Random Walker in One Dimension

The Physical Chemistry of Materials Energy and Environmental Applications 

FIGURE 5.6 One-dimensional random walker that can jump either to the left or to the right. 

since the time between jumps, or mean residence time, is x. Therefore, the jump frequency is T = X consequently, if T is constant, then for N steps where N = —, the MSD is 

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Consider now a random walker in one dimension, with probability, R, of moving to the right, and, L, for moving to the left. At, l = 0, we place the walker at x = 0, as indicated in Figure 5.6. The walker can then jump, with the above probabilities, either to the left or to the right for each time-step. Every... 

Random Walk A linear flexible polymer chain can be modeled as a random walk. The concept of the random walk gives a fundamental frame for the conformation of a polymer chain. If visiting the same site is allowed, the trajectory of the random walker is a model for an ideal chain. If not allowed, the trajectory resembles a real chain. In this section, we learn about the ideal chains in three dimensions. To familiarize ourselves with the concept, we first look at an ideal random walker in one dimension. 

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