Some Numerical Results of the Albedo Problem in Spherical Geometry with Linearly Anisotropic Scattering

Abstract

The discrete eigenvalues for varying c and b 1 are given in Table S1. These eigenvalues are the numerical solutions of Eq. ( 5) in the main paper "Some numerical results of the albedo problem in spherical geometry with linearly anisotropic scattering". We use the FindRoot command, which runs with the Newton-Raphson method, to find these eigenvalues.In Figures 1-8 the albedo value is plotted against the scattering coefficient b 1 , in Figures 9 and 10 it is plotted against secondary neutron number c, in Figures 11-14 it is plotted against the radius of the solid homogeneous sphere R, and in Figures 15 and 16 it is plotted against N . In Figure 15, we calculate the albedo values from N = 0 to N = 8 for the H N method, while in Figure 16 we calculate the albedo values from N = 500 to N = 8000 for the SVD method.We see that the albedo values decrease along the scattering coefficient −0.3 ≤ b 1 ≤ 0.3 at all c and R values from c = 0.1 to c = 0.999 and R = 1 to R = 10. This decrease can be seen in Figures 1-8. However the albedo values increase along the number of secondary neutrons 0.1 ≤ c ≤ 0.999 at all b 1 and R values from b 1 = −0.3 to b 1 = 0.3 and R = 1 to R = 10. This increase can be seen in Figures 9 and 10. Moreover the albedo values decrease along the radius of the solid homogeneous sphere 1 ≤ R ≤ 10 at all c and b 1 values from c = 0.1 to c = 0.999 and b 1 = −0.3 to b 1 = 0.3. This decrease can be seen in Figures 11-14.