In this paper, a second order linear ordinary differential equation with three-turning points is studied. This equation is as follows (dx2)/(d2y) + [lambda(2)q(1)(x) + lambda q(2)(x, lambda)]y = 0, where q(1) (x) = (x...In this paper, a second order linear ordinary differential equation with three-turning points is studied. This equation is as follows (dx2)/(d2y) + [lambda(2)q(1)(x) + lambda q(2)(x, lambda)]y = 0, where q(1) (x) = (x - mu(1))(x - mu(2))(x - mu(3))f(x), f(x) not equal 0, mu(1) < mu(2) < mu(3) and lambda is a large parameter, but q(2)(x, lambda) = Sigma(i = 0)(epsilon a) g(i)(x)lambda(-i) (here g(0)(x) not equivalent to 0). By using JL function, the complete expression of the formal uniformly, valid asymptotic solutions of the equation near turning point is obtained.展开更多
The paper presents an improved cellular automaton model according to the feature of evacuation near the outlet. We studied friction and turning factors that affect pedestrian evacuation speed. By using mathematical me...The paper presents an improved cellular automaton model according to the feature of evacuation near the outlet. We studied friction and turning factors that affect pedestrian evacuation speed. By using mathematical methods to derive expressions of friction function and turning function. The average pedestrian outflow of the simulation that includes the effect of both the frictional function and the turning function agrees well with experiment result. On the contrary, the simulation results that only include the effect of the frictional function are not corresponding to the experiment results well. Simulation results show that friction and turning can not be ignored. By analyzing the simulation results, it verified that the model can accurately reflect the actual evacuation process and has practical value.展开更多
文摘In this paper, a second order linear ordinary differential equation with three-turning points is studied. This equation is as follows (dx2)/(d2y) + [lambda(2)q(1)(x) + lambda q(2)(x, lambda)]y = 0, where q(1) (x) = (x - mu(1))(x - mu(2))(x - mu(3))f(x), f(x) not equal 0, mu(1) < mu(2) < mu(3) and lambda is a large parameter, but q(2)(x, lambda) = Sigma(i = 0)(epsilon a) g(i)(x)lambda(-i) (here g(0)(x) not equivalent to 0). By using JL function, the complete expression of the formal uniformly, valid asymptotic solutions of the equation near turning point is obtained.
文摘The paper presents an improved cellular automaton model according to the feature of evacuation near the outlet. We studied friction and turning factors that affect pedestrian evacuation speed. By using mathematical methods to derive expressions of friction function and turning function. The average pedestrian outflow of the simulation that includes the effect of both the frictional function and the turning function agrees well with experiment result. On the contrary, the simulation results that only include the effect of the frictional function are not corresponding to the experiment results well. Simulation results show that friction and turning can not be ignored. By analyzing the simulation results, it verified that the model can accurately reflect the actual evacuation process and has practical value.
