Escaping Time and Partical Collision Modelling and Simulation

Average Escaping Time Estimation Considering the following situation, a microcell within a given domain can not move by itself, it can only moving follow the flows of the domain, suppose the region is two-dimensional and given motion of this movement follows from normal distribution, then we immediately see the movement of the cell follows a Brownian Motion trajectory as we discuss before. But the questions is when will it escape from our given domain, or it is same to say when will it reach the boundary point of our domain? I will demonstrate first attempt to model this kind of problems by simuate a path follows stochastic process. We define our boundary as a circle plot the move and along with the boundary and let’s take our trajectory to be a Brownian Motion for simplicity.