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The population balance model is solved using a combined quadrature method of moments and method of characteristics (QMOM-MOCH) approach for the generic case of apparent size-dependent growth.
The population balance model is solved using the method of characteristics under the assumptions of a constant supersaturation and growth dominated process, yielding a simplified analytical expression for the size distribution.
The interaction between turbulent fluctuations and particle formation (i.e., micro-mixing) is modelled with the so-called direct quadrature method of moments coupled with the interaction and exchange with the mean approach, whereas the population balance model is solved by using the quadrature method of moments.
The population balance model is solved with three different numerical methods namely, a continuous finite element method, a discrete-continuous finite element method and a discretized method with different high-resolution finite difference schemes for the calculation of the cell flux term.
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Pure and mixed culture dynamic flux balance models were solved using the Mosek optimization toolbox (Mosek ApS, Denmark) to resolve the linear program for intracellular metabolism within Matlab (Mathworks, Natick, MA) [ 30].
The newly formulated mathematical model is solved by discretizing the convolution integral and material balance equation, and then validated by simplifying it to the traditional Forchheimer model.
The model is solved numerically.
The stoichiometric flux-balance based model was solved using time-profiles of serine alkaline protease fermentation-data at three different oxygen-transfer conditions creating perturbations on the intracellular reaction-network.
The model was solved using Microsoft Excel.
The mathematical model was solved in CFX 11.0 (Ansys Inc).
This model was solved using the Mathworks Matlab ode23tb solver.
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