2. Discrete abacus: Consider a discrete abacus with L slots and N particles. If a particle has no neighbors, it is inactive (represented as red) and does not move. On the other hand, particles that have neighbors they are active (represented as blue). The active particles try to hop if they can; all active jump or only few of them move at each step, see examples below in the figure and arrows represent their potential movement. Note that red particles can become blue if they get a neighbor or a blue become red if it looses neighbours. L = 4, N = 2 L = 4, N = 3 Minimum number of active (blue) particles NW 0 1 3 4 Number of particles, N The game is to start in any random situation and keep moving the active particles until either all particles are inactive, or the system reaches the minimum number of active particles. Consider L = 4 and N=2, in the figure, you can see that particles move but eventually will reach a stage where the 2 particles are inactive. But for L=4 and N=3, you can never have all the particles become inactive. Now we can plot the minimum number of active particles as we fill in the abacus for L = 4 will get the plot shown in the figure. a. Can you make similar plot for L = 6, 8, 10? (50 pts) b. What is the filling percentage at which you see a transition in the behavior for different L? Does this "critical" filling percentage depend on L? (20 pts)