Introduction To Percolation Theory

Stauffer, Dietrich; Aharony, Ammon

doi:10.1201/9781315274386

Cited by 943 publications

(1,445 citation statements)

References 0 publications

Supporting

Mentioning

1,343

Contrasting

Unclassified

Order By: Relevance

“…The overall forest cover map was constructed based on total subpixel proportional forest cover (0–1) within each 1‐km pixel, summed up across all pixels in the landscape. Contiguous forest cover was estimated based on Percolation theory (Stauffer ), which predicts that above 60% habitat within simulated artificial landscapes forest cover becomes highly or completely connected (i.e. contiguous), independent of the landscape size.…”

Section: Methodsmentioning

confidence: 99%

Which landscape size best predicts the influence of forest cover on restoration success? A global meta‐analysis on the scale of effect

Crouzeilles

Curran

2016

Journal of Applied Ecology

100

View full text Add to dashboard Cite

1. Landscape context is a strong predictor of species persistence, abundance and distribution, yet its influence on the success of ecological restoration remains unclear. Thus, a primary question arises: which landscape size best predicts the effects of forest cover on restoration success? 2. To answer this question, we conducted a global meta-analysis for biodiversity (mammals, birds, invertebrates, herpetofauna and plants) and measures of vegetation structure (cover, density, height, biomass and litter). Response ratios were calculated for comparisons between reference (e.g. old-growth forest) and disturbed sites (degraded or restored). Using an information-theoretic approach, mean response ratio (restoration success) and response ratio variance (restoration predictability) within each study landscape were regressed against the percentage of overall (summed forest cover) and contiguous (summed pixels of ≥60% forest cover) forest within eight different buffer sizes of radius 5-200 km (at 1-km resolution). 3. We included 247 studies encompassing 196 study landscapes and 4360 quantitative comparisons. The best buffer (landscape) size varied for the following: (i) overall and contiguous forest cover, (ii) biodiversity and vegetation structure and (iii) mean response ratio and response ratio variance. Only plant biodiversity was influenced by overall forest cover (buffer size of 5, 10 and 200 km radii), while plants (10 and 200 km radii), mammals (5, 10 and 50-200 km radii), invertebrates (5 and 10 km radii), cover (5 km radii), height (5 km radii) and litter (100 km radii) were influenced by contiguous forest cover. Overall, mean response ratio and response ratio variance were positively and negatively nonlinearly related with both overall and contiguous forest cover, respectively. 4. We reveal for the first time a clear pattern of increasing restoration success and decreasing uncertainty as contiguous forest cover increases. We also indicate preliminary recommended buffer sizes for investigating landscape restoration effects on biodiversity and vegetation structure. However, the coarse grain and variability in the data mean the optimal landscape size may not have been detected; thus, further research is needed. 5. Synthesis and applications. When setting targets for ecological restoration, policymakers and restoration practitioners should account for the following: (i) the landscape context, particularly the amount of contiguous habitat up to 10 km around a disturbed site, and (ii) the uncertainty in restoration success, as it increases when contiguous forest cover falls below about 50%.

show abstract

Section: Methodsmentioning

confidence: 99%

Which landscape size best predicts the influence of forest cover on restoration success? A global meta‐analysis on the scale of effect

Crouzeilles

Curran

2016

Journal of Applied Ecology

100

View full text Add to dashboard Cite

show abstract

“…A more accurate value of the percolation threshold was obtained by fitting the experimental data to Eq. .

normalσ \sim {(φ - φ_{c})}^{t}

…”

Section: Resultsmentioning

confidence: 99%

Electrospun Copolyamide Mats Modified by Functionalized Multiwall Carbon Nanotubes

et al. 2018

View full text Add to dashboard Cite

In this article, we report the preparation and properties of electro‐conductive mats based on the commercial copolyamide (Vestamelt X1010) and multiwall carbon nanotubes functionalized by amino groups. Vestamelt X1010 is easily soluble in n‐propanol at room temperature up to a concentration of 18 wt%. This is a significant advantage of this system because n‐propanol is considered to be a safe and relatively environmentally friendly solvent compared with the organic solvents and acids frequently used for electrospinning of common synthetic polymers. The co‐polyamide nanofibers were modified by multiwall carbon nanotubes grafted by amino groups to enhance their electrical conductivity at low filler content. The percolation threshold was found to be 0.33 vol%. Some applications of these mats were demonstrated such as the capability for sensing a selected vapor (acetone) and for oil/water separation. It was shown that neat Vestamelt X1010 mats remove around 85 wt% of oil (100 ppm of vegetable oil dispersed in water), whereas the addition of 1 wt% of CNTs enhances this ability up to 95 wt%. POLYM. COMPOS., 40:E1451–E1460, 2019. © 2018 Society of Plastics Engineers

show abstract

“…Electrical conductivity of mixtures composed of electrical conductive particles and insulating matrix could be described using a general effective media theory, GEM . According to the GEM theory, the percolation transition of the mixture depends on the volume fraction, Φ, of the high conductivity phase . The mean conductivity, σ m , of a composite material containing high (h) and low (l) conducting phases with finite values for σ h and σ l is given as:

\frac{(1 - Φ) ({normalσ}_{l}^{1 (/) t} - {normalσ}_{m}^{1 (/) t})}{{normalσ}_{l}^{1 (/) t} + A {normalσ}_{m}^{1 (/) t}} + \frac{Φ ({normalσ}_{h}^{1 (/) t} - {normalσ}_{m}^{1 (/) t})}{{normalσ}_{h}^{1 (/) t} + A {normalσ}_{m}^{1 (/) t}} = 0

where A is a constant, which is a function of the percolation threshold (Φ x ), where

A = ()(, 1 - Φ_{x}) / Φ_{x}

and t is a morphology parameter.…”

Section: Resultsmentioning

confidence: 99%

Models Proposed to Explain the Electrical Conductivity of Polymer‐Derived Silicon Carbide Fibers

et al. 2016

J. Am. Ceram. Soc.

View full text Add to dashboard Cite

Two types of silicon carbide fibers (SiCf) were prepared employing different pyrolysis techniques. The relationship between the microstructure and the electrical resistivity of the fibers was investigated. The results indicated that the carbon layer present on the fiber surface acted as the main conductive phase in the SiCf obtained by direct pyrolysis, whereas a free carbon phase determined the conductivity of the SiCf prepared by the preheated pyrolysis method. A core‐shell model and a general effective media (GEM) theory were proposed to explain the conductivity of different types of SiCf. Quantitative analysis based on these models indicated an electrical resistivity of ~10−2 Ω·cm for the carbon layer on the surface of SiCf obtained by direct pyrolysis. The electrical resistivity and the percolation threshold of the free carbon in SiCf prepared by the preheated pyrolysis method were 10−1 Ω·cm and 11.3% respectively.

show abstract

Introduction To Percolation Theory

Cited by 943 publications

References 0 publications

Which landscape size best predicts the influence of forest cover on restoration success? A global meta‐analysis on the scale of effect

Which landscape size best predicts the influence of forest cover on restoration success? A global meta‐analysis on the scale of effect

Electrospun Copolyamide Mats Modified by Functionalized Multiwall Carbon Nanotubes

Models Proposed to Explain the Electrical Conductivity of Polymer‐Derived Silicon Carbide Fibers

Contact Info

Product

Resources

About