分形几何在自然科学中的应用
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摘要
本文综述了分形几何在物理学、生物学、工程技术、生命科学、地震学等领域的应用。从中我们还可以发现大千世界中数学的优美。
The applications of fractal geometry to physics,engineering,biology,life sciences,and seismology were reviewed.We can see the mathematical beauty in the boundless universe.
The applications of fractal geometry to physics,engineering,biology,life sciences,and seismology were reviewed.We can see the mathematical beauty in the boundless universe.
引文
[1]袁继红,袁群莉.分数维数的哲学启发[J].长春师范学院学报,2002,21(2):77-79.
[2]谢南瑞.多重碎形[J].数学传播,1991,25(1):27-32.
[3]JENSEN M H,KADANOFF L P,LIBCHABER A.Globaluniversality at the onset of chaos:results of a forced Rayleigh-Bénard experiment[J].Physical Review Letters,1985,55(25):2798-2801.
[4]楚化强,郁伯铭.沸腾换热的分形分析[J].力学进展,2009,39(3):259-272.
[5]宋小弟,冯恩信,傅君眉,等.分形天线工程及其新进展[J].无线通信技术,2008,(2):48-54.
[6]于贺,李守巨,满林涛,等.岩体分形裂隙网络系统中水流动研究进展[J].哈尔滨工业大学学报,2011,43(S1):94-99.
[7]ZAZOUN R S.The fadnoun area,Tassili-n-Azjer,Algeria:Fracture network geometry analysis[J].Journal of AfricanEarth Sciences,2008,50(5):273-285.
[8]YU B M,ZOU M Q,FENG Y J.Permeability of fractal por-ous media by Monte Carlo simulations[J].International Jour-nal of Heat and Mass Transfer,2005,48(13):2787-2794.
[9]GHODOOSSI L.Thermal and hydrodynamic analysis of afractal mirochannel network[J].Energy Conversion andManagement,2005,46(5):771-788.
[10]PERATTA A.A new scheme for numerical modeling of flowand transport process in 3D fractured porous media[J].Ad-vances in Water Resources,2006,29(1):42-61.
[11]李守巨,刘迎曦.基于分形理论的煤层瓦斯渗透率参数估计方法[J].西安石油大学学报,2007,22(2):113-115.
[12]嵇晓雷,分形理论应用于植物根系形态分布的研究进展及其应用前景[J].安徽农业科学,2010,38(25):13693-13694.
[13]吕永钢,杨力.血管网分形研究进展[J].化工学报,2010,61(12):3051-3058.
[14]ZAMIR M.Fractal dimensions and multifractility in vascularbranching[J].Journal of Theoretical Biology,2001,212(2):183-190.
[15]GABRYS E,RYBACZUK M,KEDZIA A.Fractal models ofcirculatory system.Symmetrical and asymmetrical approachcomparison[J].Chaos,Solitons and Fractals,2005,24(3):707-715.
[16]PADAKI A,ULTMAN J S,BORHAN A.Ozone uptake dur-ing inspiratory flow in a model of the larynx,trachea and pri-mary bronchial bifurcation[J].Chemical Engineering Sci-ence,2009,64(22):4640-4648.
[17]罗红燕,蒋先军,谢德体.分形理论在微生物研究中的应用及展望[J].微生物学杂志,2009,29(4):75-78.
[18]BEN-JACOB E.Bacterial complexity:More is different on alllevels[J].Systems Biology,2009,1:25-35.doi:10.1007/978-4-431-87704-2_3.
[19]IBEZ J J,PREZ-GMEZ R,SAN JOSMARTNEZ F.The spatial distribution of soils across Europe:a fractal ap-proach[J].Ecological Complexity,2009,6(3):294-301.
[20]张法升,刘作新.分形理论及其在土壤空间变异研究中的应用[J].应用生态学报,2011,22(5):1351-1358.
[21]XIE S,CHENG Q,ZHANG S,HUANG K.Assessing micro-structures of pyrrhotites in basalts by multifractal analysis[J].Nonlin Processes Geophys,2010,17:319-327.doi:10.5194/npg-17-319-2010.
[22]王定华.地球的物质组成[M/OL].[2011-02-28].http://wenku.baidu.com/view/.
[23]陈颙,陈凌.分形几何学[M].北京:地震出版社,2005:163-180.
[2]谢南瑞.多重碎形[J].数学传播,1991,25(1):27-32.
[3]JENSEN M H,KADANOFF L P,LIBCHABER A.Globaluniversality at the onset of chaos:results of a forced Rayleigh-Bénard experiment[J].Physical Review Letters,1985,55(25):2798-2801.
[4]楚化强,郁伯铭.沸腾换热的分形分析[J].力学进展,2009,39(3):259-272.
[5]宋小弟,冯恩信,傅君眉,等.分形天线工程及其新进展[J].无线通信技术,2008,(2):48-54.
[6]于贺,李守巨,满林涛,等.岩体分形裂隙网络系统中水流动研究进展[J].哈尔滨工业大学学报,2011,43(S1):94-99.
[7]ZAZOUN R S.The fadnoun area,Tassili-n-Azjer,Algeria:Fracture network geometry analysis[J].Journal of AfricanEarth Sciences,2008,50(5):273-285.
[8]YU B M,ZOU M Q,FENG Y J.Permeability of fractal por-ous media by Monte Carlo simulations[J].International Jour-nal of Heat and Mass Transfer,2005,48(13):2787-2794.
[9]GHODOOSSI L.Thermal and hydrodynamic analysis of afractal mirochannel network[J].Energy Conversion andManagement,2005,46(5):771-788.
[10]PERATTA A.A new scheme for numerical modeling of flowand transport process in 3D fractured porous media[J].Ad-vances in Water Resources,2006,29(1):42-61.
[11]李守巨,刘迎曦.基于分形理论的煤层瓦斯渗透率参数估计方法[J].西安石油大学学报,2007,22(2):113-115.
[12]嵇晓雷,分形理论应用于植物根系形态分布的研究进展及其应用前景[J].安徽农业科学,2010,38(25):13693-13694.
[13]吕永钢,杨力.血管网分形研究进展[J].化工学报,2010,61(12):3051-3058.
[14]ZAMIR M.Fractal dimensions and multifractility in vascularbranching[J].Journal of Theoretical Biology,2001,212(2):183-190.
[15]GABRYS E,RYBACZUK M,KEDZIA A.Fractal models ofcirculatory system.Symmetrical and asymmetrical approachcomparison[J].Chaos,Solitons and Fractals,2005,24(3):707-715.
[16]PADAKI A,ULTMAN J S,BORHAN A.Ozone uptake dur-ing inspiratory flow in a model of the larynx,trachea and pri-mary bronchial bifurcation[J].Chemical Engineering Sci-ence,2009,64(22):4640-4648.
[17]罗红燕,蒋先军,谢德体.分形理论在微生物研究中的应用及展望[J].微生物学杂志,2009,29(4):75-78.
[18]BEN-JACOB E.Bacterial complexity:More is different on alllevels[J].Systems Biology,2009,1:25-35.doi:10.1007/978-4-431-87704-2_3.
[19]IBEZ J J,PREZ-GMEZ R,SAN JOSMARTNEZ F.The spatial distribution of soils across Europe:a fractal ap-proach[J].Ecological Complexity,2009,6(3):294-301.
[20]张法升,刘作新.分形理论及其在土壤空间变异研究中的应用[J].应用生态学报,2011,22(5):1351-1358.
[21]XIE S,CHENG Q,ZHANG S,HUANG K.Assessing micro-structures of pyrrhotites in basalts by multifractal analysis[J].Nonlin Processes Geophys,2010,17:319-327.doi:10.5194/npg-17-319-2010.
[22]王定华.地球的物质组成[M/OL].[2011-02-28].http://wenku.baidu.com/view/.
[23]陈颙,陈凌.分形几何学[M].北京:地震出版社,2005:163-180.
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