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[en] The author comments on three general subjects which are not directly related, but which in his opinion are very relevant to the objectives of the workshop. The first of these is parahydrogen moderators, about which recurring questions have been raised during the Workshop. The second topic is related to the use of simple synthetic scattering kernels in conjunction with the neutron transport equation to carry out elementary mathematical analyses and simple computational analyses in order to understand the gross physics of time-dependent neutron transport initiated by pulsed sources in cold moderators. The third subject is that of 'simple' benchmark calculations by which is meant calculations that are simple compared to the very large scale combined spallation, slowing-down, thermalization calculations using MCNP and other large Monte Carlo codes. Such benchmark problems can be created so that they are closely related to both the geometric configuration and material composition of cold moderators of interest and still can be solved using steady-state deterministic transport codes to calculate the asymptotic time-decay constant, and the time-asymptotic energy spectrum of neutrons in the cold moderator and the spectrum of the cold neutrons leaking from it (neither of which should be expected to be Maxwellian in these small leakage-dominated systems). These would provide rather precise benchmark solutions against which the results of the large scale calculations carried out for the whole spallation, slowing-down, thermalization system -- for the same decoupled cold moderator -- could be compared.
[en] The objective of the paper is to expose the reader to the basic simple and complex concepts of modern bifurcation theory, stability theory, and nonlinear dynamics, and to give some examples that arise in the dynamics of familiar nuclear systems and thereby provide the background necessary for the audience to understand and benefit from the more specific and detailed invited papers in this session. The nonlinear time evolution and stability of a dynamical system, e.g., an engineering or physical system described by coupled nonlinear differential equations (DEs), are intimately related to the local bifurcation phenomena that arise in the steady-state form of the DEs