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The amplitude statistical distribution funetion p(l) of the aerosol scattering pulse signals is measured with high resolution through combining the high-speed data acquisition card PCI-9812 and the photoelectric sensor of laser airborne particle counter. The experimental results show that the distribution founction p(l) of the whole signal group and the different pulse width subsets all fit the lognormal distribution with very high precision in the range of amplitude definition (V0,VM) under the condition of big samples, which indicates that the random signal group has a statistical fractal (self-similarity) characteristic. According to the further theoretical results, it is analyzed that function p(l) has a nonlinear scale invariance. Besides, this function shows a geometrical similarity to the power law l-(1-ε) when statistical parameter , where ε<<1.
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Keywords:
- statistical fractal /
- applitude counting distribution function of the pulse signal /
- nonlinear scale invariance /
- power law
[1] Mandelbrot B B 1982 The Fractal Geometry of Nature (San Francisco: W. H. Freeman)
[2] Yang J, Lai X M, Peng G, Bian B B, Lu J 2009 Acta Phys. Sin. 58 3008 (in Chinese)[杨 娟、 赖晓明、 彭 刚、 卞保民、 陆 建 2009 58 3008]
[3] Ren X C, Guo L X 2008 Chin. Phys. B 17 2956
[4] Chen Y, Chen L 2005 Fractal Geometry (Beijing: Earthquake Pubishing House) p76(in Chinese) [陈 顒、陈 凌 2005 分形几何学(北京: 地震出版社) 第76页]
[5] Kiss L B, Soderlund J, Granqvist C G 1999 NanoStructured Materials 12 327
[6] Park D, An M, Hwang J 2007 Aerosol Science 38 420
[7] Baker L, Giancola A J, Allahdadi F 1992 Journal of Applied Physics 72 2724
[8] Shu X M, Fang J, Shen S F, Liu Y J, Yuan H Y, Fan W C 2006 Acta Phys. Sin. 55 4466(in Chinese)[疏学明、方 俊、 〖9] Millan H, Gonzalez-Posada M, Aguilar M, Dominguez J, Cespedes L 2003 Geoderma 117 117
[9] Michael D H 2006 Journal of Volcanology and Geothermal Research 154 8
[10] Tijana B, Aleksandra V, Aleksandar K 2010 Journal of Theoretical Biology 262 214
[11] Peng G, Bian B B, Lu J 2009 Instrument Technique and Sensor 9 5(in Chinese)[彭 刚、卞保民、 陆 建 2009 仪表技术与传感器 9 5]
[12] Gu F, Yang J, Bian B B, He A Z 2007 Acta Opt. Sin. 27 1706(in Chinese) [顾 芳、杨 娟、卞保民、贺安之 2007 光学学报 27 1706]
[13] Tanaka M, Komagata M, Tsukada M, Kamiya H 2008 Powder Technology 186 1
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[1] Mandelbrot B B 1982 The Fractal Geometry of Nature (San Francisco: W. H. Freeman)
[2] Yang J, Lai X M, Peng G, Bian B B, Lu J 2009 Acta Phys. Sin. 58 3008 (in Chinese)[杨 娟、 赖晓明、 彭 刚、 卞保民、 陆 建 2009 58 3008]
[3] Ren X C, Guo L X 2008 Chin. Phys. B 17 2956
[4] Chen Y, Chen L 2005 Fractal Geometry (Beijing: Earthquake Pubishing House) p76(in Chinese) [陈 顒、陈 凌 2005 分形几何学(北京: 地震出版社) 第76页]
[5] Kiss L B, Soderlund J, Granqvist C G 1999 NanoStructured Materials 12 327
[6] Park D, An M, Hwang J 2007 Aerosol Science 38 420
[7] Baker L, Giancola A J, Allahdadi F 1992 Journal of Applied Physics 72 2724
[8] Shu X M, Fang J, Shen S F, Liu Y J, Yuan H Y, Fan W C 2006 Acta Phys. Sin. 55 4466(in Chinese)[疏学明、方 俊、 〖9] Millan H, Gonzalez-Posada M, Aguilar M, Dominguez J, Cespedes L 2003 Geoderma 117 117
[9] Michael D H 2006 Journal of Volcanology and Geothermal Research 154 8
[10] Tijana B, Aleksandra V, Aleksandar K 2010 Journal of Theoretical Biology 262 214
[11] Peng G, Bian B B, Lu J 2009 Instrument Technique and Sensor 9 5(in Chinese)[彭 刚、卞保民、 陆 建 2009 仪表技术与传感器 9 5]
[12] Gu F, Yang J, Bian B B, He A Z 2007 Acta Opt. Sin. 27 1706(in Chinese) [顾 芳、杨 娟、卞保民、贺安之 2007 光学学报 27 1706]
[13] Tanaka M, Komagata M, Tsukada M, Kamiya H 2008 Powder Technology 186 1
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