title: Hall MHD and electron inertia effects in current sheet formation at a magnetic neutral line

authors: Litvinenko, Yuri E.

subjects: Finite-time singularities

abstract: An exact self-similar solution is used to investigate current sheet formation at a magnetic neutral line in incompressible Hall magnetohydrodynamics. The collapse to a current sheet is modelled as a finite-time singularity in the solution for electric current density at the neutral line. We establish that a finite-time collapse to the current sheet can occur in Hall magnetohydrodynamics, and we find a criterion for the finite-time singularity in terms of the initial conditions. We derive an asymptotic solution for the singularity formation and a formula for the singularity formation time. The analytical results are illustrated by numerical solutions, and we also investigate an alternative similarity reduction. Finally, we generalise our solution to incorporate resistive, viscous and electron inertia terms.

text: Hall MHD and electron inertia effects in current sheet formation at a magnetic neutral line An exact self-similar solution is used to investigate current sheet formation at a magnetic neutral line in incompressible Hall magnetohydrodynamics. The collapse to a current sheet is modelled as a finite-time singularity in the solution for electric current density at the neutral line. We establish that a finite-time collapse to the current sheet can occur in Hall magnetohydrodynamics, and we find a criterion for the finite-time singularity in terms of the initial conditions. We derive an asymptotic solution for the singularity formation and a formula for the singularity formation time. The analytical results are illustrated by numerical solutions, and we also investigate an alternative similarity reduction. Finally, we generalise our solution to incorporate resistive, viscous and electron inertia terms.

year: 2015

title: Special Issue: Eigenvalues of continuous systems

authors: Ilanko, Sinniah

abstract: Editorial.  The purpose of the special session was to bring together researchers who have successfully developed established techniques for formulating or solving different types of eigenvalue problems and those who are in the process of searching for new strategies to tackle emerging or longstanding problems, to exchange ideas on furthering the knowledge base of solving eigenvalue problems, in mechanics.

text: Special Issue: Eigenvalues of continuous systems Editorial.  The purpose of the special session was to bring together researchers who have successfully developed established techniques for formulating or solving different types of eigenvalue problems and those who are in the process of searching for new strategies to tackle emerging or longstanding problems, to exchange ideas on furthering the knowledge base of solving eigenvalue problems, in mechanics.

year: 2012

title: Kia kāpuia te reo o Tāmaki ki te Tonga: Tāmaki Makaurau ki te Tonga

authors: Lee-Morgan, Jenny Bol Jun

abstract: Mai i te Papakuratanga o Mataoho tae noa ki tona Ipu. Mai i Pukaki Tapu o Poutiikeka ki Te Puketapapatanga a Hape. Mai i te tahuna o Torea i nga wai o Mokoia, mawhiti atu ki Te Arapueru e karekare mai na ko Te Manukanuka a Hoturoa, kei reira a Taramainuku raua ko Kaiwhare. Ka kawea ki nga.hau o Mangere, e topa ai taku manuhokahoka ki Te Manurewatanga a Tamapahore. Whakaterawhiti taku haere ki Otara-a-nuku, ki Otara-a-rangi koia te tikapatanga o toku tiipuna o Marutuahu. Hoki whenei mai au ki Te Pane o Mataoho, tiro kau ake au ki aku pa whakairo ko Matatukutureia, ko Matukurua nga nohoanga tapu o Huakaiwaka, o Nga Tini-o-toitehuatahi, o Maruiwi kua ngaro katoa ki te reinga.

text: Kia kāpuia te reo o Tāmaki ki te Tonga: Tāmaki Makaurau ki te Tonga Mai i te Papakuratanga o Mataoho tae noa ki tona Ipu. Mai i Pukaki Tapu o Poutiikeka ki Te Puketapapatanga a Hape. Mai i te tahuna o Torea i nga wai o Mokoia, mawhiti atu ki Te Arapueru e karekare mai na ko Te Manukanuka a Hoturoa, kei reira a Taramainuku raua ko Kaiwhare. Ka kawea ki nga.hau o Mangere, e topa ai taku manuhokahoka ki Te Manurewatanga a Tamapahore. Whakaterawhiti taku haere ki Otara-a-nuku, ki Otara-a-rangi koia te tikapatanga o toku tiipuna o Marutuahu. Hoki whenei mai au ki Te Pane o Mataoho, tiro kau ake au ki aku pa whakairo ko Matatukutureia, ko Matukurua nga nohoanga tapu o Huakaiwaka, o Nga Tini-o-toitehuatahi, o Maruiwi kua ngaro katoa ki te reinga.

year: 2017