Spectrum Of Transport Operator Research Articles

Calculating the Discrete Spectrum of the Transport Operator with Arbitrary Order Anisotropic Scattering

We consider here the numerical determination of the discrete spectrum of the neutron transport operator in a homogeneous subcritical infinite medium in the case of highly anisotropic scattering. Under mild assumptions on the scattering coefficients, one knows that the discrete spectrum is a finite set whose elements are real with absolute values larger than 1. Under these assumptions, we describe a method to compute all eigenvalues for an arbitrary order of anisotropic scattering. The method has been implemented in a C++ library using IEEE double precision arithmetic, allowing for fast calculations. Numerical results are compared to values in literature and to high‐precision calculations using Maple.

On the spectrum of the linear transport operator in a slab geometry with generalized periodic boundary conditions

The spectrum of the transport operator A in a nonhomogeneous slab with continuous energy is discussed in consideration of anisotropic scattering and fission with generalized periodic boundary conditions. We show the relative compactness of the streaming operator B, investigate the spectrum of A, especially obtain the dominant and the strictly dominant eigenvalue in L1 space which is the most natural space for the transport problem.