Problem: given a series molecules $i=1,\dots,N$, connected with junction atoms $\mathbf{x}_i^k$, for $k=1,2,…m$ if there are $m_i$ atoms from molecule $i$ that are bonded with other molecules. The connection bonds are defined as $\mathbf{b}_i := \lbrace\mathbf{x}_j^{k_1}-\mathbf{x}_i^{k_2}|\forall k_1, k_2\, \mathrm{and}\, \forall j\in \mathrm{neighbor\, of}\, i\rbrace$, assume that the center-of-mass of the molecules are fixed, but are […]

The structure factor, commonly denoted as $S(\mathbf{q})$, is an essential characterization quantity in molecular simulations. Its calculation is straightforward based on its definition. Since periodic boundary conditions are typically used in these simulations, we have $$S(\mathbf{q}) := \mathcal{FT}\lbrace\langle\rho(\mathbf{r})\rho(\mathbf{0})\rangle\rbrace(\mathbf{q})$$ which actually represents a circular convolution. This means that using the Fast Fourier Transform (FFT) can dramatically […]

In my previous post, I developed a GPC post-processing program that uses the continuous wavelet transform (CWT) to detect and correct baselines, and the MH equation to convert GPC data into a molecular weight distribution. In this follow-up work, I determine the molecular weight distributions in a two-step synthesis process. In the first step, polymers […]