title: The Electrical Properties of Interfacial Double Layers

authors: Jones, Mark Hedley

subjects: Electrode modelling

abstract: When solids and liquids are brought together, interfacial double-layers are likely to form. They are too small to feel or see so their presence goes mostly unnoticed at the macroscopic level. A double layer is essentially a cluster of ions and/or charged molecules which are drawn from the body of a liquid to the surface of a solid. They are responsible for stabilising some of our most important fluids -- blood, milk, paints, and inks. Without the protection of double-layers, these mixtures clump and lose their fluidity.

This thesis examines both electricity generation from, and the electrical impedance of, interfacial double layers.  
Interfacial double-layers represent the underlying theme of this work, which is broken into two parts. In part I, double layers are used as a means of converting fluid-mechanical energy into electrical energy. My application for this is an energy harvester that could power electronic water meters. Domestic water meters are typically installed where electrical connection is not feasible. Harvesting energy at the meter may make electronic metering a feasible long-term solution. My findings show that double layer based energy harvesters are not efficient enough for this application yet. However, recent literature on the subject suggests large gains in efficiency may be possible using more exotic materials. Such gains would allow a compact harvester to generate enough energy to operate an electronic meter with wireless transmitter.

Part II models the electrical impedance of electrodes submerged in electrolytes. Double-layers contribute to the electrical impedance between solid-fluid interfaces. This work is important to designers of medical implants. Engineers use solutions of saline to mimic the environment experienced by their implants once implanted. This provides a way to test implant electronics without putting a patient at risk. A way of characterising the interface between electrodes and an electrolyte is to model it mathematically. An electrical model of an electrode-electrolyte interface was recently developed by my supervisor, Jonathan Scott. I use that model to compare electrodes placed in solutions of saline to those placed in a living animal. Measurements of the two show that no one concentration of saline matches the situation inside a live spinal cavity. I then create a low-cost electrolyte test solution that better matches the impedance measured in a living animal's spinal cavity.

text: The Electrical Properties of Interfacial Double Layers When solids and liquids are brought together, interfacial double-layers are likely to form. They are too small to feel or see so their presence goes mostly unnoticed at the macroscopic level. A double layer is essentially a cluster of ions and/or charged molecules which are drawn from the body of a liquid to the surface of a solid. They are responsible for stabilising some of our most important fluids -- blood, milk, paints, and inks. Without the protection of double-layers, these mixtures clump and lose their fluidity.

This thesis examines both electricity generation from, and the electrical impedance of, interfacial double layers.  
Interfacial double-layers represent the underlying theme of this work, which is broken into two parts. In part I, double layers are used as a means of converting fluid-mechanical energy into electrical energy. My application for this is an energy harvester that could power electronic water meters. Domestic water meters are typically installed where electrical connection is not feasible. Harvesting energy at the meter may make electronic metering a feasible long-term solution. My findings show that double layer based energy harvesters are not efficient enough for this application yet. However, recent literature on the subject suggests large gains in efficiency may be possible using more exotic materials. Such gains would allow a compact harvester to generate enough energy to operate an electronic meter with wireless transmitter.

Part II models the electrical impedance of electrodes submerged in electrolytes. Double-layers contribute to the electrical impedance between solid-fluid interfaces. This work is important to designers of medical implants. Engineers use solutions of saline to mimic the environment experienced by their implants once implanted. This provides a way to test implant electronics without putting a patient at risk. A way of characterising the interface between electrodes and an electrolyte is to model it mathematically. An electrical model of an electrode-electrolyte interface was recently developed by my supervisor, Jonathan Scott. I use that model to compare electrodes placed in solutions of saline to those placed in a living animal. Measurements of the two show that no one concentration of saline matches the situation inside a live spinal cavity. I then create a low-cost electrolyte test solution that better matches the impedance measured in a living animal's spinal cavity.

year: 2016

title: Contractions of 2D 2nd order quantum superintegrable systems and the Askey scheme for hypergeometric orthogonal polynomials

authors: Kalnins, Ernie G.

subjects: Askey scheme

abstract: We show explicitly that all 2nd order superintegrable systems in 2 dimensions are limiting cases of a single system: the generic 3-parameter potential on the 2-sphere, S9 in our listing. We extend the Wigner-Inönü method of Lie algebra contractions to contractions of quadratic algebras and show that all of the quadratic symmetry algebras of these systems are contractions of that of S9. Amazingly, all of the relevant contractions of these superintegrable systems on flat space and the sphere are uniquely induced by the well known Lie algebra contractions of e(2) and so(3). By contracting function space realizations of irreducible representations of the S9 algebra (which give the structure equations for Racah/Wilson polynomials) to the other superintegrable systems, and using Wigner's idea of ''saving'' a representation, we obtain the full Askey scheme of hypergeometric orthogonal polynomials. This relationship directly ties the polynomials and their structure equations to physical phenomena. It is more general because it applies to all special functions that arise from these systems via separation of variables, not just those of hypergeometric type, and it extends to higher dimensions.

text: Contractions of 2D 2nd order quantum superintegrable systems and the Askey scheme for hypergeometric orthogonal polynomials We show explicitly that all 2nd order superintegrable systems in 2 dimensions are limiting cases of a single system: the generic 3-parameter potential on the 2-sphere, S9 in our listing. We extend the Wigner-Inönü method of Lie algebra contractions to contractions of quadratic algebras and show that all of the quadratic symmetry algebras of these systems are contractions of that of S9. Amazingly, all of the relevant contractions of these superintegrable systems on flat space and the sphere are uniquely induced by the well known Lie algebra contractions of e(2) and so(3). By contracting function space realizations of irreducible representations of the S9 algebra (which give the structure equations for Racah/Wilson polynomials) to the other superintegrable systems, and using Wigner's idea of ''saving'' a representation, we obtain the full Askey scheme of hypergeometric orthogonal polynomials. This relationship directly ties the polynomials and their structure equations to physical phenomena. It is more general because it applies to all special functions that arise from these systems via separation of variables, not just those of hypergeometric type, and it extends to higher dimensions.

year: 2013

title: Youth Development Circles: A Report on a School Trial

authors: Hannah, Belinda Anne

subjects: Youth Development Circles

abstract: This research traces the development and trial of the Youth Development Circle (YDC) process in a low decile secondary school in a rural community in Aotearoa New Zealand. Youth Development Circles are an intervention based on restorative justice principles initially proposed by Braithwaite (2004). They were originally suggested as a strategy for use in an alternative education centre or “activity centre”.  Increasing use of restorative approaches has enabled many schools to make significant progress in reducing suspensions, but there remains a concern for students whose behaviour is at the more serious end of the spectrum - who are at risk of suspension, or exclusion, after multiple stand-downs from school.  The possibilities for the use of YDC were proposed to the school by the researcher, who is a Deputy Principal responsible for behaviour management and pastoral care.  This proposal was supported fully by the school’s staff and Board of Trustees.  The YDC process documented in this study was developed by the researcher, informed by a range of sources including Youth Development Circles, Judge McElrea’s proposed School Community Conference (1996), and Hui Whakatika, developed at the University of Waikato (2003).  Participation in the circles was a condition for the student to remain at the school. The school is a state school, with a roll of approximately 800. The ethnic breakdown of the students is 56% Māori and 39% NZ European with 5% of Pasifika, Asian and other.  

The YDC is a deliberate and careful process which aims to bring increased focus on the individual student and their educational outcomes, through engaging a community of care in supporting them. There were many anticipated benefits of the YDC for the student. Such benefits included an opportunity to establish and maintain healthy relationships of trust (within which negative experiences can be learned from), a re-establishment of trust, improved self-confidence and improved educational outcomes. The circles included members of the student’s whānau/family, a kaumātua/elder who cared about them, and representatives from local Police, Social Welfare, and the school.  The circles were studied over a period of one year.  Circles met regularly throughout this time, at increasing intervals.

A mixed method case study approach was used for this research which includes the collection of both quantitative and qualitative data. The study evaluated the effectiveness of the YDCs by analysing student behaviour, attendance and achievement KAMAR data, minutes of each circle meeting, and interviews with circle participants.


Three student case studies are presented.  The stories have had details altered and pseudonyms used to protect the persons involved. All the students completed the academic year without receiving a further stand down or suspension.  The data showed an improvement in student attendance, achievement and engagement in all three case studies.  Other outcomes include reflections on the process used, strategies for implementation in the school, and factors that either hindered or supported student, family or community involvement in YDCs. 

This exploratory study suggests that the Youth Development Circle could offer a unique possibility for inter-sectorial collaboration in the field of restorative justice.

text: Youth Development Circles: A Report on a School Trial This research traces the development and trial of the Youth Development Circle (YDC) process in a low decile secondary school in a rural community in Aotearoa New Zealand. Youth Development Circles are an intervention based on restorative justice principles initially proposed by Braithwaite (2004). They were originally suggested as a strategy for use in an alternative education centre or “activity centre”.  Increasing use of restorative approaches has enabled many schools to make significant progress in reducing suspensions, but there remains a concern for students whose behaviour is at the more serious end of the spectrum - who are at risk of suspension, or exclusion, after multiple stand-downs from school.  The possibilities for the use of YDC were proposed to the school by the researcher, who is a Deputy Principal responsible for behaviour management and pastoral care.  This proposal was supported fully by the school’s staff and Board of Trustees.  The YDC process documented in this study was developed by the researcher, informed by a range of sources including Youth Development Circles, Judge McElrea’s proposed School Community Conference (1996), and Hui Whakatika, developed at the University of Waikato (2003).  Participation in the circles was a condition for the student to remain at the school. The school is a state school, with a roll of approximately 800. The ethnic breakdown of the students is 56% Māori and 39% NZ European with 5% of Pasifika, Asian and other.  

The YDC is a deliberate and careful process which aims to bring increased focus on the individual student and their educational outcomes, through engaging a community of care in supporting them. There were many anticipated benefits of the YDC for the student. Such benefits included an opportunity to establish and maintain healthy relationships of trust (within which negative experiences can be learned from), a re-establishment of trust, improved self-confidence and improved educational outcomes. The circles included members of the student’s whānau/family, a kaumātua/elder who cared about them, and representatives from local Police, Social Welfare, and the school.  The circles were studied over a period of one year.  Circles met regularly throughout this time, at increasing intervals.

A mixed method case study approach was used for this research which includes the collection of both quantitative and qualitative data. The study evaluated the effectiveness of the YDCs by analysing student behaviour, attendance and achievement KAMAR data, minutes of each circle meeting, and interviews with circle participants.


Three student case studies are presented.  The stories have had details altered and pseudonyms used to protect the persons involved. All the students completed the academic year without receiving a further stand down or suspension.  The data showed an improvement in student attendance, achievement and engagement in all three case studies.  Other outcomes include reflections on the process used, strategies for implementation in the school, and factors that either hindered or supported student, family or community involvement in YDCs. 

This exploratory study suggests that the Youth Development Circle could offer a unique possibility for inter-sectorial collaboration in the field of restorative justice.

year: 2015