Abstract
In this paper, we discuss the criticality problem for monoenergetic neutron transport with isotropic scattering and fission in an inhomogeneous, bounded and convex subset of R , subject to vacuum boundary conditions. Without the assumption of a finite optical diameter, we prove that the spectral radius of the Peierls integral transport operator is not greater than c 0 := maximum secondary scattering ratio, and, moreover, that c 0 can not be an eigenvalue of this operator. We also discuss the relationship between the spectral radius of the Peierls integral transport operator and the geometric size, where the latter is measured by a certain parameter A, prove the existence of a critical size λ0 for c 0 > 1 under certain special assumptions, and develop an explicit estimate for λ0.
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© 1991 Springer Basel AG
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Nelson, P., Yu, F. (1991). Criticality and Critical Size for Transport Systems. In: Greenberg, W., Polewczak, J. (eds) Modern Mathematical Methods in Transport Theory. Operator Theory: Advances and Applications, vol 51. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5675-1_28
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DOI: https://doi.org/10.1007/978-3-0348-5675-1_28
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-5677-5
Online ISBN: 978-3-0348-5675-1
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