Kinetic Investigation of Small Systems Using Different Algorithms

To investigate the kinetics of small systems, the use of a stochastic approach is necessary. The classical approach to chemical kinetics is called a deterministic approach, since once the state of the system is known at time t1, its state at any other time will be known and no fluctuation about this value is observed [1,6]. The stochastic approach uses the inherent random nature of microscopic molecular collision to build a probabilistic model for a chemical reaction. This approach is useful in studying the kinetics of small systems. For small systems the validity of the deterministic approach becomes worse [1-7]. The calculated average concentration vs. time given by a stochastic approach and deterministic approach for a linear system are found to be equal. However, the results of these two approaches for nonlinear small systems are completely different [4]. The stochastic formulation proceeds by considering the grand probability function P(X;t), the density probability of particles in volume V at time t, where Xi is the number of Si