title: Symmetry and separation of variables for the Hamilton–Jacobi equation W2t −W2x  −W2y  =0

authors: Boyer, C.P.

subjects: Mathematics

abstract: We present a detailed group theoretical study of the problem of separation of variables for the characteristic equation of the wave equation in one time and two space dimensions. Using the well-known Lie algebra isomorphism between canonical vector fields under the Lie bracket operation and functions (modulo constants) under Poisson brackets, we associate, with each R-separable coordinate system of the equation, an orbit of commuting constants of the motion which are quadratic members of the universal enveloping algebra of the symmetry algebra o (3,2). In this, the first of two papers, we essentially restrict ourselves to those orbits where one of the constants of the motion can be split off, giving rise to a reduced equation with a nontrivial symmetry algebra. Our analysis includes several of the better known two-body problems, including the harmonic oscillator and Kepler problems, as special cases.

text: Symmetry and separation of variables for the Hamilton–Jacobi equation W2t −W2x  −W2y  =0 We present a detailed group theoretical study of the problem of separation of variables for the characteristic equation of the wave equation in one time and two space dimensions. Using the well-known Lie algebra isomorphism between canonical vector fields under the Lie bracket operation and functions (modulo constants) under Poisson brackets, we associate, with each R-separable coordinate system of the equation, an orbit of commuting constants of the motion which are quadratic members of the universal enveloping algebra of the symmetry algebra o (3,2). In this, the first of two papers, we essentially restrict ourselves to those orbits where one of the constants of the motion can be split off, giving rise to a reduced equation with a nontrivial symmetry algebra. Our analysis includes several of the better known two-body problems, including the harmonic oscillator and Kepler problems, as special cases.

year: 1978-01

title: Prismatic axis, differential-drive robotic kiwifruit harvester for reduced cycle time

authors: Barnett, Josh

subjects: robotics

abstract: The New Zealand kiwifruit industry is currently worth over NZD 2 billion in annual sales revenue, this is forecast to double within the next 5-10 years due to a significant increase in production volume. The industry is already experiencing a prevalent shortage of labour which is indicative of a global trend. The objective for this study was to define important metrics for the robotic harvesting of kiwifruit and to propose a hardware configuration which could improve on the current kiwifruit harvesting module (KHM) developed by the Multipurpose Orchard Robotics (MOR) project. The research scope was focused to establishing whether a prismatic axis kinematic structure was more effective than a rotational axis kinematic structure for the multiple-robot harvesting of kiwifruit. KPI's (key performance indicators) were defined as evaluation and design measures - these included fruit damage, harvestability and nominal harvest cycle time. An equation specific to the KHM was derived for the latter which included measures of fruit per harvesting phase, time between fruit and a proposed work distribution constant W_D. A prismatic axis, linear rail constrained, kiwifruit harvesting robot (LHR) with two robot-arms was developed, built and tested. It was found to be exponentially beneficial to locate mass proximal to the X axis carriage centres which is achieved with a differential-drive of the YZ axis'. The prismatic axis kinematic structure of the LHR allowed for an 88% greater work distribution constant W_D, a 40% greater harvestable taskspace volume V_h and 2.5 times greater overall workspace efficiency when compared to the KHM. The nominal harvest cycle time was identical for both of these systems. However, the LHR and the developed `x-rank' registry algorithm were capable of maintaining W_D value despite a two-fold increase in robot-arm density. Therefore, in non-collision scenarios the LHR can operate with four robot-arms without compromising performance. In this scenario where both systems have four robot-arms, the LHR had a 44% reduction in harvest cycle time. Further study would need to be done into manipulability measures, scheduling methods and the effects on work distribution to establish whether a prismatic axis structure remains favourable if an orientation structure is implemented for end-effector dexterity.

text: Prismatic axis, differential-drive robotic kiwifruit harvester for reduced cycle time The New Zealand kiwifruit industry is currently worth over NZD 2 billion in annual sales revenue, this is forecast to double within the next 5-10 years due to a significant increase in production volume. The industry is already experiencing a prevalent shortage of labour which is indicative of a global trend. The objective for this study was to define important metrics for the robotic harvesting of kiwifruit and to propose a hardware configuration which could improve on the current kiwifruit harvesting module (KHM) developed by the Multipurpose Orchard Robotics (MOR) project. The research scope was focused to establishing whether a prismatic axis kinematic structure was more effective than a rotational axis kinematic structure for the multiple-robot harvesting of kiwifruit. KPI's (key performance indicators) were defined as evaluation and design measures - these included fruit damage, harvestability and nominal harvest cycle time. An equation specific to the KHM was derived for the latter which included measures of fruit per harvesting phase, time between fruit and a proposed work distribution constant W_D. A prismatic axis, linear rail constrained, kiwifruit harvesting robot (LHR) with two robot-arms was developed, built and tested. It was found to be exponentially beneficial to locate mass proximal to the X axis carriage centres which is achieved with a differential-drive of the YZ axis'. The prismatic axis kinematic structure of the LHR allowed for an 88% greater work distribution constant W_D, a 40% greater harvestable taskspace volume V_h and 2.5 times greater overall workspace efficiency when compared to the KHM. The nominal harvest cycle time was identical for both of these systems. However, the LHR and the developed `x-rank' registry algorithm were capable of maintaining W_D value despite a two-fold increase in robot-arm density. Therefore, in non-collision scenarios the LHR can operate with four robot-arms without compromising performance. In this scenario where both systems have four robot-arms, the LHR had a 44% reduction in harvest cycle time. Further study would need to be done into manipulability measures, scheduling methods and the effects on work distribution to establish whether a prismatic axis structure remains favourable if an orientation structure is implemented for end-effector dexterity.

year: 2018

title: Local values and the promotion and restoration of wetlands and their ecosystem services in Aotearoa-New Zealand: a case study of Tauranga’s planning regime

authors: Peat, Helen Ann

subjects: Environmental planning

abstract: Aligning wetlands restoration planning mechanisms with public perceptions and values can help gain support for and assistance with restoration. Using Tauranga as a case study, this thesis is an exploratory study that applies the Millennium Ecosystem Assessment (MEA) framework to examine the extent to which New Zealand's planning regime incorporates local values in the promotion and restoration of wetlands and their ecosystem services.

This thesis used multiple qualitative research methods in a two-pronged process. A narrative literature review and systematic statutory analysis in phase one helped identify values associated with wetland ecosystem services and how New Zealand’s, and more specifically Tauranga’s, resource management system promotes and enables the restoration of wetlands and their ecosystem services. A case study approach with analysis of primary and secondary data in phase two helped identify what Tauranga local residents value as important wetland ecosystem services and the extent to which the local policy mechanisms reflect these values. 

Through thematic analysis of semi-structured interviews and summaries of submissions, this thesis identifies six dimensions that represent values towards wetland ecosystem services and their restoration in Tauranga. Other than one dimension that consists of a single value on education from the cultural services category of the MEA framework, the remaining five dimensions comprise services from within and between the framework categories. These dimensions are wetlands as nutrient- and mineral-rich areas that support biodiversity and provide habitat; that regulate water, act as natural flood plains and sequester carbon to help protect against climate change and natural hazards; that maintain Māori cultural practices; that remove nutrients and contaminants in water; and provide recreational and aesthetic experiences. Therefore, identified dimensions could form the basis of educational programmes and toolkits that promote wetlands restoration.

The systematic policy analysis and cross-comparison with the results of the thematic analysis found that Tauranga’s planning regime partially provides for each of the six dimensions. However, the nuances and complexities of the values, including the interconnected nature of wetlands values and services, are not captured. This means Tauranga’s planning regime does not fully incorporate local values in the promotion and restoration of wetlands and their ecosystem services. Bridging the gap between wetlands restoration provisions and wetland ecosystem service values is likely to be supported by enacting the current resource management reforms. Enacting the reforms would help reduce the number of policies and plans, implement regional spatial planning, and develop outcomes-based policy mechanisms that encompass ecological, social, cultural and spiritual values, including those associated with wetlands.

text: Local values and the promotion and restoration of wetlands and their ecosystem services in Aotearoa-New Zealand: a case study of Tauranga’s planning regime Aligning wetlands restoration planning mechanisms with public perceptions and values can help gain support for and assistance with restoration. Using Tauranga as a case study, this thesis is an exploratory study that applies the Millennium Ecosystem Assessment (MEA) framework to examine the extent to which New Zealand's planning regime incorporates local values in the promotion and restoration of wetlands and their ecosystem services.

This thesis used multiple qualitative research methods in a two-pronged process. A narrative literature review and systematic statutory analysis in phase one helped identify values associated with wetland ecosystem services and how New Zealand’s, and more specifically Tauranga’s, resource management system promotes and enables the restoration of wetlands and their ecosystem services. A case study approach with analysis of primary and secondary data in phase two helped identify what Tauranga local residents value as important wetland ecosystem services and the extent to which the local policy mechanisms reflect these values. 

Through thematic analysis of semi-structured interviews and summaries of submissions, this thesis identifies six dimensions that represent values towards wetland ecosystem services and their restoration in Tauranga. Other than one dimension that consists of a single value on education from the cultural services category of the MEA framework, the remaining five dimensions comprise services from within and between the framework categories. These dimensions are wetlands as nutrient- and mineral-rich areas that support biodiversity and provide habitat; that regulate water, act as natural flood plains and sequester carbon to help protect against climate change and natural hazards; that maintain Māori cultural practices; that remove nutrients and contaminants in water; and provide recreational and aesthetic experiences. Therefore, identified dimensions could form the basis of educational programmes and toolkits that promote wetlands restoration.

The systematic policy analysis and cross-comparison with the results of the thematic analysis found that Tauranga’s planning regime partially provides for each of the six dimensions. However, the nuances and complexities of the values, including the interconnected nature of wetlands values and services, are not captured. This means Tauranga’s planning regime does not fully incorporate local values in the promotion and restoration of wetlands and their ecosystem services. Bridging the gap between wetlands restoration provisions and wetland ecosystem service values is likely to be supported by enacting the current resource management reforms. Enacting the reforms would help reduce the number of policies and plans, implement regional spatial planning, and develop outcomes-based policy mechanisms that encompass ecological, social, cultural and spiritual values, including those associated with wetlands.

year: 2022