FTS Glossary

If you don’t understand what a symbol means elsewhere in the documentation, hopefully it will be defined here.

  • \(V\) - cell volume

  • \(d\) - dimentionality of system

  • \(P\) - number of different molecule types

  • \(n = \sum_{p=1}^P n_p\) - total number of molecules

  • \(n_p = \frac{C \tilde{V} \bar{\phi}_p}{\alpha_p}\) - number of copies of p th molecule type

  • \(N_p\) - degree of polymerization of p th molecule type

  • \(N\) - reference degree of polymerization

  • \(\tilde{V} = V/R_g^d\) - scaled cell volume .

  • \(\alpha_p = N_p / N\) - scaled length of p th molecule type

  • \(\phi_p (\bm{r}) = \rho_p / \rho_0\) - spatially dependent volume fraction of p th molecule type

  • \(\bar{\phi}_p = \frac{n_p N_p}{\sum_{i=1}^P n_i N_i}\) - overall volume fraction of p th molecule type

  • \(C = \frac{\rho_0 R_g^d}{N}\) - dimentionless chain concentration, where d is dimensionality of system

  • \(\rho_0 = \sum_{p=1}^P \frac{n_p N_p}{V}\) - overall monomer number density

  • \(v_0 = 1/\rho_0\) - reference volume, average volume per monomer

  • \(w_i\) - species or exchange field. Typically if i is a letter than \(w_i\) is a species field, while if i is a number or \(\pm\) then \(w_i\) is an exchange field.

  • \(\mu_i = \gamma_i w_i N\) - rescaled (and possibly Wick rotated) exchange field

  • \(\gamma_i = {1,\sqrt{-1}}\) - depending on whether the field is Wick rotated

  • \(R_g = \sqrt{\frac{b^2N}{6}}\), the radius of gyration of reference polymer chain consisting of N+1 beads

  • \(B =\beta u_0 N^2 / R_g^d\), the dimensionless excluded volume, where d is dimensionality of system.

  • \(E = 4 \pi l_B \sigma^2 N^2 / R_g\), the dimensionless electrostatic interaction strength

  • \(\varphi\), fluctuating electrostatic potential field

  • \(a_i\), smearing length of species i

  • \(\tilde{a}_i\), smearing length of species i in units of \(R_g\). \(\tilde{a}_i = a_i / R_g\)