Equivalent transport problem, single

Implementation of the Single Scattering Approximation for an Equivalent Transport Problem Application to a Flat-Plate Photobioreactor... 

Fig. 13 presents the angular distribution of L resulting from the singlescattering approximation for the equivalent transport problem a, and Ph 4 as well as the reference solution produced by the Monte Carlo method for and k xt and the phase function of C. reinhardtii. In the reference situation, at the location in question (zq = 3 cm), the ballistic beam is completely attenuated all the photons have undergone at least one scattering event but deviated very htde from their incident direction (see Section 3.2). This situation results in a complex angular distribution centered around the incident direction (see Fig. 13A). In our equivalent transport problem, this complex distribution is replaced by the sum of a Dirac distribution (contribution of the ballistic photons, ie, 75% of the photons in the present case, see Fig. 14) and a relatively broad distribution (contribution of the scattered photons) that is simply modeled as Eqs. (62) and (63) under the single-scattering approximation (see Fig. 13B). The angular distribution of the scattered intensity at different locations is shown in Fig. 15.

The single-scattering approximation applied to the equivalent transport problem for analysis of coUimated illumination in the case of nonreflecting surfaces Eqs. (65) to (68). 

In a surfactant mixture the initial conditions, for each component, are equivalent to those for a single surfactant system. When solving the given initial and boundary condition problem the result is Eq. (4.1). The derivation of the solution was performed using Green s functions (Ward Tordai 1946, Petrov Miller 1977) or by the Laplace operator method (Hansen 1961). Appendix 4E demonstrates the application of the operator method for solving such types of transport problems. 

---