The scalar force network ensemble model for force distribution in granular system
颗粒体系中力分布的标量力网系综模型

A scalar model of force network ensemble is proposed to investigate the force distribution in static granular system. The Laplace transform method is found as an effective method to solve the integral issue of probability density under complex constraints. On the condition that the system has few layers, the analytical expression for the limit distribution is accounted for which is the product of the polynomial function and the exponential function. When the force is near the average force, the distribution has its maximum value, when it's above the average force, the distribution decreases exponentially.