Fractal and Fractional最新文献_第2页

Quasi-Cauchy Regression Modeling for Fractiles Based on Data Supported in the Unit Interval 基于单位区间数据支持的分形拟柯西回归建模

IF 5.4 2区数学

Fractal and Fractional Pub Date : 2023-09-04 DOI: 10.3390/fractalfract7090667

José Sérgio Casé de Oliveira, R. Ospina, Víctor Leiva, Jorge I. Figueroa-Zúñiga, Cecilia Castro

{"title":"Quasi-Cauchy Regression Modeling for Fractiles Based on Data Supported in the Unit Interval","authors":"José Sérgio Casé de Oliveira, R. Ospina, Víctor Leiva, Jorge I. Figueroa-Zúñiga, Cecilia Castro","doi":"10.3390/fractalfract7090667","DOIUrl":"https://doi.org/10.3390/fractalfract7090667","url":null,"abstract":"A fractile is a location on a probability density function with the associated surface being a proportion of such a density function. The present study introduces a novel methodological approach to modeling data within the continuous unit interval using fractile or quantile regression. This approach has a unique advantage as it allows for a direct interpretation of the response variable in relation to the explanatory variables. The new approach provides robustness against outliers and permits heteroscedasticity to be modeled, making it a tool for analyzing datasets with diverse characteristics. Importantly, our approach does not require assumptions about the distribution of the response variable, offering increased flexibility and applicability across a variety of scenarios. Furthermore, the approach addresses and mitigates criticisms and limitations inherent to existing methodologies, thereby giving an improved framework for data modeling in the unit interval. We validate the effectiveness of the introduced approach with two empirical applications, which highlight its practical utility and superior performance in real-world data settings.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":" ","pages":""},"PeriodicalIF":5.4,"publicationDate":"2023-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43806188","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

A Comparative Study of Time Fractional Nonlinear Drinfeld–Sokolov–Wilson System via Modified Auxiliary Equation Method 用改进的辅助方程方法对时间分数阶非线性Drinfeld–Sokolov–Wilson系统的比较研究

IF 5.4 2区数学

Fractal and Fractional Pub Date : 2023-09-03 DOI: 10.3390/fractalfract7090665

G. Akram, Maasoomah Sadaf, Iqra Zainab, Muhammad Abbas, Ali Akgül

引用次数: 0

The Effects of Thermal Memory on a Transient MHD Buoyancy-Driven Flow in a Rectangular Channel with Permeable Walls: A Free Convection Flow with a Fractional Thermal Flux 热记忆对具有可渗透壁的矩形通道中瞬态MHD浮力驱动流的影响：具有分数热通量的自由对流

IF 5.4 2区数学

Fractal and Fractional Pub Date : 2023-09-01 DOI: 10.3390/fractalfract7090664

Nehad Ali Shah, Bander N. Almutairi, D. Vieru, A. El-Deeb

{"title":"The Effects of Thermal Memory on a Transient MHD Buoyancy-Driven Flow in a Rectangular Channel with Permeable Walls: A Free Convection Flow with a Fractional Thermal Flux","authors":"Nehad Ali Shah, Bander N. Almutairi, D. Vieru, A. El-Deeb","doi":"10.3390/fractalfract7090664","DOIUrl":"https://doi.org/10.3390/fractalfract7090664","url":null,"abstract":"This study investigates the effects of magnetic induction, ion slip and Hall current on the flow of linear viscous fluids in a rectangular buoyant channel. In a hydro-magnetic flow scenario with permeable and conducting walls, one wall has a temperature variation that changes over time, while the other wall keeps a constant temperature; the research focuses on this situation. Asymmetric wall heating and suction/injection effects are also examined in the study. Using the Laplace transform, analytical solutions in the Laplace domain for temperature, velocity and induced magnetic field have been determined. The Stehfest approach has been used to find numerical solutions in the real domain by reversing Laplace transforms. The generalized thermal process makes use of an original fractional constitutive equation, in which the thermal flux is influenced by the history of temperature gradients, which has an impact on both the thermal process and the fluid’s hydro-magnetic behavior. The influence of thermal memory on heat transfer, fluid movement and magnetic induction was highlighted by comparing the solutions of the fractional model with the classic one based on Fourier’s law.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":" ","pages":""},"PeriodicalIF":5.4,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45318200","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

The Impact of Fractal Gradation of Aggregate on the Mechanical and Durable Characteristics of Recycled Concrete 骨料分形级配对再生混凝土力学性能和耐久性的影响

IF 5.4 2区数学

Fractal and Fractional Pub Date : 2023-08-31 DOI: 10.3390/fractalfract7090663

Changlong Quan, Chu-Jie Jiao, Wei-Zhi Chen, Zhi-Cheng Xue, Rui Liang, Xue-Fei Chen

{"title":"The Impact of Fractal Gradation of Aggregate on the Mechanical and Durable Characteristics of Recycled Concrete","authors":"Changlong Quan, Chu-Jie Jiao, Wei-Zhi Chen, Zhi-Cheng Xue, Rui Liang, Xue-Fei Chen","doi":"10.3390/fractalfract7090663","DOIUrl":"https://doi.org/10.3390/fractalfract7090663","url":null,"abstract":"Properties of recycled aggregate concrete (RAC) are influenced by the composition and particle size distribution of recycled coarse aggregate (RCA). The study herein designed seven distinct groups of RACs with varying aggregate fractal dimensions (D) and one group of natural concrete (NAC). The impact of D on the workability, compressive strength, resistance to chloride ion penetration, and carbonation resistance of RAC was measured. It was found that an increase in the D value led to a decrease in the slump and slump flow, with the compressive strength and chloride ion penetration increasing and then decreasing, and carbonation gradually declined. The optimal fractal dimension was thereby determined to be 2.547 by a strength model accommodating two parameters of D and the curing age. Additionally, the mass percentage of each particle size for the corresponding gradation was presented. The compressive strength and chloride permeation resistance of RAC (D = 1.0) relative to RAC (D = 2.5) was increased by 16.7% and 13.3%, respectively. Furthermore, the carbonation depth of RAC (D = 2.5) was comparable to that of NAC. Additionally, the carbonation resistance of RAC was influenced by both the size distribution and the degree of natural carbonation of RCA, resulting in four distinct features relative to NAC. It is thereby feasible to enhance RAC performance through the manipulation of RCA’s fractal dimensions.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":" ","pages":""},"PeriodicalIF":5.4,"publicationDate":"2023-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47815836","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 2

Collocation-Based Approximation for a Time-Fractional Sub-Diffusion Model 基于配置的时间分数次扩散模型近似

IF 5.4 2区数学

Fractal and Fractional Pub Date : 2023-08-31 DOI: 10.3390/fractalfract7090657

Kaido Lätt, A. Pedas, Hanna Britt Soots, M. Vikerpuur

引用次数: 0

Lagrangian Particle Dispersion in a Poor Man’s Magnetohydrodynamic Turbulence Model 穷人磁流体动力学湍流模型中的拉格朗日粒子色散

IF 5.4 2区数学

Fractal and Fractional Pub Date : 2023-08-31 DOI: 10.3390/fractalfract7090662

T. Alberti, V. Carbone

{"title":"Lagrangian Particle Dispersion in a Poor Man’s Magnetohydrodynamic Turbulence Model","authors":"T. Alberti, V. Carbone","doi":"10.3390/fractalfract7090662","DOIUrl":"https://doi.org/10.3390/fractalfract7090662","url":null,"abstract":"Lagrangian dispersion of fluid particle pairs refers to the study of how individual fluid particles disperse and move in a fluid flow, providing insights to understand transport phenomena in various environments, from laminar to turbulent conditions. Here, we explore this phenomenon in synthetic velocity and magnetic fields generated through a reduced-order model of the magnetohydrodynamic equations, which is able to mimic both a laminar and a turbulent environment. In the case of laminar conditions, we find that the average square distance between particle pairs increases linearly with time, implying a dispersion pattern similar to Brownian motion at all time steps. On the other hand, under turbulent conditions, surprisingly enough we observe a Richardson scaling, indicating a super-ballistic dispersion pattern, which aligns with the expected scaling properties for a turbulent environment. Additionally, our study reveals that the magnetic field plays an organizing role. Lastly, we explore a purely hydrodynamic case without magnetic field effects, showing that, even in a turbulent environment, the behavior remains Brownian-like, highlighting the crucial role of the magnetic field in generating the Richardson scaling observed in our model.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":"11 10","pages":""},"PeriodicalIF":5.4,"publicationDate":"2023-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41268926","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Forecasting the Active Cases of COVID-19 via a New Stochastic Rayleigh Diffusion Process 基于新随机瑞利扩散过程的COVID-19活跃病例预测

IF 5.4 2区数学

Fractal and Fractional Pub Date : 2023-08-31 DOI: 10.3390/fractalfract7090660

Ahmed Nafidi, Y. Chakroune, R. Gutiérrez-Sánchez, A. Tridane

引用次数: 0

A Physical Phenomenon for the Fractional Nonlinear Mixed Integro-Differential Equation Using a Quadrature Nystrom Method 分数阶非线性混合积分微分方程的一个物理现象

IF 5.4 2区数学

Fractal and Fractional Pub Date : 2023-08-31 DOI: 10.3390/fractalfract7090656

A. Jan, M. Abdou, M. Basseem

引用次数: 0

Association between Opioid Dependence and Scale Free Fractal Brain Activity: An EEG Study 阿片依赖与无标度分形脑活动的关联:一项脑电图研究

IF 5.4 2区数学

Fractal and Fractional Pub Date : 2023-08-31 DOI: 10.3390/fractalfract7090659

P. Sirpal, William A. Sikora, Hazem H. Refai, Yuan Yang

{"title":"Association between Opioid Dependence and Scale Free Fractal Brain Activity: An EEG Study","authors":"P. Sirpal, William A. Sikora, Hazem H. Refai, Yuan Yang","doi":"10.3390/fractalfract7090659","DOIUrl":"https://doi.org/10.3390/fractalfract7090659","url":null,"abstract":"Self-similarities at different time scales embedded within a self-organizing neural manifold are well recognized. In this study, we hypothesize that the Hurst fractal dimension (HFD) of the scalp electroencephalographic (EEG) signal reveals statistical differences between chronic pain and opioid use. We test this hypothesis by using EEG resting state signals acquired from a total of 23 human subjects: 14 with chronic pain, 9 with chronic pain taking opioid medications, 5 with chronic pain and not taking opioid medications, and 9 healthy controls. Using the multifractal analysis algorithm, the HFD for full spectrum EEG and EEG frequency band time series was computed for all groups. Our results indicate the HFD varies spatially and temporally across all groups and is of lower magnitude in patients not taking opioids as compared to those taking opioids and healthy controls. A global decrease in HFD was observed with changes in gamma and beta power in the chronic pain group compared to controls and when paired to subject handedness and sex. Our results show the loss of complexity representative of brain wide dysfunction and reduced neural processing can be used as an EEG biomarker for chronic pain and subsequent opioid use.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":" ","pages":""},"PeriodicalIF":5.4,"publicationDate":"2023-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44686741","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Fractal Analysis and FEM Assessment of Soft Tissue Affected by Fibrosis 纤维变性软组织的分形分析与有限元评估

IF 5.4 2区数学

Fractal and Fractional Pub Date : 2023-08-31 DOI: 10.3390/fractalfract7090661

Arturo Yishai Prieto-Vázquez, A. Cuautle-Estrada, Mario Alberto Grave-Capistrán, O. Ramírez, C. R. Torres-SanMiguel

{"title":"Fractal Analysis and FEM Assessment of Soft Tissue Affected by Fibrosis","authors":"Arturo Yishai Prieto-Vázquez, A. Cuautle-Estrada, Mario Alberto Grave-Capistrán, O. Ramírez, C. R. Torres-SanMiguel","doi":"10.3390/fractalfract7090661","DOIUrl":"https://doi.org/10.3390/fractalfract7090661","url":null,"abstract":"This research shows an image processing method to determine the liver tissue’s mechanical behavior under physiological damage caused by fibrosis pathology. The proposed method consists of using a liver tissue CAD/CAE model obtained from a tomography of the human abdomen, where the diaphragmatic surface of this tissue is compressed by a moving flat surface. For this work, two tools were created—the first to analyze the deformations and the second to analyze the displacements of the liver tissue. Gibbon and MATLAB® were used for numerical analysis with the FEBio computer program. Although deformation in the scenario can be treated as an orthogonal coordinate system, the relationship between the total change in height (measured) and the deformation was obtained. The outcomes show liver tissue behavior as a hyperelastic model; the Mooney–Rivlin mathematical characterization model was proposed in this case. Another method to determine the level of physiological damage caused by fibrosis is fractal analysis. This work used the Hausdorff fractal dimension (HFD) method to calculate and analyze the 2D topological surface.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":" ","pages":""},"PeriodicalIF":5.4,"publicationDate":"2023-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47441543","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1