A perturbative approach to a nonlinear advection-diffusion equation of particle transport

Discussion timeslot (ZOOM-Meeting): 16. July 2021 - 18:00
ZOOM-Meeting URL: https://icrc2021.desy.de/pf_access_abstracts
Corresponding Session: https://icrc2021-venue.desy.de/channel/Presenter-Forum-1-Evening-All-Categories/48
Abstract:
'We explore analytical techniques for modeling the nonlinear cosmic ray transport in various astrophysical environments which is of significant current research interest. While nonlinearity is most often described by coupled equations for the dynamics of thernthermal plasma and the cosmic ray transport or for the transport of the plasma waves and the cosmic rays, we rnstudy the case of a single but nonlinear advection-diffusion equation. The latter can be approximately solvedrnanalytically or semi-analytically, with the advantage that these solutions are easy to use and, thus, can rnfacilitate a quantitative comparison to data. We present our previous work in a twofold manner.rnFirst, instead of employing an integral method to the case of pure nonlinear diffusion, we apply an expansionrntechnique to the advection-diffusion equation. We use the technique systematically to analyze the effect of nonlinear diffusion for the cases of constant and spatially varying advection rncombined with time-varying source functions. Second, we extend the study from the one-dimensional, Cartesianrngeometry to the radially symmetric case, which allows us to treat more accurately the nonlinear diffusion problems on larger scalesrnaway from the source. The results are compared to numerical solutions, which are also extended to more complex situations.'

Authors: Dominik Walter | Horst Fichtner | Yuri Litvinenko | Frederic Effenberger
Indico-ID: 184
Proceeding URL: https://pos.sissa.it/395/139