@article{AseevShpritsDrozdovetal.2016,
  author    = {Aseev, Nikita and Shprits, Yuri Y. and Drozdov, Alexander and Kellerman, Adam C.},
  title     = {Numerical applications of the advective-diffusive codes for the inner magnetosphere},
  series = {Space Weather: The International Journal of Research and Applications},
  volume    = {14},
  journal   = {Space Weather: The International Journal of Research and Applications},
  publisher = {American Geophysical Union},
  address   = {Washington},
  issn      = {1542-7390},
  doi       = {10.1002/2016SW001484},
  pages     = {993 -- 1010},
  year      = {2016},
  abstract  = {In this study we present analytical solutions for convection and diffusion equations. We gather here the analytical solutions for the one-dimensional convection equation, the two-dimensional convection problem, and the one- and two-dimensional diffusion equations. Using obtained analytical solutions, we test the four-dimensional Versatile Electron Radiation Belt code (the VERB-4D code), which solves the modified Fokker-Planck equation with additional convection terms. The ninth-order upwind numerical scheme for the one-dimensional convection equation shows much more accurate results than the results obtained with the third-order scheme. The universal limiter eliminates unphysical oscillations generated by high-order linear upwind schemes. Decrease in the space step leads to convergence of a numerical solution of the two-dimensional diffusion equation with mixed terms to the analytical solution. We compare the results of the third- and ninth-order schemes applied to magnetospheric convection modeling. The results show significant differences in electron fluxes near geostationary orbit when different numerical schemes are used.},
  language  = {en}
}
@article{ShpritsDrozdovSpasojevicetal.2016,
  author    = {Shprits, Yuri Y. and Drozdov, Alexander and Spasojevic, Maria and Kellerman, Adam C. and Usanova, Maria E. and Engebretson, Mark J. and Agapitov, Oleksiy V. and Zhelavskaya, Irina and Raita, Tero J. and Spence, Harlan E. and Baker, Daniel N. and Zhu, Hui and Aseev, Nikita},
  title     = {Wave-induced loss of ultra-relativistic electrons in the Van Allen radiation belts},
  series = {Nature Communications},
  volume    = {7},
  journal   = {Nature Communications},
  publisher = {Nature Publ. Group},
  address   = {London},
  issn      = {2041-1723},
  doi       = {10.1038/ncomms12883},
  pages     = {7},
  year      = {2016},
  language  = {en}
}