Description of laminar-turbulent transition of an airfoil boundary layer measured by differential image thermography using directed percolation theory

Transition from laminar to turbulent flow is still a challenging problem. Recent studies indicate a good agreement when describing this phase transition with the directed percolation theory. This study presents a new experimental approach by means of differential image thermography (DIT) enabling to investigate this transition on the suction side of a heated airfoil. The results extend the applicability of the directed percolation theory to describe the transition on curves surfaces. The experimental effort allows for the first time an agreement between all three universal exponents of the (1+1)D directed percolation for such airfoil application. Furthermore, this study proves that the theory holds for a wide range of flows, as shown by the various conditions tested. Such a large parameter space was not covered in any examination so far. The findings underline the significance of percolation models in fluid mechanics and show that this theory can be used as a high precision tool for the problem of transition to turbulence.

Percolation Distribution in Small-World Quantum Networks

Quantum networks have good prospects for applications in the future. Compared with classical networks, small-world quantum networks have some interesting properties. The topology of the network can be changed through entanglement exchange operations, and different network topologies will result in different percolation thresholds when performing entanglement percolation. A lower percolation threshold means that quantum networks require fewer minimum resources for communication. Since a shared singlet between two nodes can still be a limitation, concurrency percolation theory (ConPT) can be used to relax the condition. In this paper, we investigate how entanglement distribution is performed in small-world quantum networks to ensure that nodes in the network can communicate with each other by establishing communication links through entanglement swapping. Any node can perform entanglement swapping on only part of the connected edges, which can reduce the influence of each node in the network during entanglement swapping. In addition, the ConPT method is used to reduce the percolation threshold even further, thus obtaining a better network structure and reducing the resources required.

The percolation model of relative conductivities and phase permeabilities

The universal mathematical model of relative conductivities of percolation clusters and phase permeabilities of oil-water-saturated rocks is presented. It is obtained on the basis of percolation theory, porous body physics and statistics. The model takes into account the influence of change in pore space surface properties and the nature of fluid flow on the studied characteristics and may be applied for comprehensive analysis and modeling of technological processes of oil production.

A Briefing Survey on Advances of Coupled Networks With Various Patterns

In real-world scenarios, networks do not exist in isolation but coupled together in different ways, including dependent, multi-support, and inter-connected patterns. And, when a coupled network suffers from structural instability or dynamic perturbations, the system with different coupling patterns shows rich phase transition behaviors. In this review, we present coupled network models with different coupling patterns developed from real scenarios in recent years for studying the system robustness. For the coupled networks with different coupling patterns, based on the network percolation theory, this paper mainly describes the influence of coupling patterns on network robustness. Moreover, for different coupling patterns, we here show readers the research background, research context, and the latest research results and applications. Furthermore, different approaches to improve system robustness with various coupling patterns and future possible research directions for coupled networks are explained and considered.

Connectomic Analysis of Alzheimer’s Disease using Percolation Theory

Alzheimer’s disease (AD) is a severe neurodegenerative disorder that affects a growing worldwide elderly population. Identification of brain functional biomarkers is expected to help determine preclinical stages for targeted mechanistic studies and development of therapeutic interventions to deter disease progression. Connectomic analysis, a graph theory-based methodology used in the analysis of brain-derived connectivity matrices was used in conjunction with percolation theory targeted attack model to investigate the network effects of AD-related amyloid deposition. We used matrices derived from resting state functional magnetic resonance imaging collected on mice with extracellular amyloidosis (TgCRND8 mice, n = 17) and control littermates (n = 17). Global, nodal, spatial, and percolation-based analysis was performed comparing AD and control mice. These data indicate a short-term compensatory response to neurodegeneration in the AD brain via a strongly connected core network with highly vulnerable or disconnected hubs. Targeted attacks demonstrated a greater vulnerability of AD brains to all types of attacks and identified progression models to mimic AD brain functional connectivity through betweenness centrality and collective influence metrics. Furthermore, both spatial analysis and percolation theory identified a key disconnect between the anterior brain of the AD mice to the rest of the brain network.