An application of box counting method for measuring phase fraction

Xu, Jun; Jian, Zengyun; Lian, Xin

doi:10.1016/j.measurement.2017.01.008

Cited by 6 publications

(2 citation statements)

References 16 publications

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“…Practically to calculate the fractal dimension, the box-counting method is used (Swapna et al, 2021;Wu et al, 2020;Xu et al, 2017). In 2D, the set of points in the space forms a surface.…”

Section: Calculation Of the Fractal Dimensionmentioning

confidence: 99%

Fractals and music

Pothiyodath

Murkoth

2022

Momentum: Physics Education Journal

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Many natural phenomena we find in our surroundings, are fractals. Studying and learning about fractals in classrooms is always a challenge for both teachers and students. We here show that the sound of musical instruments can be used as a good resource in the laboratory to study fractals. Measurement of fractal dimension which indicates how much fractal content is there, is always uncomfortable, because of the size of the objects like coastlines and mountains. A simple fractal source is always desirable in laboratories. Music serves to be a very simple and effective source for fractal dimension measurement. In this paper, we are suggesting that music which has an inherent fractal nature can be used as an object in classrooms to measure fractal dimensions. To find the fractal dimension we used the box-counting method. We studied the sound produced by different stringed instruments and some common noises. For good musical sound, the fractal dimension obtained is around 1.6882.

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“…Practically to calculate the fractal dimension, the box-counting method is used (Swapna et al, 2021;Wu et al, 2020;Xu et al, 2017). In 2D, the set of points in the space forms a surface.…”

Section: Calculation Of the Fractal Dimensionmentioning

confidence: 99%

Fractals and music

Pothiyodath

Murkoth

2022

Momentum: Physics Education Journal

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“…where N (r) is the number of boxes and r is the side length used t o cover the set (Ai et al, 2014, Xu et al, 2017.…”

Section: Fractal Dimension Of Particlesmentioning

confidence: 99%

Experimental Investigation of the Diesel Engine With Charged Agglomerator Coupling DPF

Zhou

Han

Tang

et al. 2019

Inter J Ener Clean Env

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Investigation of a charged agglomerator and a diesel particulate fi lter setup is carried out. To analyze the economical effi ciency and emission performance of the diesel engine, bench testing was conducted on the coupled setup (i.e., engine, charged agglomerator, and a diesel particulate fi lter). Aft er running the engine for 3000 s, the pressure drops and fuel consumption decreases by 0.3 kPa and 2%, respectively. Smoke intensity decreases signifi cantly under a high engine load, while fi ltering effi ciency also increases by 3.1%. The particles microstructure and morphology were obtained with the aid of a transmission electron microscopy (TEM). The accumulation and overlap phenomenon of particles increases intensely aft er going through the charged agglomerator. Aft er passing through the fi lter, small clusters of particles are distributed, with a clearer outline and improved degree of graphitization. Based on the "box counting method," the fractal dimensions of the particles were analyzed. The fractal dimensions increase aft er going through the charged agglomerator but decrease aft er passing through the fi lter, confi rming the results obtained from the TEM.

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