Persistence length, $L_p$, is a fundamental mechanical property that quantifies the bending stiffness of a polymer. It’s defined as the characteristic length scale over which the correlation of bond angles decays. This correlation is expressed as the average cosine of the angle, $\theta$, between bonds separated by a distance $s$ along the chain: $\langle\cos(\theta(s))\rangle = […]

A Gaussian chain, when averaged over all conformations and orientations, exhibits isotropic behavior. This means it can be treated as a sphere with a radius equal to its radius of gyration, $R_g$. However, an exercise in the second chapter of Rubinstein’s Polymer Physics demonstrates that $R_g^2$ becomes asymmetric when the coordinate frame is aligned with […]

iPhone one-click post-processing.

A path on energy landscape is like: and this post is a guide to generate such animations. Step 1: Generate the Energy Landscape An energy landscape is essentially an energy function $U(\mathbf{x})$. This function can be created in various ways. For example, you might generate a series of Gaussian functions with random parameters $\mu_i$, $\sigma_i$, […]