The water percolation loss beyond root zone in the soil is one of the important parameters to determine water requirement of rice plant. If the amount of water percolation rate into the soil is estimated more carefully, determination of water requirement will be evaluated better and designing for system of irrigation, drainage and related establishments will be more easily done. The purpose of ...

We derive an equation for the existence probability Ep for general percolation problem using an analytical argument based on exponential-decay behaviour of spatial correlation function. It is shown that the finite-size scaling function is well approximated by the error function. The present argument explain why it is universal. We use Monte Carlo simulation to calculate Ep for polydisperse cont...

A two-rowed array αn = ( a1 a2 . . . an b1 b2 . . . bn ) is said to be in lexicographic order if ak ≤ ak+1 and bk ≤ bk+1 if ak = ak+1. A length ` (strictly) increasing subsequence of αn is a set of indices i1 < i2 < . . . < i` such that bi1 < bi2 < . . . < bi` . We are interested in the statistics of the length of the longest increasing subsequence of αn chosen according to Dn, for distinct fam...

We study the geometry of the critical clusters in fully coordinated percolation on the square lattice. By Monte Carlo simulations (static exponents) and normal mode analysis (dynamic exponents), we find that this problem is in the same universality class with ordinary percolation statically but not so dynamically. We show that there are large differences in the number and distribution of the in...

We classify infinite networks, by introducing the new problem of percolation on the average. This classification plays a fundamental role for understanding the thermodynamic properties of statistical mechanics spin models with discrete symmetry. Indeed, in the main theorem of the paper, we prove that the qstates Potts model presents spontaneous magnetization at finite temperature if it is defin...

Percolation theory has become a useful tool for the analysis of large scale wireless networks. We investigate the fundamental problem of characterizing the critical density λc for Poisson random geometric graphs in continuum percolation theory. In two-dimensional space with the Euclidean norm, simulation studies show λc ≈ 1.44, while the best theoretical bounds obtained thus far are 0.696 < λc ...

We study numerically the roughness exponent zeta of an in-plane fracture front slowly propagating along a heterogeneous interface embedded in an elastic body, using a model based on the evolution of a process zone rather than a fracture line. We find zeta=0.60+/-0.05. For the first time, simulation results are in close agreement with experimental results. We then show that the roughness exponen...

We study the critical behavior of models for adsorbed layers in which particles reside on a square lattice and have infinite nearest-neighbor repulsions. Such particles are often described as ''hard squares.'' We consider both the equilibrium hard-square model and a nonequilibrium model. The latter involves dimer adsorption onto diagonally adjacent sites, and the desorption and possible hopping...

When directed percolation in a bond percolation process does not occur, any path to innnity on the open bonds will zigzag back and forth through the lattice. Backbends are the portions of the zigzags that go against the percolation direction. They are important in the physical problem of particle transport in random media in the presence of a eld, as they act to limit particle ow through the me...

We present a scaling Ansatz for the distribution function of the shortest paths connecting any two points on a percolating cluster which accounts for (i) the e ect of the nite size of the system, and (ii) the dependence of this distribution on the site occupancy probability p. We present evidence supporting the scaling Ansatz for the case of two-dimensional percolation. c © 1999 Elsevier Scienc...