title: Finite-time singularity formation at a magnetic neutral line in Hall magnetohydrodynamics

authors: Litvinenko, Yuri E.

subjects: Finite-time singularities

abstract: The formation of a current sheet in a weakly collisional plasma can be modelled as a finite-time singularity solution of magnetohydrodynamic equations. We use an exact self-similar solution to confirm and generalise a previous finding that, in sharp contrast to two-dimensional solutions in standard MHD, a finite-time collapse to a current sheet can occur in Hall MHD. We derive a criterion for the finite-time singularity in terms of initial conditions, and we use an intermediate asymptotic solution for the evolution of an axial magnetic field to obtain a general expression for the singularity formation time. We illustrate the analytical results by numerical solutions.

text: Finite-time singularity formation at a magnetic neutral line in Hall magnetohydrodynamics The formation of a current sheet in a weakly collisional plasma can be modelled as a finite-time singularity solution of magnetohydrodynamic equations. We use an exact self-similar solution to confirm and generalise a previous finding that, in sharp contrast to two-dimensional solutions in standard MHD, a finite-time collapse to a current sheet can occur in Hall MHD. We derive a criterion for the finite-time singularity in terms of initial conditions, and we use an intermediate asymptotic solution for the evolution of an axial magnetic field to obtain a general expression for the singularity formation time. We illustrate the analytical results by numerical solutions.

year: 2015

title: Unifying state and process determinism

authors: Reeves, Steve

subjects: computer science

abstract: If a coin is given to a deterministic robot that interacts with a deterministic vending machine then is the drink that the robot is delivered determined? Using process definitions of determinism from CSP, CCS or ACP the answer is "no", whereas state-based definitions of determinism can reasonably be construed as giving the answer "yes". In order to unify what we see as discrepancies in state- and action-based notions of determinism we will consider process algebras over two sets of actions: the active or casual actions of the robot and the passive or reactive actions of the vending machine. In addition we will add priority to the actions and when two τ actions are possible then the τ action with the highest priority will be executed.

text: Unifying state and process determinism If a coin is given to a deterministic robot that interacts with a deterministic vending machine then is the drink that the robot is delivered determined? Using process definitions of determinism from CSP, CCS or ACP the answer is "no", whereas state-based definitions of determinism can reasonably be construed as giving the answer "yes". In order to unify what we see as discrepancies in state- and action-based notions of determinism we will consider process algebras over two sets of actions: the active or casual actions of the robot and the passive or reactive actions of the vending machine. In addition we will add priority to the actions and when two τ actions are possible then the τ action with the highest priority will be executed.

year: 2004-02

title: Whakarongo mai!: Transformative teaching to support Māori identity and success in a mainstream school

authors: Gilgen, Renée

subjects: Māori and mainstream education

abstract: This thesis topic emerged following a year’s teaching experience in a mainstream classroom during 2009. My cultural assumptions of being a Māori teacher in a mainstream class were challenged predominantly by a group of Māori students in the classroom. The level of despondency I felt as a result of disruptive student behaviours forced me to reassess my own socio-cultural constructs which had influenced the formation of my identity as Māori and as a mainstream teacher. The purpose of this study was to understand and explore a transformational behavioural shift which occurred within a group of Māori students during 2009 and the level of support they felt they received as Māori within a mainstream classroom context. National and international literature demonstrates that transformative praxis is both reflective and active. Successful inclusive teaching requires a personal and professional commitment to firstly understand individual cultural constructs to then better understand how learners are perceived and positioned. Culturally responsive pedagogy ensures that all students’ cultural practices and values are acknowledged and included into classroom teaching and learning programmes. In a New Zealand mainstream context, the Treaty of Waitangi principles of ‘partnership’, ‘participation’ and ‘protection’ serve as a bi-cultural ‘power-sharing’ metaphor from which all mainstream teachers of Māori students can successfully encourage student voice and foster reciprocal teaching and learning relationships. My use of qualitative research methods and kaupapa Māori principles to guide the research process ensured that Māori cultural protocols and practices were honoured. My role as a Māori insider researcher meant that my relationship with the participants was already established. Our reflections as Māori students and a Māori teacher in a mainstream classroom context were based from shared teaching and learning experiences during 2009. Researcher reflexivity has ensured that the research integrity, validity and reliability have remained high. The research findings present the reflections of both the participants and researcher as Māori students and as a Māori teacher during 2009. Participants believed that teaching and learning programmes which incorporated te reo Māori served to honour their identity as Māori. However, their awareness of participating with tikanga Māori principles of whānaungatanga (relationships), manaakitanga (caring), ako (reciprocity) and aroha (respect) embedded within classroom activities that were exclusively in English, were not identified as being relevant to them as Māori. Similarly, the Treaty of Waitangi principles lacked transparency within my teaching pedagogy. Two key implications for teaching and learning in mainstream schools and classrooms were identified. Firstly, there is an urgency for mainstream school managers, leaders and teachers to develop an understanding of the Treaty of Waitangi and its significance for the 21st Century mainstream teacher and learner. A bi-cultural understanding of ourselves as treaty partners support Māori cultural values and practices within increasingly diverse mainstream school and classroom contexts. Māori students‟ success becomes the responsibility of all mainstream managers, leaders and teachers as treaty partners. Secondly, inclusive and culturally responsive pedagogy demonstrates that Māori and non-Māori mainstream teachers are capable of effectively engaging Māori students with learning while acknowledging and reaffirming their cultural identity and language as tangata whenua. Overall, my commitment for Māori students to be supported as Māori within mainstream school and classroom context has been enriched and strengthened as a result of this research study. The cultural and professional tensions I have experienced in mainstream contexts have challenged the socio-cultural constructs that I had accepted as being my cultural ‘norm.’

text: Whakarongo mai!: Transformative teaching to support Māori identity and success in a mainstream school This thesis topic emerged following a year’s teaching experience in a mainstream classroom during 2009. My cultural assumptions of being a Māori teacher in a mainstream class were challenged predominantly by a group of Māori students in the classroom. The level of despondency I felt as a result of disruptive student behaviours forced me to reassess my own socio-cultural constructs which had influenced the formation of my identity as Māori and as a mainstream teacher. The purpose of this study was to understand and explore a transformational behavioural shift which occurred within a group of Māori students during 2009 and the level of support they felt they received as Māori within a mainstream classroom context. National and international literature demonstrates that transformative praxis is both reflective and active. Successful inclusive teaching requires a personal and professional commitment to firstly understand individual cultural constructs to then better understand how learners are perceived and positioned. Culturally responsive pedagogy ensures that all students’ cultural practices and values are acknowledged and included into classroom teaching and learning programmes. In a New Zealand mainstream context, the Treaty of Waitangi principles of ‘partnership’, ‘participation’ and ‘protection’ serve as a bi-cultural ‘power-sharing’ metaphor from which all mainstream teachers of Māori students can successfully encourage student voice and foster reciprocal teaching and learning relationships. My use of qualitative research methods and kaupapa Māori principles to guide the research process ensured that Māori cultural protocols and practices were honoured. My role as a Māori insider researcher meant that my relationship with the participants was already established. Our reflections as Māori students and a Māori teacher in a mainstream classroom context were based from shared teaching and learning experiences during 2009. Researcher reflexivity has ensured that the research integrity, validity and reliability have remained high. The research findings present the reflections of both the participants and researcher as Māori students and as a Māori teacher during 2009. Participants believed that teaching and learning programmes which incorporated te reo Māori served to honour their identity as Māori. However, their awareness of participating with tikanga Māori principles of whānaungatanga (relationships), manaakitanga (caring), ako (reciprocity) and aroha (respect) embedded within classroom activities that were exclusively in English, were not identified as being relevant to them as Māori. Similarly, the Treaty of Waitangi principles lacked transparency within my teaching pedagogy. Two key implications for teaching and learning in mainstream schools and classrooms were identified. Firstly, there is an urgency for mainstream school managers, leaders and teachers to develop an understanding of the Treaty of Waitangi and its significance for the 21st Century mainstream teacher and learner. A bi-cultural understanding of ourselves as treaty partners support Māori cultural values and practices within increasingly diverse mainstream school and classroom contexts. Māori students‟ success becomes the responsibility of all mainstream managers, leaders and teachers as treaty partners. Secondly, inclusive and culturally responsive pedagogy demonstrates that Māori and non-Māori mainstream teachers are capable of effectively engaging Māori students with learning while acknowledging and reaffirming their cultural identity and language as tangata whenua. Overall, my commitment for Māori students to be supported as Māori within mainstream school and classroom context has been enriched and strengthened as a result of this research study. The cultural and professional tensions I have experienced in mainstream contexts have challenged the socio-cultural constructs that I had accepted as being my cultural ‘norm.’

year: 2010