The method leads to a great reduction in the system matrix, without loss of accuracy of the results, when compared to the classical method of lumping the disks at nodal points.
Until last week, his campaign website listed 12 entities under "past and present endorsements," an unusual method of lumping together groups that are currently endorsing him with ones that may have endorsed his past bids for Congress.
The Washington Post reports that as recently as this past week, Stockman's Senate campaign site listed 12 entities under "past and present endorsements," an unusual method of lumping together groups that are currently endorsing him with ones that endorsed his past bids for Congress.
The formal method of lumping demonstrated the use of a lumping matrix to simplify a model with X numbers of states to a model with Y numbers of states (where Y < X).
The method of uniform lumping presented in Part I, is generalized to permit use of unequal lumps for the order reduction of tridiagonal dynamic models of staged processes.
The work of Dokoumetzidis and Aarons consisted of two components (i) a formal method for lumping and (ii) an automated algorithm for lumping a systems model.
Compared with the traditional modelling method, the advantages of lumped stiffness method are as follows: nonlinear stiffness, time-varying curvature, and time-varying load have been integrated into the lumped stiffness model and not directly reflected in the dynamic model; the dynamic model will be established and solved easily.
The new modelling method broadens the application of lump kinetic model in the field of catalyst selection and design, and in turn makes the process of catalyst selection and design more theory-guided.
The formal method of using the lumping matrix to reduce the number of states of a model, as explained previously by Dokoumetzidis and Aarons, is described briefly below.
In our work, we used their formal method of using the lumping matrix, but instead of using their automated algorithm, we manually undertook the process to control more easily what states were lumped.
The approach combines general symbolic methods of nonlinear lumping and numerical techniques to arrive at an analytically reduced model in practical applications of homogeneous kinetic systems.
