We consider a first-passage percolation (FPP) model on a Delaunay triangulation D of the plane. In this model each edge e of D is independently equipped with a nonnegative random variable τe, with distribution function F, which is interpreted as the time it takes to traverse the edge. Vahidi-Asl and Wierman [9] have shown that, under a suitable moment condition on F, the minimum time taken to r...

The calculation of the conductance of ballistic rings requires a theory that goes well beyond the Kubo-Drude formula. Assuming “mesoscopic” circumstance of very weak environmental relaxation, the conductance is much smaller compared with the naive expectation. Namely, the electro-motiveforce induces an energy absorption with a rate that depends crucially on the possibility to make connected seq...

The interplay between two-dimensional percolation growth models and one-dimensional particle processes has been a fruitful source of interesting mathematical phenomena. In this paper we develop a connection between the construction of Busemann functions in the Hammersley last-passage percolation model with i.i.d. random weights, and the existence, ergodicity and uniqueness of equilibrium (or ti...

We investigate the quantum percolation problem in a diluted chain with long-range hopping amplitudes. Each bond is activated with probability p(r) = p1/r , where r is the distance between two sites and α characterizes the range of the interactions. The average participation ratio of all eigenstates is used as a measure of the wave-functions localization length. We found that, above a quantum pe...

The interplay between two-dimensional percolation growth models and one-dimensional particle processes has always been a fruitful source of interesting mathematical phenomena. In this paper we develop a connection between the construction of Busemann functions in the Hammersley last-passage percolation model with i.i.d. random weights, and the existence, ergodicity and uniqueness of equilibrium...

We investigate the location and nature of the para-ferro transition of interacting electrons in dispersionless bands using the example of the Hubbard model on the Tasaki lattice. This case can be analyzed as a geometric site-percolation problem where different configurations appear with nontrivial weights. We provide a complete exact solution for the one-dimensional case and develop a numerical...

The explosive percolation problem on the complete graph is investigated via extensive numerical simulations. We obtain the cluster-size distribution at the moment when the cluster size heterogeneity becomes maximum. The distribution is found to be well described by the power-law form with the decay exponent τ=2.06(2), followed by a hump. We then use the finite-size scaling method to make all th...

We consider a percolation configuration on a general lattice in which edges are included independently with probability p. We study the rigidity properties of the resulting configuration, in the sense of generic rigidity in d dimensions. We give a mathematically rigorous treatment of the problem, starting with a definition of an infinite rigid component. We prove that for a broad class of latti...

We study the problem of coexistence in a two-type competition model governed by first-passage percolation on Z or on the infinite cluster in Bernoulli percolation. Actually, we prove for a large class of ergodic stationary passage times that for distinct points x, y ∈ Z, there is a strictly positive probability that {z ∈ Z; d(y, z) < d(x, z)} and {z ∈ Z; d(y, z) > d(x, z)} are both infinite set...

abstract optimal management of water and nutrient could consider as effective on farm method to reduce pollution because agriculture is none point pollution. in this research, an optimal model was presented to reduce nitrate loss in furrow fertigation. the optimal model contains four simulation models for predicting runoff, deep percolation, nitrate concentration in runoff and nitrate concentra...