リルの分布の確率モデルについて

Abstract

Development process of rills is modeled with stochastic theory.Branching process and joining process are taken into consideration.Experimental study showed that joining ratio is in proportion to the number of rills andbranching ratio is proportional to relative width (width/depth) of rills.From the above results, next equation is derived for the stochastic process of the model.dPk(t)/dt=αKPk+1(t)+βΣ Wi-1/Di Pk-1(t)-{α(k-1)+βΣ Wi-1/Di}Pk(t)for k≠1, k≠NWhere Pk(t) is the probability that the number of rills will be k at the time t. α, β arejoining coefficient and branching coefficient respectively. Wi and Di are width and depth ofI-th rill respectively.