Single scattering assumption

We assume that the intensity of the initially scattered light from a single scattering center is the same for symmetric scattering angles 9S. This assumption does not imply that the inten-... 

Within the assumptions usually valid for small angle scattering (Bom approximation, Thomson scattering, single scattering events, etc.), the amplitude of scattering is given by ... 

Initially, we will focus on the mesoscopic description associated with the radiative transfer equation. Then, we will introduce the single-scattering approximation and two macroscopic approximations the PI approximation and two-flux approximation. AH of these discussions are based on the configuration shown in Fig. 6. Collimated emission and Lambertian emission wiU also be considered in the discussion later they correspond to the direct component and the diffuse component of solar radiation, respectively. Throughout our study, the biomass concentration Cx is homogeneous in the reaction volume V (assumption of perfect mixing), and the emission phenomena in V are negligible. The concentration Cx is selected close to the optimum for the operation of the photobioreactor the local photon absorption rate. 4 at the rear of the photobioreactor is close to the compensation point A.C (see Section 5 and chapter Industrial Photobioreactors and Scale-up Concepts by Pruvost et al.). 

The assumption of single scattering—that is, that a photon only scatters once before being detected—is implicit in the aforementioned theories. Hence, there is a limit to the turbidity of a solution whose scattering can be analyzed by these theories. Being based on these theories, the HTDSLS technique presented in this work likewise requires that only single scattering occur. 

Mead and Truhlar [10] broke new ground by showing how geometric phase effects can be systematically accommodated in scattering as well as bound state problems. The assumptions are that the adiabatic Hamiltonian is real and that there is a single isolated degeneracy hence the eigenstates n(q-, Q) of Eq. (83) may be taken in the form... 

Why, then, is the magnetisation density used The answer is that the magnetisation density is important for certain approximations which are usually made in analysing neutron scattering experiments. In the standard polarised neutron diffraction (PND) experiment [5], only one parameter is measured - the so-called flipping ratio . It is impossible to determine a vector quantity like the magnetisation density from a single number, unless some assumptions are made. The assumptions usually made are ... 

Non membership and/or binarity are not the reasons for the scatter M 67, since both low and high Li stars are confirmed radial velocity members and the spread is still present when considering single stars only. Under the very reasonable assumption that cluster stars were all born with the same Li content, the scatter is therefore intrinsic and due to different amounts of Li depletion. 

Inspection of Fig. 8 shows that there is considerable scatter in the data. Part of this may be due to the fact that we are attempting to represent a complex phenomenon with a single parameter, the dispersion coefficient. Errors would also be caused by the common practice of taking measurements at or beyond the exit of the packed section. This neglect of end conditions could lead to large errors in the calculated dispersion coefficients, as pointed out by Bischoff and Levenspiel (B14). Also, all the analyses were based on the assumption of having a perfect pulse, step. 

Because there is no general microscopic theory of liquids, the analysis of inelastic neutron scattering experiments must proceed on the basis of model calculations. Recently1 we have derived a simple interpolation model for single particle motions in simple liquids. This derivation, which was based on the correlation function formalism, depends on dispersion relation and sum rule arguments and the assumption of simple exponential decay for the damping function. According to the model, the linear response in the displacement, yft), satisfies the equation... 

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