Two-dimensional telegraphic processes and their fractional generalization

We study the planar motion of telegraphic processes. We derive the two-dimensional telegrapher's equation for isotropic and uniform motions starting from a random walk model which is the two-dimensional version of the multistate random walk with a continuum number of states representing the spa...

ver descrição completa

Detalhes bibliográficos
Autores: Masoliver, Jaume, 1951-, Lindenberg, Katja
Formato: artículo
Estado:Versión publicada
Fecha de publicación:2020
País:España
Recursos:Universidad de Barcelona
Repositorio:Dipòsit Digital de la UB
OAI Identifier:oai:diposit.ub.edu:2445/158844
Acesso em linha:https://hdl.handle.net/2445/158844
Access Level:acceso abierto
Palavra-chave:Difusió
Rutes aleatòries (Matemàtica)
Física estadística
Diffusion
Random walks (Mathematics)
Statistical physics
Descrição
Resumo:We study the planar motion of telegraphic processes. We derive the two-dimensional telegrapher's equation for isotropic and uniform motions starting from a random walk model which is the two-dimensional version of the multistate random walk with a continuum number of states representing the spatial directions. We generalize the isotropic model and the telegrapher's equation to include planar fractional motions. Earlier, we worked with the one-dimensional version [Masoliver, Phys. Rev. E 93, 052107 (2016)] and derived the three-dimensional version [Masoliver, Phys. Rev. E 96, 022101 (2017)]. An important lesson is that we cannot obtain the two-dimensional version from the three-dimensional or the one-dimensional one from the two-dimensional result. Each dimension must be approached starting from an appropriate random walk model for that dimension.