92 (1990) 792], thereby completing the existence, construction, and stability of shear-perturbed isotropic equilibria for all concentrations.
Let us assume that there is a finite number of equilibria on the perturbed torus which are all non-degenerate when (epsilon_{mathrm {LR}}neq 0), (chigeq0).
For the lattice pmm, there are at least eight equilibria on the perturbed torus (mathcal{T}_{epsilon_{mathrm {LR}}}), four of which are saddle, and the other four are nodes/foci.
We have seen that the minimal configuration, under the hypothesis that all equilibria on the perturbed torus are hyperbolic, is that of eight equilibrium points with four foci and four saddles.
As in the square case, we can deduce from these results the possible phase portraits when assuming that the equilibria on the perturbed torus are all hyperbolic and that there are exactly 18 of them, nine foci and nine saddles.
For the lattice p3m1, there are at least 18 equilibria on the perturbed torus (mathcal{T}_{epsilon_{mathrm {LR}}}), nine of which are saddle and the other nine are nodes/foci, given by the lattice (mathcal{L} [frac{2pi}{3}e_{1},frac{2pi }{3}e_{2} ]) which are centers of rotation.
The necessary phase equilibria were successfully investigated by modelling using the Perturbed Chain – Statistical Associating Fluid Theory (PC-SAFT) and measuring liquid liquid equilibria of the ternary systems substrates/solvents mixtures at the separation temperature.
More specifically, near normally hyperbolic equilibria, fast and slow dynamics within a singularly perturbed system evolve as O ( 1 ) and O , respectively.
The sorption equilibria were studied experimentally using a gravimetric apparatus and simulated by the perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state.
This allows one to assert the persistence of some steady-states (equilibria) which stand for points of maximal isotropy for the action of Γ on the perturbed torus.
