Pub Date : 2023-08-31DOI: 10.1142/s0218348x23500962
Jian Wang, Wenjing Jiang, Junseok Kim
Accurate classification of the medical signals is urgently needed in clinical medicine. This paper aims to create a classifier to shorten the time of the classification and ensure the sorting accuracy, which assists physicians in saving diagnostic time and formulating the treatment plans. We create the classifier based on Kolmogorov complexity, Shannon entropy, Higuchi’s Hurst exponent and multifractal features. We obtain a feature value from Kolmogorov complexity, Shannon entropy and Higuchi’s Hurst exponent, and three feature values based on multifractal features to compose a vector and analyze it. Furthermore, we study a vector composed of six multifractal features as a control group. Electrocardiogram (ECG) and electroencephalogram (EEG) signals are applied to examine the performance of the classifier by support vector machine (SVM). The accuracy of ECG signals based on mixed classification (MC–ECG–SVM) reaches 94.17%, which is approximately 15% higher than that of ECG signals only based on multifractal features classification (UC–ECG–SVM). The sensitivities of MC–ECG–SVM and UC–ECG–SVM are 86.09% and 64.54%, respectively. The specificities of MC–ECG–SVM and UC–ECG–SVM are 98.26% and 93.65%, respectively. Analogously, the accuracy, sensitivity, and specificity of EEG signals based on mixed classification (MC–EEG–SVM) reach 95.29%, 96.28%, and 94.55%, respectively. The accuracy, sensitivity, and specificity of EEG signals based on multifractal features classification (UC–EEG–SVM) are 87.40%, 89.28%, and 88.11%, respectively. Therefore, the mixed classification method is more accurate than the classification method only based on multifractal features.
{"title":"A NOVEL ECG AND EEG CLASSIFICATION SYSTEM BASED ON NONLINEAR STATISTICAL FEATURES","authors":"Jian Wang, Wenjing Jiang, Junseok Kim","doi":"10.1142/s0218348x23500962","DOIUrl":"https://doi.org/10.1142/s0218348x23500962","url":null,"abstract":"Accurate classification of the medical signals is urgently needed in clinical medicine. This paper aims to create a classifier to shorten the time of the classification and ensure the sorting accuracy, which assists physicians in saving diagnostic time and formulating the treatment plans. We create the classifier based on Kolmogorov complexity, Shannon entropy, Higuchi’s Hurst exponent and multifractal features. We obtain a feature value from Kolmogorov complexity, Shannon entropy and Higuchi’s Hurst exponent, and three feature values based on multifractal features to compose a vector and analyze it. Furthermore, we study a vector composed of six multifractal features as a control group. Electrocardiogram (ECG) and electroencephalogram (EEG) signals are applied to examine the performance of the classifier by support vector machine (SVM). The accuracy of ECG signals based on mixed classification (MC–ECG–SVM) reaches 94.17%, which is approximately 15% higher than that of ECG signals only based on multifractal features classification (UC–ECG–SVM). The sensitivities of MC–ECG–SVM and UC–ECG–SVM are 86.09% and 64.54%, respectively. The specificities of MC–ECG–SVM and UC–ECG–SVM are 98.26% and 93.65%, respectively. Analogously, the accuracy, sensitivity, and specificity of EEG signals based on mixed classification (MC–EEG–SVM) reach 95.29%, 96.28%, and 94.55%, respectively. The accuracy, sensitivity, and specificity of EEG signals based on multifractal features classification (UC–EEG–SVM) are 87.40%, 89.28%, and 88.11%, respectively. Therefore, the mixed classification method is more accurate than the classification method only based on multifractal features.","PeriodicalId":55144,"journal":{"name":"Fractals-Complex Geometry Patterns and Scaling in Nature and Society","volume":null,"pages":null},"PeriodicalIF":4.7,"publicationDate":"2023-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43165215","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}
This paper presents a novel approach for modeling Boost converters using the Caputo–Fabrizio (C-F) definition-based fractional-order model to address singular characteristics in fractional-order definitions and enhance model accuracy. A small signal modeling method is proposed to improve the accuracy of circuit parameter design and to derive state-averaged models, state-space equations, and transfer functions. The influence of capacitor and inductor orders on steady-state characteristics is analyzed and the influence of fractional-order on ripple characteristics is investigated through simulation. When the fractional-order approaches 1, the output voltage increases and the inductance current decreases, with waveform jitter mitigation. Moreover, boundary conditions for continuous conduction mode operation are established based on ripple characteristics. The numerical and circuit-oriented simulations verify the correctness of the proposed model. Finally, the orders and accurate parameters of capacitors and inductors based on the C-F definition are determined and the experiments are conducted. The comparison between the experimental and simulation results demonstrates that the proposed model can accurately describe the steady-state characteristics of the practical circuit systems, which further validates the accuracy of the proposed method.
{"title":"MODELING AND CHARACTERISTIC ANALYSIS OF FRACTIONAL-ORDER BOOST CONVERTER BASED ON THE CAPUTO–FABRIZIO FRACTIONAL DERIVATIVES","authors":"Donghui Yu, X. Liao, Y. Wang, Manjie Ran, Dalin, Jinhui Xia","doi":"10.1142/s0218348x23500822","DOIUrl":"https://doi.org/10.1142/s0218348x23500822","url":null,"abstract":"This paper presents a novel approach for modeling Boost converters using the Caputo–Fabrizio (C-F) definition-based fractional-order model to address singular characteristics in fractional-order definitions and enhance model accuracy. A small signal modeling method is proposed to improve the accuracy of circuit parameter design and to derive state-averaged models, state-space equations, and transfer functions. The influence of capacitor and inductor orders on steady-state characteristics is analyzed and the influence of fractional-order on ripple characteristics is investigated through simulation. When the fractional-order approaches 1, the output voltage increases and the inductance current decreases, with waveform jitter mitigation. Moreover, boundary conditions for continuous conduction mode operation are established based on ripple characteristics. The numerical and circuit-oriented simulations verify the correctness of the proposed model. Finally, the orders and accurate parameters of capacitors and inductors based on the C-F definition are determined and the experiments are conducted. The comparison between the experimental and simulation results demonstrates that the proposed model can accurately describe the steady-state characteristics of the practical circuit systems, which further validates the accuracy of the proposed method.","PeriodicalId":55144,"journal":{"name":"Fractals-Complex Geometry Patterns and Scaling in Nature and Society","volume":null,"pages":null},"PeriodicalIF":4.7,"publicationDate":"2023-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43946185","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 : 2023-08-29DOI: 10.1142/s0218348x23500792
Dayu Ye, Guannan Liu, Bo-ming Yu, Xutong Zhang, Feng Gao
The key to shale gas exploration is the characterization of gas migration under the combination of multiple factors. To address the long-standing energy challenge of rapidly and accurately quantifying the behavior of natural fractures and matrix pores in shale at an engineering scale in interaction with gas migration. This study proposes an interdisciplinary model for shale gas extraction by adopting fractal theory. Five innovative microstructural parameters are developed to characterize the size and scale of natural matrix pores/fractures in shale, so as to investigate the contributions of fractal distributed pores and fractal power-law distributed fractures to shale gas extraction. The present results of the proposed model are consistent with the exploitation state of the UK Bowland Shale #114 well. The evolution of the shale microstructure will lead to changes in gas migration behavior throughout the reservoir and in turn affect shale stress, temperature and gas adsorption–desorption effect, and finally have a significant impact on permeability. It is found that in the present analysis of the entire Bowland Shale, the overall permeability changes by 10.8% with the evolution of fractal distributed pores and by 41.3% with the evolution of fractal power-law fractures. This work provides a new approach for rapidly exploring the behavior of shale fractures and matrix pores at engineering scales. This work also offers a new and practical baseline for shale gas extraction assessment and fossil energy management.
{"title":"EVALUATION OF SHALE GAS EXPLORATION BY MICROSTRUCTURE BEHAVIOR AND SHALE PERMEABILITY BASED ON FRACTAL THEORY AND UNDER MULTI-FIELD EFFECTS","authors":"Dayu Ye, Guannan Liu, Bo-ming Yu, Xutong Zhang, Feng Gao","doi":"10.1142/s0218348x23500792","DOIUrl":"https://doi.org/10.1142/s0218348x23500792","url":null,"abstract":"The key to shale gas exploration is the characterization of gas migration under the combination of multiple factors. To address the long-standing energy challenge of rapidly and accurately quantifying the behavior of natural fractures and matrix pores in shale at an engineering scale in interaction with gas migration. This study proposes an interdisciplinary model for shale gas extraction by adopting fractal theory. Five innovative microstructural parameters are developed to characterize the size and scale of natural matrix pores/fractures in shale, so as to investigate the contributions of fractal distributed pores and fractal power-law distributed fractures to shale gas extraction. The present results of the proposed model are consistent with the exploitation state of the UK Bowland Shale #114 well. The evolution of the shale microstructure will lead to changes in gas migration behavior throughout the reservoir and in turn affect shale stress, temperature and gas adsorption–desorption effect, and finally have a significant impact on permeability. It is found that in the present analysis of the entire Bowland Shale, the overall permeability changes by 10.8% with the evolution of fractal distributed pores and by 41.3% with the evolution of fractal power-law fractures. This work provides a new approach for rapidly exploring the behavior of shale fractures and matrix pores at engineering scales. This work also offers a new and practical baseline for shale gas extraction assessment and fossil energy management.","PeriodicalId":55144,"journal":{"name":"Fractals-Complex Geometry Patterns and Scaling in Nature and Society","volume":null,"pages":null},"PeriodicalIF":4.7,"publicationDate":"2023-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44929778","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 : 2023-08-28DOI: 10.1142/s0218348x23500949
A. Elías-Zúñiga, O. Martínez-Romero, Daniel Olvera Trejo, L. M. Palacios-Pineda
This paper elucidates how the two-scale fractal dimension transform, and a transformation method can be applied to replace the Warner–Gent equation that models the fractal dynamic response of porous viscohyperelastic materials with an equivalent power-form equation. Furthermore, this research work elucidates the advantages of modeling viscohyperlastic materials using the fractal Warner–Gent’s model since the values of the fractal dimension parameter unveil how the global molecular structure of viscohyperelastic materials varies as a function of the vibration frequency wavelength. Compared to the original one, the accuracy attained from the Warner–Gent power-form equivalent equation is examined by plotting the frequency–amplitude and time–amplitude curves obtained from the corresponding numerical integration solutions. It is found that both numerical integration solutions agree well since the root-mean-square-error (RMSE) values remain small.
{"title":"A WEIGHTED POWER-FORM FORMULATION FOR THE FRACTAL WARNER–GENT VISCOHYPERLASTIC MODEL","authors":"A. Elías-Zúñiga, O. Martínez-Romero, Daniel Olvera Trejo, L. M. Palacios-Pineda","doi":"10.1142/s0218348x23500949","DOIUrl":"https://doi.org/10.1142/s0218348x23500949","url":null,"abstract":"This paper elucidates how the two-scale fractal dimension transform, and a transformation method can be applied to replace the Warner–Gent equation that models the fractal dynamic response of porous viscohyperelastic materials with an equivalent power-form equation. Furthermore, this research work elucidates the advantages of modeling viscohyperlastic materials using the fractal Warner–Gent’s model since the values of the fractal dimension parameter unveil how the global molecular structure of viscohyperelastic materials varies as a function of the vibration frequency wavelength. Compared to the original one, the accuracy attained from the Warner–Gent power-form equivalent equation is examined by plotting the frequency–amplitude and time–amplitude curves obtained from the corresponding numerical integration solutions. It is found that both numerical integration solutions agree well since the root-mean-square-error (RMSE) values remain small.","PeriodicalId":55144,"journal":{"name":"Fractals-Complex Geometry Patterns and Scaling in Nature and Society","volume":null,"pages":null},"PeriodicalIF":4.7,"publicationDate":"2023-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44477586","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 : 2023-08-28DOI: 10.1142/s0218348x23500913
Lin Chai, Jian Liu, Guanrong Chen, Xiaotong Zhang, Yiqun Li
Many real-world systems are connected together, in natural and man-made networks. A complex-valued laser network can simulate the working mechanism of human brain. However, amplitude control of a complex-valued laser network is seldom studied. In this paper, a ring network of complex-valued Lorenz laser systems is investigated. The ring network exhibits complex dynamics including hyper-chaos, quasi-periodic orbits, and coexisting hyper-chaos. Three kinds of single-parameter oriented amplitude controls are realized with varying or unvarying Lyapunov exponents in the ring network. Meanwhile, a simple knob can realize the amplitude rescaling of hyper-chaotic signals, which reduces the cost of circuit implementation. Moreover, a criterion of chaotic complete synchronization among all the nodes is established for a network with strong coupling. For relatively weak coupling, quasi-periodic complete synchronization is found, and the performance of chaotic synchronization is studied in terms of the cross-correlation coefficient. It is moreover revealed that the improvement and trend of synchronization performance are robust to the parity of the number of nodes for the same-scale laser networks.
{"title":"AMPLITUDE CONTROL AND CHAOTIC SYNCHRONIZATION OF A COMPLEX-VALUED LASER RING NETWORK","authors":"Lin Chai, Jian Liu, Guanrong Chen, Xiaotong Zhang, Yiqun Li","doi":"10.1142/s0218348x23500913","DOIUrl":"https://doi.org/10.1142/s0218348x23500913","url":null,"abstract":"Many real-world systems are connected together, in natural and man-made networks. A complex-valued laser network can simulate the working mechanism of human brain. However, amplitude control of a complex-valued laser network is seldom studied. In this paper, a ring network of complex-valued Lorenz laser systems is investigated. The ring network exhibits complex dynamics including hyper-chaos, quasi-periodic orbits, and coexisting hyper-chaos. Three kinds of single-parameter oriented amplitude controls are realized with varying or unvarying Lyapunov exponents in the ring network. Meanwhile, a simple knob can realize the amplitude rescaling of hyper-chaotic signals, which reduces the cost of circuit implementation. Moreover, a criterion of chaotic complete synchronization among all the nodes is established for a network with strong coupling. For relatively weak coupling, quasi-periodic complete synchronization is found, and the performance of chaotic synchronization is studied in terms of the cross-correlation coefficient. It is moreover revealed that the improvement and trend of synchronization performance are robust to the parity of the number of nodes for the same-scale laser networks.","PeriodicalId":55144,"journal":{"name":"Fractals-Complex Geometry Patterns and Scaling in Nature and Society","volume":null,"pages":null},"PeriodicalIF":4.7,"publicationDate":"2023-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46621176","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 : 2023-08-28DOI: 10.1142/s0218348x23500883
Kangkang Wang, Peng Xu, Feng Shi
This paper derives a new fractional (3+1)-dimensional modified Zakharov–Kuznetsov equation based on the conformable fractional derivative for the first time. Some new types of the fractal traveling wave solutions are successfully constructed by applying a novel approach which is called the fractal semi-inverse variational method. To our knowledge, the obtained results are all new and have not reported in the other literature. In addition, the dynamic characteristics of the different solutions on the fractal space are discussed and presented via the 3D plots, 2D contour and 2D curves. It can be found that: (1) The fractal order can not only affect the peak value of the fractal traveling waves, but also affect the wave structures, that is, the smaller the fractional order value is, the more curved the waveform is, and the slower waveform changes. (2) In the fractal space, the fractal wave keeps its shape unchanged in the process of the propagation and still meets the energy conservation. The methods in this paper can be used to study the other fractal PDEs in the physics, and the findings are expected to bring some new thinking and inspiration toward the fractal theory in physics.
{"title":"NONLINEAR DYNAMIC BEHAVIORS OF THE FRACTIONAL (3+1)-DIMENSIONAL MODIFIED ZAKHAROV–KUZNETSOV EQUATION","authors":"Kangkang Wang, Peng Xu, Feng Shi","doi":"10.1142/s0218348x23500883","DOIUrl":"https://doi.org/10.1142/s0218348x23500883","url":null,"abstract":"This paper derives a new fractional (3+1)-dimensional modified Zakharov–Kuznetsov equation based on the conformable fractional derivative for the first time. Some new types of the fractal traveling wave solutions are successfully constructed by applying a novel approach which is called the fractal semi-inverse variational method. To our knowledge, the obtained results are all new and have not reported in the other literature. In addition, the dynamic characteristics of the different solutions on the fractal space are discussed and presented via the 3D plots, 2D contour and 2D curves. It can be found that: (1) The fractal order can not only affect the peak value of the fractal traveling waves, but also affect the wave structures, that is, the smaller the fractional order value is, the more curved the waveform is, and the slower waveform changes. (2) In the fractal space, the fractal wave keeps its shape unchanged in the process of the propagation and still meets the energy conservation. The methods in this paper can be used to study the other fractal PDEs in the physics, and the findings are expected to bring some new thinking and inspiration toward the fractal theory in physics.","PeriodicalId":55144,"journal":{"name":"Fractals-Complex Geometry Patterns and Scaling in Nature and Society","volume":null,"pages":null},"PeriodicalIF":4.7,"publicationDate":"2023-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44432325","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 : 2023-08-22DOI: 10.1142/s0218348x23500871
R. M. Jena, S. Chakraverty, Shengda Zeng, V. T. Nguyen
A new definition of fractional differentiation of nonlocal and non-singular kernels has recently been developed to overcome the shortcomings of the traditional Riemann–Liouville and Caputo fractional derivatives. In this study, the dynamic behaviors of the fractional financial chaotic model have been investigated. Singular and non-singular kernel fractional derivatives are used to examine the proposed model. To solve the financial chaotic model with nonlocal operators, the fractional Adams–Bashforth method (ABM) is applied based on Lagrange polynomial interpolation (LPI). The existence and uniqueness of the solution of the model can be demonstrated using fixed point theory and nonlinear analysis. Further, the error analysis of the present method and Ulam–Hyers stability of the considered model have also been included. Obtained numerical simulations reveal that the model based on three different fractional derivatives shows various chaotic behaviors that may be useful in a practical sense which may not be observed in the integer case.
{"title":"ADAMS–BASHFORTH NUMERICAL METHOD-BASED SOLUTION OF FRACTIONAL ORDER FINANCIAL CHAOTIC MODEL","authors":"R. M. Jena, S. Chakraverty, Shengda Zeng, V. T. Nguyen","doi":"10.1142/s0218348x23500871","DOIUrl":"https://doi.org/10.1142/s0218348x23500871","url":null,"abstract":"A new definition of fractional differentiation of nonlocal and non-singular kernels has recently been developed to overcome the shortcomings of the traditional Riemann–Liouville and Caputo fractional derivatives. In this study, the dynamic behaviors of the fractional financial chaotic model have been investigated. Singular and non-singular kernel fractional derivatives are used to examine the proposed model. To solve the financial chaotic model with nonlocal operators, the fractional Adams–Bashforth method (ABM) is applied based on Lagrange polynomial interpolation (LPI). The existence and uniqueness of the solution of the model can be demonstrated using fixed point theory and nonlinear analysis. Further, the error analysis of the present method and Ulam–Hyers stability of the considered model have also been included. Obtained numerical simulations reveal that the model based on three different fractional derivatives shows various chaotic behaviors that may be useful in a practical sense which may not be observed in the integer case.","PeriodicalId":55144,"journal":{"name":"Fractals-Complex Geometry Patterns and Scaling in Nature and Society","volume":null,"pages":null},"PeriodicalIF":4.7,"publicationDate":"2023-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43438981","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 : 2023-08-22DOI: 10.1142/s0218348x23500925
Yunxiu Zhou, Jiagen Liao, T. Du
In this paper, two weighted parameterized fractal identities are first proposed, wherein the mappings involved are second-order local fractional differentiable. Based upon these equalities, a series of the weighted parameterized inequalities, which are related to the fractal convex mappings, are then deduced. Moreover, making use of boundedness and [Formula: see text]-Lipschitzian mappings, some error estimates are attained as well. Finally, certain fractal outcomes in accordance to random variable and the weighted formula, respectively, are presented as applications.
{"title":"THE WEIGHTED PARAMETERIZED INEQUALITIES IN RELATION TO TWICE DIFFERENTIABLE MAPPINGS IN THE FRACTAL DOMAINS ALONG WITH SOME APPLICATIONS","authors":"Yunxiu Zhou, Jiagen Liao, T. Du","doi":"10.1142/s0218348x23500925","DOIUrl":"https://doi.org/10.1142/s0218348x23500925","url":null,"abstract":"In this paper, two weighted parameterized fractal identities are first proposed, wherein the mappings involved are second-order local fractional differentiable. Based upon these equalities, a series of the weighted parameterized inequalities, which are related to the fractal convex mappings, are then deduced. Moreover, making use of boundedness and [Formula: see text]-Lipschitzian mappings, some error estimates are attained as well. Finally, certain fractal outcomes in accordance to random variable and the weighted formula, respectively, are presented as applications.","PeriodicalId":55144,"journal":{"name":"Fractals-Complex Geometry Patterns and Scaling in Nature and Society","volume":null,"pages":null},"PeriodicalIF":4.7,"publicationDate":"2023-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47652862","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 : 2023-08-18DOI: 10.1142/s0218348x23500895
Jian-Hui Li, Zuguo Yu, V. Anh, JIN-LONG Liu, AN-QI Peng
The fractal and small-word properties are two important properties of complex networks. In this paper, we propose a new random rewiring method to transform fractal networks into small-world networks. We theoretically prove that the proposed method can retain the degree of all nodes (hence the degree distribution) and the connectivity of the network. Further, we also theoretically prove that our method also retains the tree structure of tree graphs. Our method can transform many different types of fractal networks into small-world networks while the degree distribution and connectivity of these networks remain unchanged, demonstrating the generality of small-world networks. In addition, the method also works for other types of complex networks. The rewiring method proposed in this paper can be used in a broader range of applications of network analysis.
{"title":"A NEW RANDOM REWIRING METHOD TO TRANSFORM FRACTAL NETWORKS INTO SMALL-WORLD NETWORKS","authors":"Jian-Hui Li, Zuguo Yu, V. Anh, JIN-LONG Liu, AN-QI Peng","doi":"10.1142/s0218348x23500895","DOIUrl":"https://doi.org/10.1142/s0218348x23500895","url":null,"abstract":"The fractal and small-word properties are two important properties of complex networks. In this paper, we propose a new random rewiring method to transform fractal networks into small-world networks. We theoretically prove that the proposed method can retain the degree of all nodes (hence the degree distribution) and the connectivity of the network. Further, we also theoretically prove that our method also retains the tree structure of tree graphs. Our method can transform many different types of fractal networks into small-world networks while the degree distribution and connectivity of these networks remain unchanged, demonstrating the generality of small-world networks. In addition, the method also works for other types of complex networks. The rewiring method proposed in this paper can be used in a broader range of applications of network analysis.","PeriodicalId":55144,"journal":{"name":"Fractals-Complex Geometry Patterns and Scaling in Nature and Society","volume":null,"pages":null},"PeriodicalIF":4.7,"publicationDate":"2023-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46658217","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 : 2023-08-18DOI: 10.1142/s0218348x23500809
Yuanyuan Wang, Hongguang Sun, T. Ni, M. Zaccariotto, U. Galvanetto
Richards’ equation is a classical differential equation describing water transport in unsaturated porous media, in which the moisture content and the soil matrix depend on the spatial derivative of hydraulic conductivity and hydraulic potential. This paper proposes a nonlocal model and the peridynamic formulation replace the temporal and spatial derivative terms. Peridynamic formulation utilizes a spatial integration to describe the path-dependency, so the fast diffusion process of water transport in unsaturated porous media can be captured, while the Caputo derivative accurately describes the sub-diffusion phenomenon caused by the fractal nature of heterogeneous media. A one-dimensional water transport problem with a constant permeability coefficient is first addressed. Convergence studies on the nonlocal parameters are carried out. The excellent agreement between the numerical and analytical solutions validates the proposed model for its accuracy and parameter stability. Subsequently, the wetting process in two porous building materials is simulated. The comparison of the numerical results with experimental observations further demonstrates the capability of the proposed model in describing water transport phenomena in unsaturated porous media.
{"title":"A HYBRID FRACTIONAL-DERIVATIVE AND PERIDYNAMIC MODEL FOR WATER TRANSPORT IN UNSATURATED POROUS MEDIA","authors":"Yuanyuan Wang, Hongguang Sun, T. Ni, M. Zaccariotto, U. Galvanetto","doi":"10.1142/s0218348x23500809","DOIUrl":"https://doi.org/10.1142/s0218348x23500809","url":null,"abstract":"Richards’ equation is a classical differential equation describing water transport in unsaturated porous media, in which the moisture content and the soil matrix depend on the spatial derivative of hydraulic conductivity and hydraulic potential. This paper proposes a nonlocal model and the peridynamic formulation replace the temporal and spatial derivative terms. Peridynamic formulation utilizes a spatial integration to describe the path-dependency, so the fast diffusion process of water transport in unsaturated porous media can be captured, while the Caputo derivative accurately describes the sub-diffusion phenomenon caused by the fractal nature of heterogeneous media. A one-dimensional water transport problem with a constant permeability coefficient is first addressed. Convergence studies on the nonlocal parameters are carried out. The excellent agreement between the numerical and analytical solutions validates the proposed model for its accuracy and parameter stability. Subsequently, the wetting process in two porous building materials is simulated. The comparison of the numerical results with experimental observations further demonstrates the capability of the proposed model in describing water transport phenomena in unsaturated porous media.","PeriodicalId":55144,"journal":{"name":"Fractals-Complex Geometry Patterns and Scaling in Nature and Society","volume":null,"pages":null},"PeriodicalIF":4.7,"publicationDate":"2023-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47950282","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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