Article
Environmental Sciences
Shengyang Feng, Yurong Wu, Yong Liu, Xiangyang Li, Xiaodong Wang, Puxin Chen
Summary: A novel model combining fractal theory and DFN is proposed to simulate radon migration, revealing the impact of different parameters on radon migration. Fractal dimension of fracture lengths and dip angle are identified as key factors influencing radon migration.
Article
Mathematics, Interdisciplinary Applications
Hugo Mondragon-Nava, Didier Samayoa, Baltasar Mena, Alexander S. Balankin
Summary: This work focuses on modeling fracture networks, particularly the fractal features of fracture systems in geological formations and reservoirs. Two new fracture network models are introduced: one based on Bernoulli percolation in regular lattices and the other exploring site percolation in scale-free networks in two- and three-dimensional lattices. The key attributes of the model fracture networks are outlined. Surprisingly, the number of effective spatial degrees of freedom in the scale-free fracture network models is determined by the network embedding dimension, not the degree distribution. The effects of degree distribution on other fractal features of the model fracture networks are examined.
FRACTAL AND FRACTIONAL
(2023)
Article
Physics, Fluids & Plasmas
Fabian Coupette, Tanja Schilling
Summary: This study proposes a simple percolation criterion for solving various percolation problems, which can accurately calculate the percolation threshold for many solved problems. The criterion has a wide range of applicability, including random graphs, small-world networks, and percolation problems on various lattices. In addition, the study introduces a method to generate simple planar lattices with a prescribed percolation threshold.
Article
Mathematics
Zoltan Buczolich, Esa Jarvenpaa, Maarit Jarvenpaa, Tamas Keleti, Tuomas Poyhtari
Summary: The study reveals the existence of a threshold value alpha(0) within certain parameters, such that fractal percolation is almost surely purely alpha-unrectifiable for all alpha values greater than the threshold.
ADVANCES IN MATHEMATICS
(2021)
Article
Engineering, Mechanical
Wei Zheng, Jianjun Sun, Chenbo Ma, Qiuping Yu
Summary: This study analyzes the composition and formation mechanism of fluid film pressure, establishes a calculation method for the film pressure coefficient of contact mechanical seal based on percolation theory, and verifies its correctness. The results show that the film pressure coefficient is related to the morphology parameters and porosity of the sealing interface.
TRIBOLOGY INTERNATIONAL
(2022)
Article
Multidisciplinary Sciences
Hongyu Jiang, Jiyu Xu, Qinghua Zhang, Qian Yu, Laiquan Shen, Ming Liu, Yitao Sun, Chengrong Cao, Dong Su, Haiyang Bai, Sheng Meng, Baoan Sun, Lin Gu, Weihua Wang
Summary: This study directly observed the fractal atomic structure in thin metallic glassy membranes, with the fractal dimension depending on atomic density. The atomic configuration in the metallic glass membrane consists of various polygons with bonding angles concentrated on 45 degrees-55 degrees. The fractal atomic structure is consistent with percolation theory analysis and may explain the enhanced relaxation dynamics and ease of glass transition observed in thin metallic glassy films or surfaces.
Article
Engineering, Civil
Xiaohong Wang, Jun Zheng, Hongyue Sun
Summary: This study presents a theoretical method to identify the connecting status of 3-D fractured rock masses based on 2-D geometric information. The percolation threshold can be determined using the average number of intersections per fracture. Numerical experiments confirm the validity of the proposed method, and estimation methods for the geometric information parameter are also discussed.
JOURNAL OF HYDROLOGY
(2022)
Article
Green & Sustainable Science & Technology
Xinyu Hu, Yidian Wang, Hui Wang, Yi Shi
Summary: This study examines the urban central area of Lujiazui, Shanghai from the perspective of street network percolation and identifies the connotation and fractal nature of its hierarchical structure. The findings contribute to sustainability and propose a new method for studying the hierarchical structure of urban central areas.
Article
Physics, Multidisciplinary
Ludovica Falsi, Marco Aversa, Fabrizio Di Mei, Davide Pierangeli, Feifei Xin, Aharon J. Agranat, Eugenio DelRe
Summary: Percolation analysis was conducted on crossed-polarizer transmission images in a biased nanodisordered bulk KTN:Li perovskite. Two distinct percolative transitions were observed at two electric field thresholds, involving directional fractal chains of different dimensions and direct cluster imaging using high-resolution orthographic 3D projections. Percolation was attributed to a full-3D domain reorientation mediating the transition from a ferroelectric supercrystal state to a disordered domain mosaic.
PHYSICAL REVIEW LETTERS
(2021)
Review
Mathematics, Interdisciplinary Applications
Miguel-Angel Martinez Cruz, Julian Patino Ortiz, Miguel Patino Ortiz, Alexander Balankin
Summary: The purpose of this survey is two-fold: first, to survey the studies of percolation on fractal networks in order to assess the current state of the art and highlight the main findings and gaps in understanding; second, to provide guidelines for future research by focusing on the effects of fractal attributes on percolation in self-similar networks and outlining challenging questions.
FRACTAL AND FRACTIONAL
(2023)
Article
Mathematics
Tianxiang Ren, Jinwen Wu
Summary: Percolation theory, widely used in various fields, has experienced significant growth. The weak law of large numbers for the length of the longest head run and the limiting behaviors of the longest increasing path in a special tree are explored using Stein's method and other probabilistic methods.
Article
Physics, Fluids & Plasmas
Geet Rakala, Kedar Damle, Deepak Dhar
Summary: We study the distribution of lengths and other statistical properties of worms constructed by Monte Carlo worm algorithms in the power-law three-sublattice ordered phase of frustrated triangular and kagome lattice Ising antiferromagnets. The persistence exponent and dynamical exponent of the random walk depend only on the universal power-law exponents of the critical phase. The worms represent a discrete-time realization of a fractional Brownian motion characterized by subdiffusive values of the dynamical exponent.
Article
Green & Sustainable Science & Technology
Jingyun Zhu, Guannan Liu, Ning Luo, Jiayi Gu, Hu Liu, Dayu Ye
Summary: In this study, a novel method for measuring the interplay between pore microstructure and thermal-hydrological-mechanical coupling was provided. The fractal geothermal model developed in this study was validated for correctness and found to be superior to the traditional cubic seepage model for studying thermal conduction, seepage, and fracture-matrix interactions in geothermal reservoirs. Different structural parameters have a variety of effects on seepage resulting from geothermal extraction, which cannot be predicted using cubic permeability models. This provides new ideas for geothermal extraction practitioners.
Article
Mathematics, Applied
Alireza Khalili Golmankhaneh, Ines Tejado, Hamdullah Sevli, Juan E. Napoles Valdes
Summary: This paper provides a brief summary of fractal calculus, presenting fractal functional differential equations as a mathematical model for phenomena with fractal time and structure. The method of steps and Laplace transform are used to solve fractal retarded, neutral, and renewal delay differential equations with constant coefficients, and the graphs of solutions are provided to illustrate the details.
APPLIED MATHEMATICS AND COMPUTATION
(2023)
Article
Geosciences, Multidisciplinary
Tingchang Yin, Teng Man, Ling Li, Sergio Andres Galindo-Torres
Summary: We propose a finite-size scaling hypothesis to predict the global permeability of fracture networks. To validate the hypothesis, we generate numerous discrete fracture networks and numerically calculate the permeability. Our results show that the dimensionless permeability, scaled by moments of local conductivity and fracture sizes and corrected by two stereological ratios, can capture variations in fracture attributes. The universal form obtained in this study can also explain contradictory observations regarding the permeability and domain size of fracture networks. We demonstrate how a clear transition point is obtained from this universal form, where the permeability remains constant with changing domain size. This study provides a solid theoretical foundation to understand the connection between fracture attributes and field-scale hydraulic properties.
GEOPHYSICAL RESEARCH LETTERS
(2023)
Article
Physics, Multidisciplinary
H. J. Seybold, U. Eberhard, E. Secchi, R. L. C. Cisne, J. Jimenez-Martinez, R. F. S. Andrade, A. D. Araujo, M. Holzner, J. S. Andrade
Summary: Through high-resolution microfluidic experiments and extensive numerical simulations, we demonstrate how the flow patterns inside a swiss-cheese type of pore geometry can be systematically controlled by the intrinsic rheological properties of the fluid. The observed flow localization can be explained by the strong interplay between the disordered geometry of the pore space and the nonlinear rheology of the fluid, highlighting the potential enhancement of chemical reactors and chromatographic devices by controlling the channeling patterns inside disordered porous media.
FRONTIERS IN PHYSICS
(2021)
Article
Physics, Multidisciplinary
Danilo S. Borges, Hans J. Herrmann, Humberto A. Carmona, Jose S. Andrade Jr, Ascanio D. Araujo
Summary: Magnetic beads form chains and create self-similar patterns in an inclined Hele-Shaw cell. The patterns differ based on the angle of inclination, with one resembling stacked ropes and the other looking like a fortress from above. The morphological transition between the two patterns is characterized by a competition between friction-induced buckling and gravity, with both patterns exhibiting power law size distributions.
PHYSICAL REVIEW LETTERS
(2021)
Article
Multidisciplinary Sciences
Debora Torres, Wagner R. Sena, Humberto A. Carmona, Andre A. Moreira, Hernan A. Makse, Jose S. Andrade
Summary: Eye-tracking experiments reveal a strong correlation between the average magnetization of fixation configurations and text complexity. The study also suggests that coherent texts are closer to their corresponding critical points than non-coherent texts, indicating that different texts may induce distinct cohesive reading activities.
Article
Mathematics, Applied
Higor S. Monteiro, Ian Leifer, Saulo D. S. Reis, Jose S. Andrade, Hernan A. Makse
Summary: Recent studies have shown the relationship between the structure of network circuits with fibration symmetries and the functionality of biological networks. A fast and memory efficient algorithm has been proposed to identify fibration symmetries in networks, which is an improvement over current approaches used in the literature.
Article
Physics, Multidisciplinary
Michael T. Ramirez, Jose S. Andrade, Andre A. Moreira
Summary: This article explains the method of obtaining exponential cutoffs by adding radial deformation in space, and shows the derivation of two well-known screening potentials in the central force problem.
Article
Biochemical Research Methods
Matteo Serafino, Higor S. Monteiro, Shaojun Luo, Saulo D. S. Reis, Carles Igual, Antonio S. Lima Neto, Matias Travizano, Jose S. Andrade Jr, Hernan A. Makse
Summary: This article investigates the transmission chain of COVID-19 and proposes an optimized quarantine protocol through contact tracing and network analysis. The study finds that although lockdown measures reduce human mobility and disrupt the transmission network, they do not completely halt the spread of the disease. The authors suggest an optimized strategy to break the transmission chain by quarantining a minimal number of "weak links" connecting the large transmission cores.
PLOS COMPUTATIONAL BIOLOGY
(2022)
Article
Physics, Multidisciplinary
J. M. A. Sales, H. J. Seybold, C. L. N. Oliveira, J. S. Andrade
Summary: Two-phase flow through porous media can lead to the formation of drops and fingers, affecting macroscopic properties. In our simulation, we found that the system is ergodic for large volume fractions of the less viscous phase and high capillary numbers. Drop sizes follow a power-law scaling, with the exponent depending on the capillary number. The flow behavior changes at a characteristic capillary number, with large drops below and small droplets and finger-like structures dominating above. The temporal mean velocity of the mixture can be described by a generalized Darcy's law, and the exponent is sensitive to surface tension. In the limit of infinite capillary numbers, the mobility term increases exponentially with the saturation of the less viscous phase.
FRONTIERS IN PHYSICS
(2022)
Article
Mechanics
Rute Oliveira, Samurai Brito, Luciano R. da Silva, Constantino Tsallis
Summary: Systems consisting of localized constituents interacting with each other can be represented by complex networks. Numerical analysis can be used to study the growth and connectivity distribution of these networks, which is important for understanding various natural, artificial, and social systems.
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
(2022)
Article
Physics, Multidisciplinary
K. J. C. C. de Lacerda, L. R. da Silva, G. M. Viswanathan, J. C. Cressoni, M. A. A. da Silva
Summary: The theory of Markovian random walks is well understood, but the theory of non-Markovian random walks, which has a rich phenomenology, poses many challenges. This study proposes a model of a random walk that evolves based on selected past memories from rectangular and exponentially decaying memory profiles. The diffusive behavior of the walk is examined numerically, and it is shown that the model can be mapped onto a random walk model with a rectangular memory profile, even without exact solutions.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2022)
Article
Physics, Multidisciplinary
Saulo D. S. D. Reis, Lucas Boettcher, Joao P. da C. Nogueira, Geziel S. Sousa, Antonio S. Lima S. Neto, Hans J. J. Herrmann, Jose S. Andrade
Summary: Based on a dataset of dengue cases in Fortaleza from 2011 to 2016, this study examines the spatio-temporal characteristics of dengue outbreaks and identifies differences between epidemic and non-epidemic years. The research suggests that factors like citizen mobility play a significant role in the spatial spread of the disease and that there are higher spatial correlations in epidemic years.
FRONTIERS IN PHYSICS
(2022)
Article
Physics, Fluids & Plasmas
Ervin K. Lenzi, Aloisi Somer, Rafael S. Zola, Luciano R. da Silva, Marcelo K. Lenzi
Summary: In this study, the solutions of a generalized diffusion-like equation are investigated, taking into account spatial and time fractional derivatives as well as non-local terms. The Green function approach is used to obtain solutions and analyze the spreading of the system, revealing a diverse range of behaviors. The obtained results are also connected to anomalous diffusion processes.
Article
Mathematics, Interdisciplinary Applications
Aloisi Somer, Andressa Novatski, Marcelo Kaminski Lenzi, Luciano Rodrigues da Silva, Ervin Kaminski Lenzi
Summary: We accurately predict the contribution of thermoelastic bending to the Photoacoustic signal by analyzing an extension of the dual-phase lag model of thermal diffusion theory. Incorporating the effects of fractional differential operators, we determine the temperature distribution and accurately assess the thermoelastic effects in solid samples. This study emphasizes the importance of considering fractional differential operators in the analysis of thermoelastic bending and contributes to understanding the mechanisms behind the PA signal.
FRACTAL AND FRACTIONAL
(2023)
Article
Mathematics
Ervin Kaminski Lenzi, Luiz Roberto Evangelista, Luciano Rodrigues da Silva
Summary: We investigated two different approaches, fractional calculus and the extension of entropy concept, in order to extend standard quantum statistical mechanics. By using the thermal Green function formalism, we analyzed the dynamics and thermodynamics aspects of each case, examining how the extensions affect the behavior of system-related quantities, particularly fluctuations.
Article
Physics, Multidisciplinary
Hygor P. M. Melo, Diogo P. Mota, Jose S. Andrade, Nuno A. M. Araujo
Summary: The research found that even without traffic congestion, there is asymmetry between the shortest route from home to work and the shortest route from work to home, mainly due to the presence of a significant proportion of one-way streets. It was also discovered that the amplitude of fluctuations decays in accordance with the power law of the shortest path length, and the proportion of one-way streets in the shortest path also decreases accordingly.
PHYSICAL REVIEW RESEARCH
(2022)
Article
Physics, Fluids & Plasmas
S. Tizdast, Z. Ebadi, J. Cheraghalizadeh, M. N. Najafi, Jose S. Andrade, Hans J. Herrmann
Summary: The study explores the generalized two-dimensional Loewner exploration process with self-similar random forces and positively correlated increments, focusing on the characteristics of self-similar traces lacking conformal invariance. The model is investigated based on the input diffusivity parameter kappa, with results showing scale invariance of the generated traces.
