\(f\ (subscript)\) |
Fluid phase |
- |
\(m\ (subscript)\) |
Matrix phase |
- |
\(n\ (subscript)\) |
Experiment index |
- |
\(n\) (superscript) |
Grain size dependence exponent |
- |
\(t\) |
Time |
\(s\) |
\(V\) |
Volume |
\(m^{3}\) |
\(\rho\) |
Density |
\(\text{kg\ m}^{-3}\) |
\(A\) |
Area |
\(m^{2}\) |
\(v\) |
Velocity |
\(\text{m\ s}^{-1}\) |
\(z\) |
Depth |
\(g\) |
\(\sigma\) |
Total stress tensor |
Pa |
\(g\) |
Gravitational constant |
\(\text{m\ }s^{-2}\) |
\(H\) |
Interfacial traction tensor |
Pa |
\(c_{1}\) |
Drag coefficient |
\(\text{Pa\ s\ }m^{-2}\) |
\(P\) |
Thermodynamic pressure |
Pa |
\(\eta_{f}\) |
Dynamic viscosity of fluid |
Pa s |
d |
Grain size (diameter) |
mm or
μm
|
\(\kappa\) |
Matrix permeability |
\(m^{2}\) |
\(\tau\) |
Viscous stress tensor |
Pa |
\(\pi\) |
Geometric constant |
- |
\(\eta\) |
Matrix shear viscosity |
Pa s |
\(\eta_{s}\) |
Matrix shear viscosity as \(\phi\ \rightarrow 0\)
|
Pa s |
\(K\) |
Matrix bulk viscosity |
Pa s |
\(f_{\eta}\) |
Shear viscosity dependence on \(\phi\)
|
- |
\(f_{K}\) |
Bulk viscosity dependence on \(\phi\)
|
- |
\(\mathbf{v}_{\mathbf{0}}\) |
Reference velocity |
\(\text{m\ }s^{-1}\) |
\(v_{H}\) |
Boundary velocity |
\(\text{m\ }s^{-1}\) |
\(S\) |
Segregation velocity |
\(\text{m\ }s^{-1}\) |
\(y\) |
Unitless depth |
- |
\(H\) |
Height of compacting domain |
\(m\) |
\(H_{0}\) |
Initial height of compacting domain |
\(m\) |
\(\xi\) |
Effective matrix viscosity |
Pa s |
\(\xi_{\text{ref}}\) |
Reference viscosity |
Pa s |
\(\phi\) |
Porosity or melt fraction |
- |
\(\phi_{m}\) |
Maximum packing fraction |
- |
\(\phi_{\text{dis}}\) |
Disaggregation melt fraction |
- |
\(\mu_{\text{friction}}\) |
Friction coefficient |
- |
\(\sum\ \) |
Applied stress on piston |
Pa |
\(d\) |
Displacement |
mm |
\(\zeta\) |
\(\frac{\text{πξ}}{\phi}\) |
Pa s |
\(c\) |
\(\frac{\eta_{f}\phi^{2}}{\kappa}\) |
\(\frac{\text{Pa\ s}}{m^{2}}\) |
\(\beta\) |
\(\frac{c}{\phi^{2}}\) |
\(\frac{\text{Pa\ s}}{m^{2}}\) |
\(\delta_{c}\) |
Compaction length |
\(m\) |
\(L_{0}\) |
Misfit |
\(\text{Pa}^{2}\) or unitless |
\(\Pi\) |
Observed data |
Pa or unitless |
\(\vartheta\) |
Model |
Pa or unitless |
\(m\) |
Vector of model parameters |
Mixed |
\(N\) |
# of MCMC iterations |
- |
\(\mu[\ ]\) |
Mean of posterior distribution of given
parameter |
- |
\(\sigma[\ ]\) |
Standard deviation of posterior
distribution of given parameter |
- |