High-precision Monte Carlo study of directed percolation in (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>d</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math>) dimensions

Wang, Junfeng; Zhou, Zongzheng; Liu, Qingquan; Garoni, Timothy M.; Deng, Youjin

doi:10.1103/physreve.88.042102

Cited by 31 publications

(30 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…On the other hand, π c corresponds to the percolation threshold which separates an absorbing (i.e., no particles permeating) from a percolating state. This value is also completely independent of the physics discussed here and depends only on the dimension of the problem and the pore lattice [55]. From (3) and 4, it is clear that our understanding of particle permeation eventually relies on finding the probability function G(∆P ), interpreted here as the likelihood that δp > δp c for any pore in the network.…”

Section: Network Permeability and Percolation Theorymentioning

confidence: 77%

Mechanical instability and percolation of deformable particles through porous networks

et al. 2018

View full text Add to dashboard Cite

The transport of micron-sized particles such as bacteria, cells, or synthetic lipid vesicles through porous spaces is a process relevant to drug delivery, separation systems, or sensors, to cite a few examples. Often, the motion of these particles depends on their ability to squeeze through small constrictions, making their capacity to deform an important factor for their permeation. However, it is still unclear how the mechanical behavior of these particles affects collective transport through porous networks. To address this issue, we present a method to reconcile the pore-scale mechanics of the particles with the Darcy scale to understand the motion of a deformable particle through a porous network. We first show that particle transport is governed by a mechanical instability occurring at the pore scale, which leads to a binary permeation response on each pore. Then, using the principles of directed bond percolation, we are able to link this microscopic behavior to the probability of permeating through a random porous network. We show that this instability, together with network uniformity, are key to understanding the nonlinear permeation of particles at a given pressure gradient. The results are then summarized by a phase diagram that predicts three distinct permeation regimes based on particle properties and the randomness of the pore network.

show abstract

Section: Network Permeability and Percolation Theorymentioning

confidence: 77%

Mechanical instability and percolation of deformable particles through porous networks

et al. 2018

View full text Add to dashboard Cite

show abstract

“…For d < dc however, there are no exact results neither for critical exponents nor thresholds. However, a very precise estimates of critical exponents and thresholds on several lattices can be found in [247,248] in 1 + 1 dimensions, and in a recent work [249] (and references therein) in higher dimensions.…”

Section: Directed Percolationmentioning

confidence: 96%

Recent advances in percolation theory and its applications

2015

View full text Add to dashboard Cite

Percolation is the simplest fundamental model in statistical mechanics that exhibits phase transitions signaled by the emergence of a giant connected component. Despite its very simple rules, percolation theory has successfully been applied to describe a large variety of natural, technological and social systems. Percolation models serve as important universality classes in critical phenomena characterized by a set of critical exponents which correspond to a rich fractal and scaling structure of their geometric features. We will first outline the basic features of the ordinary model.Over the years a variety of percolation models has been introduced some of which with completely different scaling and universal properties from the original model with either continuous or discontinuous transitions depending on the control parameter, dimensionality and the type of the underlying rules and networks. We will try to take a glimpse at a number of selective variations including Achlioptas process, half-restricted process and spanning cluster-avoiding process as examples of the so-called explosive percolation. We will also introduce non-self-averaging percolation and discuss correlated percolation and bootstrap percolation with special emphasis on their recent progress. Directed percolation process will be also discussed as a prototype of systems displaying a nonequilibrium phase transition into an absorbing state.In the past decade, after the invention of stochastic Löwner evolution (SLE) by Oded Schramm, two-dimensional (2D) percolation has become a central problem in probability theory leading to the two recent Fields medals. After a short review on SLE, we will provide an overview on existence of the scaling limit and conformal invariance of the critical percolation. We will also establish a connection with the magnetic models based on the percolation properties of the Fortuin-Kasteleyn and geometric spin clusters. As an application we will discuss how percolation theory leads to the reduction of the 3D criticality in a 3D Ising model to a 2D critical behavior.Another recent application is to apply percolation theory to study the properties of natural and artificial landscapes. We will review the statistical properties of the coastlines and watersheds and their relations with percolation. Their fractal structure and compatibility with the theory of SLE will also be discussed. The present mean sea level on Earth will be shown to coincide with the critical threshold in a percolation description of the global topography.

show abstract

“…For D = 1 one gets β ≈ 0.28, ν ⊥ ≈ 1.1, ν ∥ ≈ 1.7, and for D = 2, β ≈ 0.58, ν ⊥ ≈ 0.73, ν ∥ ≈ 1.3. For more information consult the reference book by Henkel et al (2008) and for D > 2, of less direct interest here, the recent work by Wang et al (2013).…”

Section: Directed Percolation: Critical Propertiesmentioning

confidence: 99%

Transition to turbulence in wall-bounded flows: Where do we stand?

Manneville

2016

Mechanical Engineering Reviews

View full text Add to dashboard Cite

In this essay, we recall the specificities of the transition to turbulence in wall-bounded flows and present recent achievements in the understanding of this problem. The transition is abrupt with laminar-turbulent coexistence over a finite range of Reynolds numbers, the transitional range. The archetypical cases of Poiseuille pipe flow and plane Couette flow are first reviewed at the phenomenological level, together with a few other flow configurations. Theoretical approaches are then examined with particular emphasis on the existence of special nontrivial solutions to the Navier-Stokes equations at finite distance from laminar flow. Dynamical systems theory is most appropriate to analyze their role, in particular with respect to the transient character of turbulence in the lower transitional range. The extensions needed to deal with the prominent spatiotemporal features of the transition are then discussed. Turbulence growth/decay in terms of statistical physics of many-body systems and the relevance of directed percolation as a stochastic process able to account for it are next scrutinized. To conclude, we advocate the recourse to well-designed modeling able to provide us with a conceptually coherent picture of the full transitional range and put forward some open issues.

show abstract

High-precision Monte Carlo study of directed percolation in (d+1) dimensions

Cited by 31 publications

References 29 publications

Mechanical instability and percolation of deformable particles through porous networks

Mechanical instability and percolation of deformable particles through porous networks

Recent advances in percolation theory and its applications

Transition to turbulence in wall-bounded flows: Where do we stand?

Contact Info

Product

Resources

About