The kinetics equations in a multiplying medium with free boundaries | Zendy

BelleniMorante A. | Zendy; Lauro G. | Zendy

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The kinetics equations in a multiplying medium with free boundaries

Author(s) -

BelleniMorante A.,

Lauro G.

Publication year - 1990

Publication title -

mathematical methods in the applied sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.719

H-Index - 65

eISSN - 1099-1476

pISSN - 0170-4214

DOI - 10.1002/mma.1670130307

Subject(s) - mathematics , ordinary differential equation , multiplication (music) , differential equation , stability (learning theory) , mathematical analysis , neutron , slab , physics , combinatorics , nuclear physics , machine learning , geophysics , computer science

We study a mathematical model of neutron multiplication in a slab , by taking into account temperature feedback effects and considering one group of delayed neutrons. The thickness 2 a of is time dependent because of temperature variations due to the energy released by fissions. Starting from a quite detailed picture of the physical phenomena occurring in , we derive a system of three coupled ordinary differential equations for the total number of neutrons F̂ = F̂( t ), for the total number of precursors Ĉ = Ĉ( t ), and for the half‐thickness of , a = a ( t ). We finally examine some stability properties of such a system of ordinary differential equations.

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