Random Walk

#Physics

Topics

• Persistence Length
• Radius of Gyration
• Polymer Extension

$\displaystyle {\left\langle{R}\right\rangle}=0$

• $\displaystyle R$ is the end to end length

$\displaystyle {\left\langle{R^{2}}\right\rangle}=Na^{2}$

• $\displaystyle N$ is the number of segments
• $\displaystyle a$ is the length of a segment

$\displaystyle P(R; N) = \frac{1}{\sqrt{2\pi N a^2}} e^{-R^2 /2N a^2}$

• 1D version

$\displaystyle P(\vec{R};N)=\left( \frac{3}{2\pi Na^{2}} \right)^{3 /2}e^{-3R^{2} /2Na^{2}}$

• 3D version