迷向增长曲面的结构表达式

Abstract

Abstract:

The isotropic growth surface in complex 3-space is investigated by evolving an isotropic curve as dictated growth velocity. The structure expression form of the isotropic growth surface is explored by the aid of the structure function of its generating isotropic curve. As an important application, the isotropic growth surface initiated by the isotropic helix is discussed deeply and explicitly. At the same time, several typical examples are constructed to characterize the generating process of such growth surfaces.

Key words: Complex space, Isotropic curve, Growth surface, Isotropic helix, Structure function

CLC Number:

O186

Qian Jinhua,Bian Jinxin,Fu Xueshan. Structure Expression Form of Isotropic Growth Surface[J].Acta mathematica scientia,Series A, 2023, 43(3): 657-668.

Trendmd

Figures/Tables 16

References 13

[1]	Pollack J, Hubickyj O, Bodenheimer P, Lissauer J, Podolak M, Greenzweig Y. Formation of the giant planets by concurrent accretion of solids and gas. Icarus, 1996, 124(1): 62-85 doi: 10.1006/icar.1996.0190
[2]	Fournier M, Bailleres H, Chanson B. Tree biomechanics: growth, cumulative prestresses, and reorientations. Biomimetics, 1994, 2: 229-251
[3]	Hodge N, Papadopoulos P. Continuum modeling and numerical simulation of cell motility. J Math Biol, 2012, 64(7): 1253-1279 doi: 10.1007/s00285-011-0446-0 pmid: 21710139
[4]	Tsui Y C, Clyne T W. An analytical model for predicting residual stresses in progressively deposited coatings. Part 1: planar geometry. Thin Solid Films, 1997, 306(1): 23-33 doi: 10.1016/S0040-6090(97)00199-5
[5]	Moseley H. On the geometrical forms of turbinated and discoid shells. Phil Trans R Soc Lond, 1838, 128: 351-370
[6]	Thompson D. On Growth and Form. London: Cambridge University Press, 1942
[7]	Illert C. Formulation and solution of the classical problem: II. Tubular three dimensional surfaces. Nuovo Cimento, 1989, 11: 761-780 doi: 10.1007/BF02451562
[8]	Cowin S C. Bone stress adaptation models. J Biomech Eng, 1993, 115: 528-533 doi: 10.1115/1.2895535
[9]	Huiskes R, Hollister S J. From structure to process, from organ to cell: recent developments of FE-analysis in orthopedic biomechanics. J Biomech Eng, 1993, 115: 520-527 doi: 10.1115/1.2895534
[10]	Illert C. Formulation and solution of the classical problem: I. Seashell geometry. Nuovo Cimento, 1987, 9: 791-814
[11]	Yilmaz S, Ünlütürk Y. Contributions to differential geometry of isotropic curves in the complex space ${\Bbb C}^{3}$ -II. J Math Anal Appl, 2016, 440: 561-577 doi: 10.1016/j.jmaa.2016.02.072
[12]	Qian J H, Yin P, Fu X S, Wang H Z. Representations of rectifying isotropic curves and their centrodes in complex 3-space. Mathematics, 2021, 9: 1451 doi: 10.3390/math9121451
[13]	Qian J H, Kim Y H. Some isotropic curves and representation in complex space ${\Bbb C}^3$ . Bull Korean Math Soc, 2015, 52(3): 963-975 doi: 10.4134/BKMS.2015.52.3.963

Metrics

Viewed

Full text

199

HTML			PDF

Just accepted	Online first	Issue	Just accepted	Online first	Issue
0	0	9	0	0	190

From	Others	local

Times	10	189
Rate	5%	95%

Abstract

102

Just accepted	Online first	Issue

0	0	102

From	Others	local

Times	101	1
Rate	99%	1%

Cited

Web of Science	Crossref	ScienceDirect	Search for Citations in Google Scholar >>


This page requires you have already subscribed to WoS.

Shared

Discussed

Comments

Recommended 10

[1]	He Suxiang;Zhang Liwei. A Modified Lagrangian Algorithm for Solving Nonlinear Constrained Optimization Problems[J]. Acta mathematica scientia,Series A, 2006, 26(1): 49 -062 .
[2]	Jia Jia. The Two-Dimensional Steady Chaplygin Gas Flows Passing a Straight Wedge[J]. Acta mathematica scientia,Series A, 2021, 41(5): 1270 -1282 .
[3]	Xueli Jiang,Xuan Deng,Qiuhao Wen,Yanqin Xiong. Limit Circle Bifurcations of Polynomial Differential System with Two Parallel Switch Straight Lines[J]. Acta mathematica scientia,Series A, 2022, 42(2): 353 -364 .
[4]	Xiaoli Chen,Dongxiang Chen,Hongyan Zhu. Weighted Estimates for Some Multilinear Square Operator and Commutator with Generalized Kernel[J]. Acta mathematica scientia,Series A, 2021, 41(4): 954 -967 .
[5]	Jiaolang Wang,Donghui Fang. Approximate Optimality Conditions and Mixed Type Duality for a Class of Non-Convex Optimization Problems[J]. Acta mathematica scientia,Series A, 2022, 42(3): 651 -660 .
[6]	Juan Wang,Jie Zhao. Homogenization of the Oscillating Robin Mixed Boundary Value Problems[J]. Acta mathematica scientia,Series A, 2021, 41(1): 81 -90 .
[7]	Dingdong Gong,Yuqin Guo. The Singular Integral Equations on the Intersection of Two Balls in ${\Bbb C}^n$ [J]. Acta mathematica scientia,Series A, 2022, 42(1): 18 -25 .
[8]	Qing Chen. Optimal Time Decay Rate of the Highest Derivative of Solutions to the Compressible Navier-Stokes Equations[J]. Acta mathematica scientia,Series A, 2021, 41(2): 345 -356 .
[9]	Xiaojing Guo,Fujie Chai,Daochun Sun. Normal Family Theorems for Meromorphic Functions with Discrete Values of One Leaf[J]. Acta mathematica scientia,Series A, 2021, 41(6): 1598 -1605 .
[10]	Rui Hua,Yaru Qi. The Essential Spectrum of a Class of Anti-Triangular Operator Matrices[J]. Acta mathematica scientia,Series A, 2022, 42(6): 1611 -1618 .

Structure Expression Form of Isotropic Growth Surface

RichHTML

PDF (PC)

Abstract

Cite this article

share this article

Figures/Tables 16

References 13

Related Articles 1

Metrics

Comments

Recommended 10