Symbols and Conventions
Here we collect the physical meaning of the symbols and the corresponding storage
convention use in package flory. Note that the first column is always dimensionless.
Counts
Symbol |
Unit |
Physical Meaning |
Convention |
|---|---|---|---|
\(N_\mathrm{C}\) |
1 |
Number of components |
Integer |
\(N_\mathrm{S}\) |
1 |
Number of features |
Integer |
\(N_\mathrm{P}\) |
1 |
Number of phases |
Integer |
\(N_\mathrm{U}\) |
1 |
Number of unstable modes |
Integer |
\(N_\mathrm{A}\) |
1 |
Number of constraints |
Integer |
\(N_\mathrm{M}\) |
1 |
Number of compartments |
Integer |
\(i,j,k\) |
1 |
Indexes for components. 1-Based in documentation |
Integer \(\in [1, N_\mathrm{C}]\) |
\(r,s,t\) |
1 |
Indexes for features. 1-Based in documentation |
Integer \(\in [1, N_\mathrm{S}]\) |
\(p\) |
1 |
Index for phases. 1-Based in documentation |
Integer \(\in [1, N_\mathrm{P}]\) |
\(\alpha\) |
1 |
Index for constraints. 1-Based in documentation |
Integer \(\in [1, N_\mathrm{A}]\) |
\(m\) |
1 |
Index for compartments. 1-Based in documentation |
Integer \(\in [1, N_\mathrm{M}]\) |
Common Variables
Here we collect the common symbols used in the user interface.
Symbol |
Unit |
Physical Meaning |
Convention |
|---|---|---|---|
\(\phi_i\) |
1 |
Volume fraction of component \(i\). |
\(N_\mathrm{C}\) |
\(\mu_i\) |
\(k_\mathrm{B}T/\nu\) |
Chemical potential of component \(i\) by unit volume. |
\(N_\mathrm{C}\) |
\(\phi_{p,i}\) |
1 |
Volume fraction of component \(i\) in compartment \(p\). |
\(N_\mathrm{P} \times N_\mathrm{C}\) |
\(\bar{\phi}_i\) |
1 |
Average volume fraction of component \(i\). |
\(N_\mathrm{C}\) |
\(l_i\) |
\(\nu\) |
Relative molecule volume of component \(i\). |
\(N_\mathrm{C}\) |
\(J_p\) |
Total \(V\) |
Relative volume of phase \(p\). |
\(N_\mathrm{P}\) |
\(f\) |
\(k_\mathrm{B}T/\nu\) |
Free energy density. |
\(N_\mathrm{P}\) |
Advanced Variables
Here we collect the advances symbols used in the package. Note that the major difference from the common ones is that in most of cases, the index of the compartment \(m\) is the last index, namely the fastest-varying index (C-convention), to improve performance.
Symbol |
Unit |
Physical Meaning |
Convention |
|---|---|---|---|
\(\phi_r\) |
1 |
Volume fraction of feature \(r\). |
\(N_\mathrm{S}\) |
\(\bar{\phi}_r\) |
1 |
Mean volume fraction of feature \(r\). |
\(N_\mathrm{S}\) |
\(\phi_i^{(m)}\) |
1 |
Volume fractions of component \(i\) in compartment \(m\). |
\(N_\mathrm{C} \times N_\mathrm{M}\) |
\(\phi_r^{(m)}\) |
1 |
Volume fractions of feature \(r\) in compartment \(m\). |
\(N_\mathrm{S} \times N_\mathrm{M}\) |
\(w_r^{(m)}\) |
1 |
Conjugate variable of (mean field felt by) \(\phi_r^{(m)}\). |
\(N_\mathrm{S} \times N_\mathrm{M}\) |
\(p_i^{(m)}\) |
1 |
Boltzmann factor of component \(i\) in compartment \(m\). |
\(N_\mathrm{C} \times N_\mathrm{M}\) |
\(Q_i\) |
1 |
Single molecule partition function of component \(i\). |
\(N_\mathrm{C}\) |
\(J_m\) |
Arbitrary volume |
Relative volume of compartment \(m\). |
\(N_\mathrm{M}\) |
\(C_{\alpha,r}\) |
1 |
Coefficients of features for linear constraint \(\alpha\). |
\(N_\mathrm{A} \times N_\mathrm{S}\) |
\(T_\alpha\) |
1 |
Target (right-hand-side) of constraint \(\alpha\). |
\(N_\mathrm{A}\) |
\(\kappa\) |
1 |
Elasticity of constraints. |
Scaler |