title: Dynamic magnetic reconnection at an X-type neutral point

authors: Craig, Ian J.D.

abstract: The relaxation of a two-dimensional "X-type" neutral point magnetic field disturbed from equilibrium is considered. Perturbations are shown to possess well-defined azimuthal modes which allow an exact determination of the magnetic annihilation rate. Free magnetic energy is dissipated by oscillatory reconnection which couples resistive diffusion at the neutral point to global advection of the outer field. The decay of azimuthally symmetric (m = 0) modes - the only modes associated with topological reconnection - is limited by the dissipation time scale of the "fundamental" (n = 0) mode with no radial nodes. This mode decays over typically 100 Alfvén times. An analytic treatment shows that the oscillation and decay time scales couple according to τosc ≈ 2 ln S and τdecay ≈ τosc 2/(2π2), where S is the Lundquist number (4π/c2)υA R/η and the times are in units of R/υA, with R the distance from the neutral point to the boundary, υA the Alfvén speed at the boundary, and η the resistivity.

text: Dynamic magnetic reconnection at an X-type neutral point The relaxation of a two-dimensional "X-type" neutral point magnetic field disturbed from equilibrium is considered. Perturbations are shown to possess well-defined azimuthal modes which allow an exact determination of the magnetic annihilation rate. Free magnetic energy is dissipated by oscillatory reconnection which couples resistive diffusion at the neutral point to global advection of the outer field. The decay of azimuthally symmetric (m = 0) modes - the only modes associated with topological reconnection - is limited by the dissipation time scale of the "fundamental" (n = 0) mode with no radial nodes. This mode decays over typically 100 Alfvén times. An analytic treatment shows that the oscillation and decay time scales couple according to τosc ≈ 2 ln S and τdecay ≈ τosc 2/(2π2), where S is the Lundquist number (4π/c2)υA R/η and the times are in units of R/υA, with R the distance from the neutral point to the boundary, υA the Alfvén speed at the boundary, and η the resistivity.

year: 1991

title: Mixed mutually orthogonal frequency squares

authors: Poulose, Jilmy

abstract: A frequency square of type F(n; λ1, λ2, λ3, . . . , λt) is an array n × n filled with symbols ai, where each ai occurs λi times in every row and column, and n = Pt i=1 λi.
Two such frequency squares F1(n; λ1, λ2, λ3, . . . , λt) and F2(n; µ1, µ2, µ3, . . . , µs) are mutually orthogonal, when superimposed, each of the ts possible ordered pairs (i, j), where 1 ≤ i ≤ t and 1 ≤ j ≤ s, occurs exactly λiµj times.
This thesis generalizes the classical theory of mutually orthogonal Latin squares to mixed frequency settings, where symbols may appear with different frequencies. The non-uniform frequencies lead to a wider range of combinatorial structures with new methods of construction. Then, the thesis investigates maximizing the set of mixed mutually orthogonal frequency squares (MMOFS), focusing on theoretical methods rather than computational tools.
The following lemmas and theorems are new results presented in Chapter 3. In Lemma 4.1, we define mappings from two Latin squares to form two MOFS. Then in Theorem 4.7, we apply this to explore the maximum size of the sets of higher-order MMOFS by using mixed orthogonal arrays. Moreover, Section 2.2 gives an original alternative proof of an existing upper bound for sets of MOFS. Furthermore, we identify sets of MMOFS for small orders in the final chapter by using the new results and the previous theories. These new results include Corollary 4.5, Lemma 5.1, Example 22, Corollary 5.6 and Example 24.

text: Mixed mutually orthogonal frequency squares A frequency square of type F(n; λ1, λ2, λ3, . . . , λt) is an array n × n filled with symbols ai, where each ai occurs λi times in every row and column, and n = Pt i=1 λi.
Two such frequency squares F1(n; λ1, λ2, λ3, . . . , λt) and F2(n; µ1, µ2, µ3, . . . , µs) are mutually orthogonal, when superimposed, each of the ts possible ordered pairs (i, j), where 1 ≤ i ≤ t and 1 ≤ j ≤ s, occurs exactly λiµj times.
This thesis generalizes the classical theory of mutually orthogonal Latin squares to mixed frequency settings, where symbols may appear with different frequencies. The non-uniform frequencies lead to a wider range of combinatorial structures with new methods of construction. Then, the thesis investigates maximizing the set of mixed mutually orthogonal frequency squares (MMOFS), focusing on theoretical methods rather than computational tools.
The following lemmas and theorems are new results presented in Chapter 3. In Lemma 4.1, we define mappings from two Latin squares to form two MOFS. Then in Theorem 4.7, we apply this to explore the maximum size of the sets of higher-order MMOFS by using mixed orthogonal arrays. Moreover, Section 2.2 gives an original alternative proof of an existing upper bound for sets of MOFS. Furthermore, we identify sets of MMOFS for small orders in the final chapter by using the new results and the previous theories. These new results include Corollary 4.5, Lemma 5.1, Example 22, Corollary 5.6 and Example 24.

year: 2025

title: Developing culturally responsive psychology curriculum in Aotearoa New Zealand

authors: Wairoa-Harrison, Sophia

abstract: There are some significant wins in the development of a culturally competent undergraduate psychology curriculum in Aotearoa New Zealand. These include how Mātauranga Māori is incorporated into research methodology papers, neuroimaging papers, and degree offerings. However, the number of specifically Māori-focused papers has halved since 2007. Further research is needed to gauge students' experiences of the quality of cultural competency in these papers.

text: Developing culturally responsive psychology curriculum in Aotearoa New Zealand There are some significant wins in the development of a culturally competent undergraduate psychology curriculum in Aotearoa New Zealand. These include how Mātauranga Māori is incorporated into research methodology papers, neuroimaging papers, and degree offerings. However, the number of specifically Māori-focused papers has halved since 2007. Further research is needed to gauge students' experiences of the quality of cultural competency in these papers.

year: 2023-02-01