scholarly journals Disproof of the conjectured subexponentiality of certain functions in percolation theory

1984 ◽  
Vol 16 (3) ◽  
pp. 690-691
Author(s):  
J. Van den berg
Keyword(s):  
Percolation Theory ◽  
Bond Percolation ◽  
Open Path

Consider bond-percolation on a graph G with sites S(G). We disprove the conjecture of Hammersley (1957) that the function n → sups ϵ S(G)E [the number of sites s′ at distance n from s which can be reached from s by an open path which, except for s′, only passes through sites at distance smaller than n from s] is always subexponential.

Critical sponge dimensions in percolation theory

1981 ◽  
Vol 13 (02) ◽  
pp. 314-324 ◽  
Author(s):  
G. R. Grimmett
Keyword(s):  
Positive Constant ◽  
Percolation Theory ◽  
Square Lattice ◽  
Bond Percolation ◽  
Critical Probability ◽  
Percolation Process ◽  
Open Path ◽  
Image Position

In the bond percolation process on the square lattice, with let S(k) be the probability that some open path joins the longer sides of a sponge with dimensions k by a log k. There exists a positive constant α = αp such that Consequently, the subset of the square lattice {(x, y):0 ≦ y ≦ f(x)} which lies between the curve y = f(x) and the x-axis has the same critical probability as the square lattice itself if and only if f(x)/log x → ∞ as x → ∞.

Critical sponge dimensions in percolation theory

1981 ◽  
Vol 13 (2) ◽  
pp. 314-324 ◽  
Author(s):  
G. R. Grimmett
Keyword(s):  
Positive Constant ◽  
Percolation Theory ◽  
Square Lattice ◽  
Bond Percolation ◽  
Critical Probability ◽  
Percolation Process ◽  
Open Path ◽  
Image Position

In the bond percolation process on the square lattice, with let S(k) be the probability that some open path joins the longer sides of a sponge with dimensions k by a log k. There exists a positive constant α = αp such that Consequently, the subset of the square lattice {(x, y):0 ≦ y ≦ f(x)} which lies between the curve y = f(x) and the x-axis has the same critical probability as the square lattice itself if and only if f(x)/log x → ∞ as x → ∞.

scholarly journals Disproof of the conjectured subexponentiality of certain functions in percolation theory

1984 ◽  
Vol 16 (03) ◽  
pp. 690-691
Author(s):  
J. Van den berg
Keyword(s):  
Percolation Theory ◽  
Bond Percolation ◽  
Open Path

Consider bond-percolation on a graph G with sites S(G). We disprove the conjecture of Hammersley (1957) that the function n → sup s ϵ S(G) E [the number of sites s′ at distance n from s which can be reached from s by an open path which, except for s′, only passes through sites at distance smaller than n from s] is always subexponential.

Cooperate epidemic spreading on multiplex networks with heterogeneous population

2020 ◽  
Vol 31 (09) ◽  
pp. 2050132
Author(s):  
Tianqiao Zhang ◽  
Yang Zhang ◽  
Jinming Ma ◽  
Junliang Chen ◽  
Xuzhen Zhu
Keyword(s):  
Phase Transition ◽  
Numerical Simulations ◽  
Percolation Theory ◽  
Bond Percolation ◽  
Epidemic Spreading ◽  
Final State ◽  
Multiplex Networks ◽  
Spreading Dynamics ◽  
Discontinuous Phase ◽  
Outbreak Size

Cooperate epidemic spreading dynamics has attracted much attention from the field of network science. In this paper, we study the cooperate epidemic spreading dynamics on multiplex networks with heterogeneous populations, which induces the heterogeneous coinfection susceptibility. We propose a spreading model to describe the evolution mechanisms. To predict the final state of the epidemic outbreak size, a generalized bond percolation theory is suggested. Through numerical simulations and theoretical analyses, we find that the system exhibits a discontinuous phase transition for large average and small variance of the distribution of coinfection susceptibility on ER–ER multiplex networks, while the phase transition is continuous on SF–SF networks. In addition, the final outbreak size increases with the average coinfection susceptibility and decreases with the variance of the coinfection susceptibility. Our suggested bond percolation theory can well predict the numerical simulations.

A geometrical approach to percolation through random fractured rocks

1985 ◽  
Vol 122 (2) ◽  
pp. 157-162 ◽  
Author(s):  
N. Rivier ◽  
E. Guyon ◽  
E. Charlaix
Keyword(s):  
Percolation Threshold ◽  
Percolation Theory ◽  
Fractured Rocks ◽  
Statistical Characteristics ◽  
Bond Percolation ◽  
Geometrical Approach ◽  
Random Lattice ◽  
Voronoi Partition ◽  
Percolation Problem

AbstractThe permeability of rocks fractured by random, planar cracks, is expressed as a classical bond percolation problem on a random lattice, by Voronoi partition of space. The percolation threshold is determined as a function of the statistical characteristics of the cracks, or of their traces on an arbitrary face of the rock, by using an empirical quasi-invariant of percolation theory.

Workload Perception of Air Traffic Control Officers and Pilots During Continuous Descent Operations Approach Procedures

2019 ◽  
Vol 9 (1) ◽  
pp. 2-11
Author(s):  
Marina Efthymiou ◽  
Frank Fichert ◽  
Olaf Lantzsch
Keyword(s):  
Fuel Consumption ◽  
Traffic Control ◽  
Air Traffic Control ◽  
Negative Impact ◽  
Air Traffic ◽  
Reduce Fuel Consumption ◽  
Total Load ◽  
Open Path

Abstract. The paper examines the workload perceived by air traffic control officers (ATCOs) and pilots during continuous descent operations (CDOs), applying closed- and open-path procedures. CDOs reduce fuel consumption and noise emissions. Therefore, they are supported by airports as well as airlines. However, their use often depends on pilots asking for CDOs and controllers giving approval and directions. An adapted NASA Total Load Index (TLX) was used to measure the workload perception of ATCOs and pilots when applying CDOs at selected European airports. The main finding is that ATCOs’ workload increased when giving both closed- and open-path CDOs, which may have a negative impact on their willingness to apply CDOs. The main problem reported by pilots was insufficient distance-to-go information provided by ATCOs. The workload change is important when considering the use of CDOs.

Sign in / Sign up

Export Citation Format

Share Document