Crowd dynamics - being stuck

In physics, a phase transition from liquid to solid means that molecules are stuck between their neighbours. We investigate a similar effect in a crowd at a small exit. People cross the exit one by one, but the majority moves very slowly. Those from behind press, and if the density is large enough, it is impossible to move with respect to our neighbours. Can one withdraw from the crowd or he/she will be thrown out through the exit against his/her will? that is our question. The system is simulated according to the Helbing model of crowd dynamics [1]. In our simulation, N individuals are going to leave a room 30 × 20 m, with an exit of width of 1 m in the middle of the shorter wall. Initial positions of the individuals are chosen randomly with a homogeneous distribution , where overlaps are excluded. The time dependence of the positions is determined by the set of equations of motion [1], which include the interper-sonal mechanical and psychological forces and the mechanical interaction of human bodies with walls. The mechanical forces include repulsion and friction. The psychological forces include the human tendency to keep distance from other persons and the desired direction to the exit. The equations and all model parameters are adopted from [1]. To determine if a person is stuck or not, a numerical experiment is performed as follows. The sum S i of compressive mechanical forces acting on each individual i is registered during the motion. Once for some individual X the sum S x exceeds some threshold value S prescribed at the beginning of the simulation, the desired direction of motion for this individual is reverted. Now this direction is not to the exit but opposite. If X crosses the exit despite this change of her/his intention, we call the crowd 'jammed'. The experiment is repeated 70 times for