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The deficiency of the approximation relative to the full process is given by taking the limit of the mean squared error (MSE) of Y ˜ − Y (equivalent to the stationary variance of Y ˜ − Y ), which, as shown in the proof of Lemma 1, is an expression of the sum over all neglected reactions.
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In the presented case study typical simplifications in step 4) amount to lumping and neglecting reactions that do not affect any model output.
Although the effect of competitive adsorption (MAPP, HDA) and mutual solubility of the components (PP, MAPP, surfactant, reaction products) cannot be neglected, chemical reactions play a crucial role in structure formation in PP nanocomposites containing a functionalized polymer.
Blue: existing species and reactions in the model in Tay et al. (2010) ; Red: newly introduced species and reactions; Gray: neglected species and reactions.
The model calculation indicates that the exchange can be neglected for reaction limited systems but becomes important for mass transfer limited systems.
We further assume that for all states which are not fully modified or unmodified, reactions from the ternary complex are dominant and thus neglect binary reactions from these configurations.
In the incompressible isothermal case, neglecting chemical reactions and other forces, the model reduces to an evolution system which governs the fluid velocity u and the order parameter ϕ.
Stripping voltammetry in diluted solutions of catalyst allowed to neglect bulk reactions of catalyst and revealed the transformation of adsorbed Ni(I) complex catalyst into the catalytically inactive Ni(0) carbonyl deposit.
Because transcription factor activity is being measured in vivo, we can neglect sub reactions such as binding of arabinose to AraC, or cAMP to CRP, and binding of these two complexes to their respective operator sites.
It is shown that a rigorous numerical solution of the differential equations describing the mass transfer gives more insight into the actual process than analytical approximations based on a reduction of the number of reactions by neglecting or lumping reactions.
It is shown that a rigorous numerical solutions of the differential equations describing the mass transfer gives more insight into the actual process than analytical and numerical approximations based on a reduction of the number of reactions by neglecting or lumping reactions.
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