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: Subcubic trades in Steiner triple systems

authors: Cavenagh, Nicholas J.

subjects: Science & Technology

abstract: We consider the problem of classifying trades in Steiner triple systems such that each block of the trade contains one of three fixed elements. We show that the fundamental building blocks for such trades are 3-regular graphs that are 1-factorisable. In the process we also generate all possible 2- and 3-way simultaneous edge colourings of graphs with maximum degree 3 using at most 3 colours, where multiple edges but not loops are allowed. Moreover, we generate all possible Latin trades within three rows.

text: Subcubic trades in Steiner triple systems We consider the problem of classifying trades in Steiner triple systems such that each block of the trade contains one of three fixed elements. We show that the fundamental building blocks for such trades are 3-regular graphs that are 1-factorisable. In the process we also generate all possible 2- and 3-way simultaneous edge colourings of graphs with maximum degree 3 using at most 3 colours, where multiple edges but not loops are allowed. Moreover, we generate all possible Latin trades within three rows.

year: 2017

title: Reimagining community resilience through a Te Ao Maori worldview

authors: Boston, Megan

abstract: Efforts to improve community resilience have seen universal efforts to grow capabilities in disaster management for the built environment. Although comprehensive frameworks exist, the perspective used to derive these frameworks fails to address marginalised communities' vulnerabilities, including Indigenous Māori people. Colonization and socio-economic deprivation on Māori mean community response frameworks fail to reflect their values and specific needs when preparing and responding to natural disasters. The nature of Māori culture and values presents an opportunity to reimagine the scope of community resilience for an inclusive framework. The Māori history has resilient practices weaved into the very fabric of their culture, which knowledge has survived through the oral transmission of waiata, whakataukī, whakairo, and pūrakau. The practice of community resilience amongst ancient Māori was not consigned to singular events but instead is a holistic perspective to the manner of living. Sourcing and qualifying this information from people aligned and immersed in nature is the knowledge required to improve the frameworks to respond to natural disasters while expanding the literature on community resilience. A comprehensive analysis of traditional Māori resilience is conducted by evaluating a variety of Mātauranga Māori that relate to the resilient nature of Māori. This information is compared to modern Māori perceptions of community resilience using a derived earthquake scenario for the local Iwi Ngati Toa, located in the city of Porirua within the Wellington region. This information will enable a comprehensive definition of community resilience and improve disaster response frameworks to be more inclusive, safe, sustainable, and resilient.

text: Reimagining community resilience through a Te Ao Maori worldview Efforts to improve community resilience have seen universal efforts to grow capabilities in disaster management for the built environment. Although comprehensive frameworks exist, the perspective used to derive these frameworks fails to address marginalised communities' vulnerabilities, including Indigenous Māori people. Colonization and socio-economic deprivation on Māori mean community response frameworks fail to reflect their values and specific needs when preparing and responding to natural disasters. The nature of Māori culture and values presents an opportunity to reimagine the scope of community resilience for an inclusive framework. The Māori history has resilient practices weaved into the very fabric of their culture, which knowledge has survived through the oral transmission of waiata, whakataukī, whakairo, and pūrakau. The practice of community resilience amongst ancient Māori was not consigned to singular events but instead is a holistic perspective to the manner of living. Sourcing and qualifying this information from people aligned and immersed in nature is the knowledge required to improve the frameworks to respond to natural disasters while expanding the literature on community resilience. A comprehensive analysis of traditional Māori resilience is conducted by evaluating a variety of Mātauranga Māori that relate to the resilient nature of Māori. This information is compared to modern Māori perceptions of community resilience using a derived earthquake scenario for the local Iwi Ngati Toa, located in the city of Porirua within the Wellington region. This information will enable a comprehensive definition of community resilience and improve disaster response frameworks to be more inclusive, safe, sustainable, and resilient.

year: 2023