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written by
Kostas Papamichalis *

In this application we study the evolution of a system consisted of N=800 identical, but discrete, cells placed at the vertices of a lattice. Each cell can exist in one of two states A or B. If at time t the j-cell is in state A, the probability p to get transitioned to the state B in the infinitesimal interval [t,t+Dt] equals wDt, where w is a real constant, named "transition probability per unit time". The value of w is chosen by the user. However, if at time t the j-cell is in state B, it remains in state B with probability 1.

In the simulation a cell is in the state A if its color is orange, and in B if its color is purple. By playing the simulation, we see in real time the transition of each individual cell from state A to state B. The transition happens or not, in one of the time-intervals [tk,tk+Dt], where k=0,1,2,... and Dt=0.1. The decision of each transition is taken by using the random-number generator of JavaScript, with probability p=wDt. In the adjacent, right-sided window, we see two graphs concerning the change with time of a certain Lyapunov functional corresponding to the master equation which describes the evolution of the system toward its equilibrium state. The red graph is the theoretical prediction. The blue one is the experimental graph achieved by counting the cells in state A in real time. The main objective of the simulation is to compare the theoretical predictions with the experimental results.

Last Modified *December 1, 2023*

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