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Percolation Theory Using Python
This course-based open access textbook delves into percolation theory, examining the physical properties of random media—materials characterized by...
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Introduction to Percolation
In this chapter we motivate the study of disordered media through the example of a porous system. The basic terms in percolation theory are...
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Understanding congestion propagation by combining percolation theory with the macroscopic fundamental diagram
The science of cities aims to model urban phenomena as aggregate properties that are functions of a system’s variables. Following this line of...
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Infinite-Dimensional Percolation
In this chapter we address the percolation problem on an infinite-dimensional lattice without loops. In this case, it is possible to calculate...
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One-Dimensional Percolation
The percolation problem can be solved exactly in two limits: in the one-dimensional and the infinite dimensional cases. Here, we will first address...
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Scaling electrical percolation networks based on renormalization group theory
Many natural disordered systems such as percolation metal films may be approximated as fractals. Probing their properties can be difficult depending...
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On the density of 2D critical percolation gaskets and anchored clusters
We prove a formula, first obtained by Kleban, Simmons and Ziff using conformal field theory methods, for the (renormalized) density of a critical...
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Finite-Dimensional Percolation
In this chapter we apply the scaling theories developed in the one-dimensional system and the infinite-dimensional system to systems of finite...
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Continuous percolation in a Hilbert space for a large system of qubits
The development of percolation theory was historically shaped by its numerous applications in various branches of science, in particular in...
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3D DEM investigation on percolation of lubricant particles during uniaxial metal powder compaction
Based on the discrete element method, a 3D particle size model including MoS 2 lubricant and iron powder particles has been used to simulate the...
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Concurrence percolation threshold of large-scale quantum networks
Quantum networks describe communication networks that are based on quantum entanglement. A concurrence percolation theory has been recently developed...
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Analysis of traffic in communication networks based on percolation transition
Studying the phase transition process from free flow to congested state in communication networks is one of the hot topics of dynamically complex...
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Percolation Thresholds for Spherical Aggregates: Impact of the Primary Particle Aspect Ratio
A model is developed for the geometric percolation thresholds of spherically symmetric fractal aggregates comprised of cylindrical primary particles....
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Dynamic Isotropic Percolation Process: Renormalization Group Analysis
Paradigmatic model of dynamic isotropic percolation is analyzed by the means of field theoretic methods. In particular, we employ powerful analytical...
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Exchange Interactions and Magnetic Percolation in Diluted Magnetic Semiconductors
We propose a theory that combines first-principles evaluations of interatomic exchange interactions with a classical Heisenberg model and Monte Carlo...
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On the Spreading of Epidemics and Percolation Theory
In a typical epidemic like COVID-19, infected individuals are contagious over a certain time span...
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Complex Media and Percolation Theory
Percolation theory describes the effects of the connectivity of microscopic or small-scale elements of a complex medium to its macroscopic or...
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Nanograin network memory with reconfigurable percolation paths for synaptic interactions
The development of memory devices with functions that simultaneously process and store data is required for efficient computation. To achieve this,...
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The Percolation Model of Viscosity of Colloidal Systems Rubber/Disperse Filler
The rheological properties of colloidal systems rubber/disperse filler where studied within the framework of percolation theory. The model of random...
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No-exclaves percolation
Network robustness has been a pivotal issue in the study of system failure in network science since its inception. To shed light on this subject, we...
