, 178-191(2015)
[5] Wang, D., Yin, Y. J., Wu, J. Y., and Zhong, Z. Interaction potential between parabolic rotator and an outside particle. Journal of Nanomaterials, 2014, 1-6(2014)
[6] Wang, D., Yin, Y. J., Wu, J. Y., and Zhong, Z. Curvature-based interaction potential between micro/nano curved surface body and an outside particle. Journal of Computational and Theoretical Nanoscience, 12(12), 1-12(2015)
[7] Wang, D., Yin, Y. J., Wu, J. Y., and Zhong, Z. Curvature-based interaction potential between micro/nano curved surface body and a particle on the surface of the body. Journal of Biological Physics, 42(1), 33-51(2015)
[8] Peter, J. Y., Tim, S., Matthew, A. L., and Yodh, A. G. Suppression of the coffee-ring effect byshape-dependent capillary interactions. nature, 476(18), 308-311(2011)
[9] Zhao, Y. P. Physical Mechanics of Surfaces and Interfaces, Science Press, Beijing (2012)
[10] Johnson, H. H. Hydrogen embrittlement. Science, 179, 228-230(1973)
[11] Rustom, A., Saffrich, R., and Markovic, I. Nanotubular highways for intercellular organelle transport. Science, 303, 1007-1010(2004)
[12] Blanchfield, R. C. Intersection theory of manifolds with operators with applications to knot theory. Annals of Mathematics, 65(2), 340-356(1957)
[13] Hilbert, D. and Cohn-Vossen, S. Geometry and the Imagination, 2nd ed., Chelsea, New York, 119-128(1952)
[14] Negrepontis, J. W. Duality in analysis from the point of view of triples. Journal of Algebra, 19(2), 228-253(1971)
[15] Israelachvili, J. Intermolecular and Surface Forces, 3nd ed., Academic Press, London (2011)
[16] Su, B. Q., Hu, H. S., Shen, C. L., Pan, Y. L., and Zhang, G. L. Differential Geometry, People's Education Press, Beijing, 16-18(1979)
[17] Wu, J. Y. Biomembrane Free Energy and the Driving Forces Induced by Curvature Gradients (in Chinese), Ph. D. dissertation, Tsinghua University, 40-45(2012)

Duality in interaction potentials for curved surface bodies and inside particles

Duality in interaction potentials for curved surface bodies and inside particles

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