Growth kinematics of fractal super snowflakes  

作　　者：YIN YaJun YANG Fan FAN QinShan 

机构地区：[1]Department of Engineering Mechanics, School of Aerospace, AML, Tsinghua University, Beijing 100084, China [2]Division of Mechanics, Nanjing University of Technology, Nanjing 211816, China

出　　处：《Chinese Science Bulletin》2010年第7期573-580,共8页

基　　金：supported by the National Natural Science Foundation of China(Grant No.10872114);Natural Science Foundation of Jiangsu Province(Grant No.BK2008370)

摘　　要：Based on the recent research progress in fractal super fibers,the growth kinematics(or pattern kinematics) of(6+1) -circle fractal super fiber with snowflake-like cross section(abbreviated as"fractal super snowflake") is explored.The following results are obtained.(1) The fractal super snowflake obeys simply the straight-line growth mode.(2) At a given movement,the growth speed of the snowflake distributes uniformly in space.At a given point in space,the growth speed decreases along with the time.(3) The growth kinematics of the fractal super snowflake is intensively influenced by the self-similar ratio:If and only if the self-similar ratio is equal to 1/3,the macro speed equals to the micro speed,and the macro density equals to the micro density.If the self-similar ratio is smaller than 1/3,the micro speed is larger than the macro speed,and the micro density is larger than the macro density.If the self-similar ratio is larger than 1/3,the macro speed is larger than the micro speed,and the macro density is larger than the micro density.These results provide references for us to understand the complicated fractal growing phenomena in nature.Based on the recent research progress in fractal super fibers, the growth kinematics （or pattern kinematics） of （6＋1）-circle fractal super fiber with snowflake-like cross section （abbreviated as ＂fractal super snowflake＂） is explored. The following results are obtained. （1） The fractal super snowflake obeys simply the straight-line growth mode. （2） At a given movement, the growth speed of the snowflake distributes uniformly in space. At a given point in space, the growth speed decreases along with the time. （3） The growth kinematics of the fractal super snowflake is intensively influenced by the self-similar ratio： If and only if the self-similar ratio is equal to 1/3, the macro speed equals to the micro speed, and the macro density equals to the micro density. If the self-similar ratio is smaller than 1/3, the micro speed is larger than the macro speed, and the micro density is larger than the macro density. If the self-similar ratio is larger than 1/3, the macro speed is larger than the micro speed, and the macro density is larger than the micro density. These results provide references for us to understand the complicated fractal growing phenomena in nature.

关 键 词：分形生长 运动学 雪花 超级纤维 速度比 密度比 相似比 空间分布 

分 类 号：O484.1[理学—固体物理] O311[理学—物理]