title: Linear theory of fast reconnection at an X-type neutral point

authors: Craig, Ian J.D.

abstract: A linear theory is developed for the dissipation of the free magnetic energy in small disturbances imposed on the potential field of an X-type neutral point. An eigenmode analysis, using cylindrical coordinates centered on the neutral point, extends the work of Craig & McClymont (1991) to include non-azimuthally symmetric perturbations on the flux function. We demonstrate that all physically significant disturbances, both reconnective and nonreconnective, decay resistively on a "fast" time scale ∼|ln η|, where η is the nondimensional resistivity. Thus resistive diffusion is remarkably effective as a dissipation mechanism for all classes of perturbation not only those modes which induce changes in the field topology. The fundamental reason for the fast dissipation is the focusing of wave energy onto the neutral point by the gradient in Alfvén speed. This occurs for all types of disturbances launched from the outer boundary, but reconnective modes propagate purely radially while nonreconnective modes correspond to waves with an azimuthal motion and a smaller wave speed in the radial direction. Dissipation of reconnective disturbances takes place in a diffusion region of diameter ≈η1/2 around the neutral point, on a time scale ∝ |ln η|2, but nonreconnective perturbations decay before penetrating to the neutral point, because of the increased path lengths due to their azimuthal motion. These modes release their energy in an annulus of radius ≈[(m3/ 4k)η]1/2, where m and k are azimuthal and radial wavenumbers: because of their longer transit time, nonreconnective waves decay on a |ln η|3 time scale. We conclude by discussing the significance of the linear theory within the general context of steady state and dynamic reconnection studies. It is pointed out that, dynamically, disturbances can be expected to focus explosively in the vicinity of the neutral point. This suggests the formation of a "flux pile-up" current layer in which the bulk of the magnetic energy is released as heat rather than kinetic energy of mass motion.

text: Linear theory of fast reconnection at an X-type neutral point A linear theory is developed for the dissipation of the free magnetic energy in small disturbances imposed on the potential field of an X-type neutral point. An eigenmode analysis, using cylindrical coordinates centered on the neutral point, extends the work of Craig & McClymont (1991) to include non-azimuthally symmetric perturbations on the flux function. We demonstrate that all physically significant disturbances, both reconnective and nonreconnective, decay resistively on a "fast" time scale ∼|ln η|, where η is the nondimensional resistivity. Thus resistive diffusion is remarkably effective as a dissipation mechanism for all classes of perturbation not only those modes which induce changes in the field topology. The fundamental reason for the fast dissipation is the focusing of wave energy onto the neutral point by the gradient in Alfvén speed. This occurs for all types of disturbances launched from the outer boundary, but reconnective modes propagate purely radially while nonreconnective modes correspond to waves with an azimuthal motion and a smaller wave speed in the radial direction. Dissipation of reconnective disturbances takes place in a diffusion region of diameter ≈η1/2 around the neutral point, on a time scale ∝ |ln η|2, but nonreconnective perturbations decay before penetrating to the neutral point, because of the increased path lengths due to their azimuthal motion. These modes release their energy in an annulus of radius ≈[(m3/ 4k)η]1/2, where m and k are azimuthal and radial wavenumbers: because of their longer transit time, nonreconnective waves decay on a |ln η|3 time scale. We conclude by discussing the significance of the linear theory within the general context of steady state and dynamic reconnection studies. It is pointed out that, dynamically, disturbances can be expected to focus explosively in the vicinity of the neutral point. This suggests the formation of a "flux pile-up" current layer in which the bulk of the magnetic energy is released as heat rather than kinetic energy of mass motion.

year: 1993

title: Construction of Good Rank-1 Lattice Rules Based on the Weighted Star Discrepancy

authors: Joe, Stephen

subjects: mathematics

abstract: The ‘goodness’ of a set of quadrature points in [0, 1]d may be measured by the weighted star discrepancy. If the weights for the weighted star discrepancy are summable, then we show that for n prime there exist n-point rank-1 lattice rules whose weighted star discrepancy is O(n−1+δ) for any δ>0, where the implied constant depends on δ and the weights, but is independent of d and n. Further, we show that the generating vector z for such lattice rules may be obtained using a component-by-component construction. The results given here for the weighted star discrepancy are used to derive corresponding results for a weighted Lp discrepancy.

text: Construction of Good Rank-1 Lattice Rules Based on the Weighted Star Discrepancy The ‘goodness’ of a set of quadrature points in [0, 1]d may be measured by the weighted star discrepancy. If the weights for the weighted star discrepancy are summable, then we show that for n prime there exist n-point rank-1 lattice rules whose weighted star discrepancy is O(n−1+δ) for any δ>0, where the implied constant depends on δ and the weights, but is independent of d and n. Further, we show that the generating vector z for such lattice rules may be obtained using a component-by-component construction. The results given here for the weighted star discrepancy are used to derive corresponding results for a weighted Lp discrepancy.

year: 2006

title: Mahi Toi Skills in Contemporary Education, Training and Maori Development

authors: Joseph, Makarita Ngapine Tangitu

subjects: Kia mau ki nga taonga tuku iho o nga tupuna

abstract: Since the 1980’s, national investment in human capital and skill formation policy in education has been promoted as key to economic success and social inclusion. Social inclusion, however, is often expressed as helping citizens to become employable. Although employability is a key focus of skills formation and education policy, the context of the western ideologies that it derives from and caters to perpetuates the exclusion of mahi toi (arts and crafts) skills in education. Using a kaupapa Māori approach, two key informants who specialise and teach mahi toi skills, either rāranga (weaving) or pounamu (jade/greenstone), were interviewed. The aim was to get a better understanding of how these skills can contribute to personal, professional and Māori development in the 21st century, and to provide information indicating where and how these skills can be learnt, either through private training enterprises (PTE) or public tertiary educational institutions (TEI), thereby highlighting the value of teaching and learning rāranga and pounamu skills. Findings from analysing their pūrākau indicate that learning rāranga or pounamu skills can provide a foundation for believing in your potential, contribute to cultural identity, improve confidence and communication skills, help an individual be bestowed or acquire mana, offer a type of therapy, enhance career progression and professional identity, provide financial rewards and stability, and help with the revitalisation and transfer of cultural knowledge. Ultimately, it is concluded that mahi toi skills such as rāranga and pounamu can contribute to the development of an individual’s personal and professional lives, but also has benefits for the organisation where they become employed as well as extended whānau, hapū and iwi.

text: Mahi Toi Skills in Contemporary Education, Training and Maori Development Since the 1980’s, national investment in human capital and skill formation policy in education has been promoted as key to economic success and social inclusion. Social inclusion, however, is often expressed as helping citizens to become employable. Although employability is a key focus of skills formation and education policy, the context of the western ideologies that it derives from and caters to perpetuates the exclusion of mahi toi (arts and crafts) skills in education. Using a kaupapa Māori approach, two key informants who specialise and teach mahi toi skills, either rāranga (weaving) or pounamu (jade/greenstone), were interviewed. The aim was to get a better understanding of how these skills can contribute to personal, professional and Māori development in the 21st century, and to provide information indicating where and how these skills can be learnt, either through private training enterprises (PTE) or public tertiary educational institutions (TEI), thereby highlighting the value of teaching and learning rāranga and pounamu skills. Findings from analysing their pūrākau indicate that learning rāranga or pounamu skills can provide a foundation for believing in your potential, contribute to cultural identity, improve confidence and communication skills, help an individual be bestowed or acquire mana, offer a type of therapy, enhance career progression and professional identity, provide financial rewards and stability, and help with the revitalisation and transfer of cultural knowledge. Ultimately, it is concluded that mahi toi skills such as rāranga and pounamu can contribute to the development of an individual’s personal and professional lives, but also has benefits for the organisation where they become employed as well as extended whānau, hapū and iwi.

year: 2018