%0 Journal Article
%T Shortcut Node Classification for Membrane Residue Curve Maps
%J Journal of Membrane Science and Research
%I FIMTEC & MPRL
%Z 2476-5406
%A Stacey, Neil Thomas
%A Hildebrandt, Diane
%A Glasser, David
%A Peters, Mark
%D 2017
%\ 04/01/2017
%V 3
%N 2
%P 84-89
%! Shortcut Node Classification for Membrane Residue Curve Maps
%K Membranes
%K Separation
%K Residue Curve Maps
%K Lyapunov's Theorem
%K Permeation
%R 10.22079/jmsr.2016.21846
%X comNode classification within Membrane Residue Curves (M-RCMs) currently hinges on Lyapunovâ€™s Theorem and therefore the computation of mathematically complex eigenvalues. This paper presents an alternative criterion for the classification of nodes within M-RCMs based on the total membrane flux at node compositions. This paper demonstrates that for a system exhibiting simple permeation behaviour, this flux criterion is mathematically identical to Lyapunovâ€™s theorem for all possible values of relative permeability. This means that in membrane permeation systems with simple permeation, the stationary point with maximum flux is an unstable node while the stationary with minimum flux is a stable node and stationary points with intermediate fluxes are saddle points. This proof is also extended to two-membrane systems with simple permeation behaviour, resulting in a system of equations useful for finding membrane area ratios with desired node properties. It is also shown that the flux criterion does not hold for systems exhibiting complex permeation.
%U http://www.msrjournal.com/article_21846_2e3b555cf9ba0762ccfd38716ec4e737.pdf