title: Visco-resistive shear wave dissipation in magnetic X-points

authors: Fruit, G.

subjects: magnetic fields

abstract: We consider the viscous and resistive dissipation of perpendicularly polarized shear waves propagating within a planar magnetic X-point. To highlight the role played by the two-dimensional geometry, the damping of travelling Alfvèn waves that propagate within an unbounded, but non-orthogonal X-point topology is analyzed. It is shown that the separatrix geometry affects both the dissipation time and the visco-resistive scaling of the energy decay. Our main focus, however, is on developing a theoretical description of standing wave dissipation for orthogonal, line-tied X-points. A combination of numerical and analytic treatments confirms that phase mixing provides a very effective mechanism for dissipating the wave energy. We show that wave decay comprises two main phases, an initial rapid decay followed by slower eigenmode evolution, both of which are only weakly dependent on the visco-resistive damping coefficients.

text: Visco-resistive shear wave dissipation in magnetic X-points We consider the viscous and resistive dissipation of perpendicularly polarized shear waves propagating within a planar magnetic X-point. To highlight the role played by the two-dimensional geometry, the damping of travelling Alfvèn waves that propagate within an unbounded, but non-orthogonal X-point topology is analyzed. It is shown that the separatrix geometry affects both the dissipation time and the visco-resistive scaling of the energy decay. Our main focus, however, is on developing a theoretical description of standing wave dissipation for orthogonal, line-tied X-points. A combination of numerical and analytic treatments confirms that phase mixing provides a very effective mechanism for dissipating the wave energy. We show that wave decay comprises two main phases, an initial rapid decay followed by slower eigenmode evolution, both of which are only weakly dependent on the visco-resistive damping coefficients.

year: 2006

title: Making mathematics meaningful: Using student-initiated problems to situate mathematics

authors: Brough, Chris Jane

abstract: Mathematics is everywhere-from the minute we open our eyes to check the alarm clock and calculate how many minutes extra we can afford to lie in bed, to measuring out our cereal for breakfast and estimating if we have enough petrol to make the 18 kilometre journey to work. As teachers of mathematics. we must ask ourselves if the way we teach reflects the real-life problem-solving situations our students will experience within their everyday world.

text: Making mathematics meaningful: Using student-initiated problems to situate mathematics Mathematics is everywhere-from the minute we open our eyes to check the alarm clock and calculate how many minutes extra we can afford to lie in bed, to measuring out our cereal for breakfast and estimating if we have enough petrol to make the 18 kilometre journey to work. As teachers of mathematics. we must ask ourselves if the way we teach reflects the real-life problem-solving situations our students will experience within their everyday world.

year: 2014

title: Te Pai Tawhiti: Exploring the Horizons of Maori Economic Performance through Effective Collaboration

authors: Joseph, Robert

abstract: Effective collaboration, good governance and active management provide a potential platform for enhanced economic performance for Ngāti Pikiao, in line with its self-determination aspirations to
work better as a collective of entities on behalf of iwi members.

Literature and case study data analyses show a pathway forward for Ngāti Pikiao in the form of 9 key principles for working towards a foundation for effective collaborative action that enhances economic
performance.

text: Te Pai Tawhiti: Exploring the Horizons of Maori Economic Performance through Effective Collaboration Effective collaboration, good governance and active management provide a potential platform for enhanced economic performance for Ngāti Pikiao, in line with its self-determination aspirations to
work better as a collective of entities on behalf of iwi members.

Literature and case study data analyses show a pathway forward for Ngāti Pikiao in the form of 9 key principles for working towards a foundation for effective collaborative action that enhances economic
performance.

year: 2016