Pub Date : 2023-08-02DOI: 10.1142/s0218348x23500731
Haipeng Chen, Lixuan Zheng
Given [Formula: see text], we study the Assouad dimension and weak tangents of closed [Formula: see text]-popcorn graphs. For all [Formula: see text], we prove that [Formula: see text] is a weak tangent of the closed [Formula: see text]-popcorn graphs by using some arguments on prime numbers. For all [Formula: see text], we first show that the Assouad dimension of the closed [Formula: see text]-popcorn graphs is 1, and then prove that [Formula: see text] is a weak tangent of them. We also discuss some specific weak tangents of closed [Formula: see text]-popcorn graphs when [Formula: see text] and [Formula: see text].
{"title":"WEAK TANGENTS ON CLOSED POPCORN GRAPHS","authors":"Haipeng Chen, Lixuan Zheng","doi":"10.1142/s0218348x23500731","DOIUrl":"https://doi.org/10.1142/s0218348x23500731","url":null,"abstract":"Given [Formula: see text], we study the Assouad dimension and weak tangents of closed [Formula: see text]-popcorn graphs. For all [Formula: see text], we prove that [Formula: see text] is a weak tangent of the closed [Formula: see text]-popcorn graphs by using some arguments on prime numbers. For all [Formula: see text], we first show that the Assouad dimension of the closed [Formula: see text]-popcorn graphs is 1, and then prove that [Formula: see text] is a weak tangent of them. We also discuss some specific weak tangents of closed [Formula: see text]-popcorn graphs when [Formula: see text] and [Formula: see text].","PeriodicalId":55144,"journal":{"name":"Fractals-Complex Geometry Patterns and Scaling in Nature and Society","volume":" ","pages":""},"PeriodicalIF":4.7,"publicationDate":"2023-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49229966","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this work, we have given an analogical method for estimating the fractal dimension for three-dimensional fracture tortuosity (3D-FT). The comparison and error analysis of analogical and rigorous methods on fractal dimension for 3D-FT were carried out in this work. The fractal dimension [Formula: see text] for 3D-FT from the proposed analogical method is the function of 3D fracture average tortuosity ([Formula: see text] and average fracture length ([Formula: see text]. The analogical method for estimating fractal dimension ([Formula: see text] with high accuracy indicates good consistency with the rigorous method ([Formula: see text]. The fractal dimension ([Formula: see text] from the rigorous method is the embodiment of the physical meaning of [Formula: see text]. The fractal dimension ([Formula: see text] from the analogical method is relatively convenient for calculating the premise of ensuring accuracy.
{"title":"AN ANALOGICAL METHOD ON FRACTAL DIMENSION FOR THREE-DIMENSIONAL FRACTURE TORTUOSITY IN COAL BASED ON CT SCANNING","authors":"Gaofeng Liu, Zhen Zhang, Yunxing Cao, Xiaoming Wang, Huan Liu, Baolin Li, Nian Si, W. Guan","doi":"10.1142/s0218348x2350072x","DOIUrl":"https://doi.org/10.1142/s0218348x2350072x","url":null,"abstract":"In this work, we have given an analogical method for estimating the fractal dimension for three-dimensional fracture tortuosity (3D-FT). The comparison and error analysis of analogical and rigorous methods on fractal dimension for 3D-FT were carried out in this work. The fractal dimension [Formula: see text] for 3D-FT from the proposed analogical method is the function of 3D fracture average tortuosity ([Formula: see text] and average fracture length ([Formula: see text]. The analogical method for estimating fractal dimension ([Formula: see text] with high accuracy indicates good consistency with the rigorous method ([Formula: see text]. The fractal dimension ([Formula: see text] from the rigorous method is the embodiment of the physical meaning of [Formula: see text]. The fractal dimension ([Formula: see text] from the analogical method is relatively convenient for calculating the premise of ensuring accuracy.","PeriodicalId":55144,"journal":{"name":"Fractals-Complex Geometry Patterns and Scaling in Nature and Society","volume":" ","pages":""},"PeriodicalIF":4.7,"publicationDate":"2023-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46151960","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-29DOI: 10.1142/s0218348x23500743
Lipeng Wang, Wenxia Li
We introduce a class of sets defined by digit restrictions in [Formula: see text] and study its fractal dimensions. Let [Formula: see text] be a set defined by digit restrictions in [Formula: see text]. We obtain the Hausdorff and lower box dimensions of [Formula: see text]. Under some condition, we gain the packing and upper box dimensions of [Formula: see text]. We get the Assouad dimension of [Formula: see text] and show that it is 2 if and only if [Formula: see text] contains arbitrarily large arithmetic patches. Under some conditions, we study the upper spectrum, quasi-Assouad dimension and Assouad spectrum of [Formula: see text]. Finally, we give an intermediate value property of fractal dimensions of the class of sets.
在[公式:见文]中引入了一类由数字限制定义的集合，并研究了它的分形维数。设[Formula: see text]是由[Formula: see text]中的数字限制定义的集合。我们得到了[公式:见文]的Hausdorff和下盒维数。在一定条件下，我们得到了[公式:见文]的包装尺寸和上盒尺寸。我们得到[Formula: see text]的assad维数，并证明它是2当且仅当[Formula: see text]包含任意大的算术补丁。在一定条件下，我们研究了[公式:见文]的上谱、拟联维数和联谱。最后，给出了这类集合的分形维数的一个中间值性质。
{"title":"FRACTAL DIMENSIONS OF SETS DEFINED BY DIGIT RESTRICTIONS IN ℝ2","authors":"Lipeng Wang, Wenxia Li","doi":"10.1142/s0218348x23500743","DOIUrl":"https://doi.org/10.1142/s0218348x23500743","url":null,"abstract":"We introduce a class of sets defined by digit restrictions in [Formula: see text] and study its fractal dimensions. Let [Formula: see text] be a set defined by digit restrictions in [Formula: see text]. We obtain the Hausdorff and lower box dimensions of [Formula: see text]. Under some condition, we gain the packing and upper box dimensions of [Formula: see text]. We get the Assouad dimension of [Formula: see text] and show that it is 2 if and only if [Formula: see text] contains arbitrarily large arithmetic patches. Under some conditions, we study the upper spectrum, quasi-Assouad dimension and Assouad spectrum of [Formula: see text]. Finally, we give an intermediate value property of fractal dimensions of the class of sets.","PeriodicalId":55144,"journal":{"name":"Fractals-Complex Geometry Patterns and Scaling in Nature and Society","volume":" ","pages":""},"PeriodicalIF":4.7,"publicationDate":"2023-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46114626","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-26DOI: 10.1142/s0218348x23401710
Gang Li, Y. Miao, Jinsui Wu, Feng Zhang, Shangxian Yin, Bin Xu, Yuan-Yuan Li
{"title":"Analysis of stress and structural characteristics of sandstone using CT scanning and fractal theory","authors":"Gang Li, Y. Miao, Jinsui Wu, Feng Zhang, Shangxian Yin, Bin Xu, Yuan-Yuan Li","doi":"10.1142/s0218348x23401710","DOIUrl":"https://doi.org/10.1142/s0218348x23401710","url":null,"abstract":"","PeriodicalId":55144,"journal":{"name":"Fractals-Complex Geometry Patterns and Scaling in Nature and Society","volume":" ","pages":""},"PeriodicalIF":4.7,"publicationDate":"2023-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48141323","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-26DOI: 10.1142/s0218348x23401692
Gaoliang Tao, Fan Zhang, Wei Zhao, Heng-lin Xiao, Qingsheng Chen, S. Basack, Lisheng Liu
{"title":"A New Fractal Model for Predicting Saturated Soil Perme-ability Under Different Deformation","authors":"Gaoliang Tao, Fan Zhang, Wei Zhao, Heng-lin Xiao, Qingsheng Chen, S. Basack, Lisheng Liu","doi":"10.1142/s0218348x23401692","DOIUrl":"https://doi.org/10.1142/s0218348x23401692","url":null,"abstract":"","PeriodicalId":55144,"journal":{"name":"Fractals-Complex Geometry Patterns and Scaling in Nature and Society","volume":" ","pages":""},"PeriodicalIF":4.7,"publicationDate":"2023-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46843893","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-26DOI: 10.1142/s0218348x23401795
Rou Chen, Ying Zhou, Weiwei Yan, Hua Li
{"title":"Non-invasive diagnosis of lung cancer based on CFD modeling and fractal analysis","authors":"Rou Chen, Ying Zhou, Weiwei Yan, Hua Li","doi":"10.1142/s0218348x23401795","DOIUrl":"https://doi.org/10.1142/s0218348x23401795","url":null,"abstract":"","PeriodicalId":55144,"journal":{"name":"Fractals-Complex Geometry Patterns and Scaling in Nature and Society","volume":" ","pages":""},"PeriodicalIF":4.7,"publicationDate":"2023-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46843675","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-26DOI: 10.1142/s0218348x23401758
Habib Ullah, M. Fiza, H. Ullah, M. Shoaib, M. Asif, Zahoor Raja, A. Akgul, J. Asad, Mohammad Kanan
{"title":"Intelligent computing paradigm for Second-Grade Fluid in a Rotating Frame in a Fractal Porous Medium","authors":"Habib Ullah, M. Fiza, H. Ullah, M. Shoaib, M. Asif, Zahoor Raja, A. Akgul, J. Asad, Mohammad Kanan","doi":"10.1142/s0218348x23401758","DOIUrl":"https://doi.org/10.1142/s0218348x23401758","url":null,"abstract":"","PeriodicalId":55144,"journal":{"name":"Fractals-Complex Geometry Patterns and Scaling in Nature and Society","volume":" ","pages":""},"PeriodicalIF":4.7,"publicationDate":"2023-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45237447","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-26DOI: 10.1142/s0218348x23401783
Hongqing Song, J. Lao, Hongen Yang, Chiyu Xie, Jiulong Wang
{"title":"Multifractal modeling of gas-water relative permeability considering multiscale and multieffects: investigation of unconventional gas development","authors":"Hongqing Song, J. Lao, Hongen Yang, Chiyu Xie, Jiulong Wang","doi":"10.1142/s0218348x23401783","DOIUrl":"https://doi.org/10.1142/s0218348x23401783","url":null,"abstract":"","PeriodicalId":55144,"journal":{"name":"Fractals-Complex Geometry Patterns and Scaling in Nature and Society","volume":" ","pages":""},"PeriodicalIF":4.7,"publicationDate":"2023-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42419765","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-26DOI: 10.1142/s0218348x23401849
Hailong Chen, Bingxin Ji, Fei Wang, Yuchen Wang, Faming Zeng, Z. Li, Qi Jiang
{"title":"Experimental investigation on fractal characterization of in-situ foam in porous media","authors":"Hailong Chen, Bingxin Ji, Fei Wang, Yuchen Wang, Faming Zeng, Z. Li, Qi Jiang","doi":"10.1142/s0218348x23401849","DOIUrl":"https://doi.org/10.1142/s0218348x23401849","url":null,"abstract":"","PeriodicalId":55144,"journal":{"name":"Fractals-Complex Geometry Patterns and Scaling in Nature and Society","volume":" ","pages":""},"PeriodicalIF":4.7,"publicationDate":"2023-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45887735","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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