Source term definition

Mass-Transfer Mechanisms in Source-Term Definition... 

Source Term Definition—Dispersion Modeling Applications ... 

To examine the derivation of the population balance source term closures, the bubble diameter is henceforth chosen as the only internal coordinate (i.e., jc = d) as it is the most frequent choice. Adopting the generalized source term definitions as defined in this subsection, the diameter based source terms occurs directly by substituting the diameter into the different source term equations noting from (9.79) that the third diameter is computed in terms of the other two d = (d - and the Jacobian... 

The resulting local source term definitions are listed below ... 

The integrals (with respect to ) in the source term definitions (see (9.87)-(9.90)) can be expressed in terms of a quadrature as a sum of integrals over the sub-intervals. Replacing the corresponding integrals in all the source terms with such a quadrature sum, the macroscopic equation can be formulated as ... 

This symposium concerns models for predicting the fate of chemicals in the environment. Strictly speaking, the topic of this paper does not fall into the usual definition of fate models. However, every fate model has at least one source term. Although the source term for one fate model may be the output of another fate model (as when air transport models provide the deposition rates that are the inputs to an aquatic fate model), the chain always has to be traced to the original sources, whether they are natural or associated with human activities. 

By definition of the reaction-progress variables, Y2 and T22 are zero for the inlet streams, and nonnegative inside the reactor due to the chemical source term. Once the CFD model has been solved, the reactant concentrations in each environment n are found from... 

Due to the conservation of elements, the rank of J will lie less than or equal to K — E 1 In general, rank(J) = Ny < K - E, which implies that V = K — T eigenvalues of J are null. Moreover, since M is a similarity transformation, (5.51) implies that the eigenvalues of J and those of J are identical. We can thus limit the definition of the chemical time scales to include only the Nr finite ra found from (5.50). The other N components of the transformed composition vector correspond to conserved scalars for which no chemical-source-term closure is required. The same comments would apply if the Nr non-zero singular values of J were used to define the chemical time scales. 

A transport equation for could be derived starting from its definition in (5.321). However, the resulting expression would be unduly complicated and not necessarily agree with our assumption of independence between Y and f.133 Instead, Y can be treated as any other scalar so that the transport equation for (Y ) has the form of (3.88) on p. 81 with (j a = T and a chemical source term given by... 

An excellent source for definitions of these terms may be found at http // www.google.com/. In the search statement, use the syntax definerxyz where xyz is the term for which a definition is sought. 

Considering the two source terms (emission and in-scattering) and the two sink terms (absorption and out-scattering) defined on the right-hand side of the previous expression, one can transform the preceding fimdamental law in a more formal mathematical definition ... 

For file periodic case, we just change the definition of file dimensionless time variable source term, as follows for the parallel-plates geometry ... 

Entries are easy to read and written in a straightforward style. Difficult words are defined within the text. Each entry also includes a Words to Know sidebar that defines technical words and scientific terms. This enables students to learn vocabulary appropriate to chemistry without having to consult other sources for definitions. 

The main challenge in formulating these equations is related to the definition of the collision operator. So far this approach has been restricted to the formulation of the population balance equation. That is, in most cases a general transport equation which is complemented with postulated source term formulations for the particle behavior is used. Randolph [80] and Randolph and Larson [81] used this approach deriving a microscopic population balance equation for the purpose of describing the behavior of particulate systems. Ramkrishna [79] provides further details on this approach considering also fluid particle systems. 

Standards are an excellent source for definitions. Because standards should convey the same meaning to different groups, a great deal of care is exercised in the use and definition of terms. Examples of standards dealing entirely with definitions include ASTM D 16-47 and D 16-48T covering terms relating to paint, varnish, lacquer, and related prod-... 

In order to account for variable particle numbers, we generalize the collision term iSi to include changes in IVp due to nucleation, aggregation, and breakage. These processes will also require models in order to close Eq. (4.39). This equation can be compared with Eq. (2.16) on page 37, and it can be observed that they have the same general form. However, it is now clear that the GPBE cannot be solved until mesoscale closures are provided for the conditional phase-space velocities Afp)i, (Ap)i, (Gp)i, source term 5i. Note that we have dropped the superscript on the conditional phase-space velocities in Eq. (4.39). Formally, this implies that the definition of (for example) [Pg.113]

Note that, in general, the transport and source terms in Eq. (4.85) will not be in closed form. Erom the definition in Eq. (4.84), we can identify three limiting cases. 

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