In this paper, two molecular mathematical models which simulate the conformations of a random flight chain and a freely rotating chain were suggested separately from the theory of stochastic process. We had obtained a...In this paper, two molecular mathematical models which simulate the conformations of a random flight chain and a freely rotating chain were suggested separately from the theory of stochastic process. We had obtained a series of results relating to conformations by means of these models. These results are not only mathematically stricter but also include the results obtained by previous workers. In an ideal state, conformation of a random flight chain is simulated as a 3-dimensional Brownian motion {r_t(ω), t>0}. We pointed out the objective meaning which was endowed to the different variables involved in a 3-dimensional Brownian motion. On this basis, the bond vector and the end-to-end state vector were defined; the distribution function and the reduced functions were thus obtained, e.g. the distribution of the end-to-end state vector which is a measure of the flexibility of a polymer chain,展开更多
文摘In this paper, two molecular mathematical models which simulate the conformations of a random flight chain and a freely rotating chain were suggested separately from the theory of stochastic process. We had obtained a series of results relating to conformations by means of these models. These results are not only mathematically stricter but also include the results obtained by previous workers. In an ideal state, conformation of a random flight chain is simulated as a 3-dimensional Brownian motion {r_t(ω), t>0}. We pointed out the objective meaning which was endowed to the different variables involved in a 3-dimensional Brownian motion. On this basis, the bond vector and the end-to-end state vector were defined; the distribution function and the reduced functions were thus obtained, e.g. the distribution of the end-to-end state vector which is a measure of the flexibility of a polymer chain,
