title: Integrability, Stäckel spaces, and rational potentials

authors: Kalnins, Ernie G.

subjects: Mathematics

abstract: For a variety of classical mechanical systems embeddable into flat space with Cartesian coordinates {xi} and for which the Hamilton–Jacobi equation can be solved via separation of variables in a particular curvalinear system {uj}, we answer the following question. When is the separable potential function v expressible as a polynomial (or as a rational function) in the defining coordinates {xi}? Many examples are given.

text: Integrability, Stäckel spaces, and rational potentials For a variety of classical mechanical systems embeddable into flat space with Cartesian coordinates {xi} and for which the Hamilton–Jacobi equation can be solved via separation of variables in a particular curvalinear system {uj}, we answer the following question. When is the separable potential function v expressible as a polynomial (or as a rational function) in the defining coordinates {xi}? Many examples are given.

year: 1997-05

title: 15 yr of interstellar neutral hydrogen observed with the Interstellar Boundary Explorer

authors: Galli, A

abstract: The interactions of our heliosphere with the surrounding local interstellar medium (LISM) lead to a range of observable phenomena such as energetic neutral atoms (ENAs) from the boundary regions of the heliosphere and the influx of interstellar neutrals (ISNs) into the inner solar system. Hydrogen is the dominant neutral species in the LISM, but due to ionization and radiation pressure, only a fraction of the ISN H atoms reach the inner solar system close to Earth. Monitoring this signal therefore provides observational constraints on our assumptions of the LISM and the solar-activity-dependent loss processes inside the heliosphere. The IBEX-Lo instrument on board the Interstellar Boundary Explorer has been the only instrument so far to measure ISN H atoms directly, together with ISN D, He, Ne, O, and ENAs in the energy range from tens of eV to 2 keV. This study covers 15 yr of IBEX-Lo ISN H observations, i.e., more than one solar cycle and includes two solar minima when the ISN H signal in IBEX-Lo is strongest. Despite the very intense ISN He signal, the ISN H signal can be retrieved with appropriate knowledge of the instrument, choice of optimum observation season, and supporting modeling. The retrieved ISN H signal shows a clear anticorrelation with solar activity. The resulting ISN H maps are available in orbit format and in ecliptic coordinates and will be the basis for future more detailed comparison with heliosphere models.

text: 15 yr of interstellar neutral hydrogen observed with the Interstellar Boundary Explorer The interactions of our heliosphere with the surrounding local interstellar medium (LISM) lead to a range of observable phenomena such as energetic neutral atoms (ENAs) from the boundary regions of the heliosphere and the influx of interstellar neutrals (ISNs) into the inner solar system. Hydrogen is the dominant neutral species in the LISM, but due to ionization and radiation pressure, only a fraction of the ISN H atoms reach the inner solar system close to Earth. Monitoring this signal therefore provides observational constraints on our assumptions of the LISM and the solar-activity-dependent loss processes inside the heliosphere. The IBEX-Lo instrument on board the Interstellar Boundary Explorer has been the only instrument so far to measure ISN H atoms directly, together with ISN D, He, Ne, O, and ENAs in the energy range from tens of eV to 2 keV. This study covers 15 yr of IBEX-Lo ISN H observations, i.e., more than one solar cycle and includes two solar minima when the ISN H signal in IBEX-Lo is strongest. Despite the very intense ISN He signal, the ISN H signal can be retrieved with appropriate knowledge of the instrument, choice of optimum observation season, and supporting modeling. The retrieved ISN H signal shows a clear anticorrelation with solar activity. The resulting ISN H maps are available in orbit format and in ecliptic coordinates and will be the basis for future more detailed comparison with heliosphere models.

year: 2025-04-14

title: Mai uta ki tai: Cyclone-driven suspended sediment effects on early benthic juvenile kōura (Jasus edwardsii), Te Ākau o Tokomaru, Aotearoa

authors: Karaha-Paki, Vijuan

abstract: Kōura (Jasus edwardsii) are ecologically, culturally, and economically significant taonga species central to mahinga kai systems throughout Aotearoa New Zealand. In Te Tairāwhiti, particularly Te Ākau o Tokomaru, Cyclone Gabrielle (February 2023) resulted in unprecedented sediment loads being delivered to coastal waters, smothering inshore rocky reefs that serve as critical nursery habitats for settling puerulus and juvenile kōura. This research investigated how repeated suspended sediment exposure affects the body condition, survival, and physiological condition of early benthic juvenile kōura, integrating Western scientific methods with mātauranga Māori perspectives to support kaitiakitanga and ecosystem recovery. 

A 52-day pulse-based laboratory experiment exposed 81 early benthic juvenile kōura to three treatment levels: Control (0 mg/L), Tobserved (1,000 mg/L), and Tmaximised (5,000 mg/L) suspended sediment concentrations, alternating between exposure phases and recovery periods to simulate natural post-storm sedimentation dynamics. Sediment was sourced from the Mangahauini River mouth to reflect local conditions. Kōura were initially housed communally (Days 1-19), and then separated into individual tāruke following observed cannibalism. Across the experiment, body weight to carapace length (BW:CL) ratios, survival, blood refractive index, gill condition, and moult stage were assessed. 

All treatment groups began with statistically equivalent body condition (p = 0.135), but cumulative effects emerged over time. During communal housing, mortality was highest in the Tobserved treatment (51.9%) compared with Control and Tmaximised treatments (both 18.5%). After separation, Tmaximised individuals showed the greatest losses (45.5%), mostly during the recovery rather than exposure phases. Overall mortality reached 45.7%, with sediment-exposed treatments experiencing 55% (Tmaximised) to 59% (Tobserved) losses compared with 22.2% in the Controls (p = 0.001). 

By Day 52, sediment exposure significantly reduced body condition (p = 0.016), with the Controls maintaining higher BW:CL ratios than Tmaximised (p = 0.013). Gill assessments indicated universal and severe damage in sediment-exposed kōura (100%) but none in the Controls (0%). Quantitative image analysis confirmed strong sediment concentration- dependent effects across all damage metrics – particle lodgement, filament integrity, surface discolouration, and composite scores (all p < 0.001) – with structural deformities in 66.7% of Tobserved and 100% of Tmaximised individuals. Blood refractive index showed no treatment differences, and 84.1% of kōura remained in intermoult stage at Day 52, with no significant difference in moult stage distribution between treatments (p = 0.328). However, moult frequency during the individual phase was lower in sediment-exposed groups compared to the Controls (Control: n = 11, Tobserved: n = 4, Tmaximised: n = 5). 

These findings show that suspended sediment exposure poses population-level threats to kōura recruitment through irreversible gill damage and delayed mortality. Elevated cannibalism during communal holding, particularly observed in the Tobserved treatment, likely resulted from temporal clustering of moult events rather than sediment-induced behaviour. For Te Ākau o Tokomaru and the wider CRA 3 fishery, this highlights the need for integrated catchment-to- coast management addressing land-derived sediment inputs and protecting coastal nursery habitats. From a Te Ao Māori perspective, sedimentation represents a disruption to whakapapa relationships with Tangaroa and a weakening of mauri in coastal ecosystems. Restoring these connections requires co-governance frameworks that embed mātauranga Māori, empower kaitiaki-led monitoring and rāhui, and address the cumulative impacts of land-use intensification and repeated cyclone events on ecosystem resilience in Te Tairāwhiti.

text: Mai uta ki tai: Cyclone-driven suspended sediment effects on early benthic juvenile kōura (Jasus edwardsii), Te Ākau o Tokomaru, Aotearoa Kōura (Jasus edwardsii) are ecologically, culturally, and economically significant taonga species central to mahinga kai systems throughout Aotearoa New Zealand. In Te Tairāwhiti, particularly Te Ākau o Tokomaru, Cyclone Gabrielle (February 2023) resulted in unprecedented sediment loads being delivered to coastal waters, smothering inshore rocky reefs that serve as critical nursery habitats for settling puerulus and juvenile kōura. This research investigated how repeated suspended sediment exposure affects the body condition, survival, and physiological condition of early benthic juvenile kōura, integrating Western scientific methods with mātauranga Māori perspectives to support kaitiakitanga and ecosystem recovery. 

A 52-day pulse-based laboratory experiment exposed 81 early benthic juvenile kōura to three treatment levels: Control (0 mg/L), Tobserved (1,000 mg/L), and Tmaximised (5,000 mg/L) suspended sediment concentrations, alternating between exposure phases and recovery periods to simulate natural post-storm sedimentation dynamics. Sediment was sourced from the Mangahauini River mouth to reflect local conditions. Kōura were initially housed communally (Days 1-19), and then separated into individual tāruke following observed cannibalism. Across the experiment, body weight to carapace length (BW:CL) ratios, survival, blood refractive index, gill condition, and moult stage were assessed. 

All treatment groups began with statistically equivalent body condition (p = 0.135), but cumulative effects emerged over time. During communal housing, mortality was highest in the Tobserved treatment (51.9%) compared with Control and Tmaximised treatments (both 18.5%). After separation, Tmaximised individuals showed the greatest losses (45.5%), mostly during the recovery rather than exposure phases. Overall mortality reached 45.7%, with sediment-exposed treatments experiencing 55% (Tmaximised) to 59% (Tobserved) losses compared with 22.2% in the Controls (p = 0.001). 

By Day 52, sediment exposure significantly reduced body condition (p = 0.016), with the Controls maintaining higher BW:CL ratios than Tmaximised (p = 0.013). Gill assessments indicated universal and severe damage in sediment-exposed kōura (100%) but none in the Controls (0%). Quantitative image analysis confirmed strong sediment concentration- dependent effects across all damage metrics – particle lodgement, filament integrity, surface discolouration, and composite scores (all p < 0.001) – with structural deformities in 66.7% of Tobserved and 100% of Tmaximised individuals. Blood refractive index showed no treatment differences, and 84.1% of kōura remained in intermoult stage at Day 52, with no significant difference in moult stage distribution between treatments (p = 0.328). However, moult frequency during the individual phase was lower in sediment-exposed groups compared to the Controls (Control: n = 11, Tobserved: n = 4, Tmaximised: n = 5). 

These findings show that suspended sediment exposure poses population-level threats to kōura recruitment through irreversible gill damage and delayed mortality. Elevated cannibalism during communal holding, particularly observed in the Tobserved treatment, likely resulted from temporal clustering of moult events rather than sediment-induced behaviour. For Te Ākau o Tokomaru and the wider CRA 3 fishery, this highlights the need for integrated catchment-to- coast management addressing land-derived sediment inputs and protecting coastal nursery habitats. From a Te Ao Māori perspective, sedimentation represents a disruption to whakapapa relationships with Tangaroa and a weakening of mauri in coastal ecosystems. Restoring these connections requires co-governance frameworks that embed mātauranga Māori, empower kaitiaki-led monitoring and rāhui, and address the cumulative impacts of land-use intensification and repeated cyclone events on ecosystem resilience in Te Tairāwhiti.

year: 2025