# Taylor expansions for random-walk polymers

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Original entry by Joerg Fritz, AP225 Fall 2009

## Outline

This entry investigates a small aspect of the very elegant derivation for the scaling of end-to-end distance as described in detail here. We specifically ask the following question: Can we predict the probability $p(n,\vec{r}-\vec{r_1})$ that a polymer with n segments has a vector $\vec{r_1}$ connecting its two ends, if $\vec{r_1}$ is close to $\vec{r}$ and we know the probability for $\vec{r}$, that is $p(n,\vec{r})$ and its spacial derivatives? Even more specifically, if $p(n,\vec{r})$

## Taylor expansion in several variables

Fig.2 Geometric representation of the flat sheet shown in figure 1, the numerical discretization and the result of the simulation in case of successful folding.