title: Superintegrability and higher-order constants for classical and quantum systems

authors: Kalnins, Ernie G.

subjects: mathematics

abstract: We extend recent work by Tremblay, Turbiner, and Winternitz which analyzes an infinite family of solvable and integrable quantum systems in the plane, indexed by the positive parameter k. Key components of their analysis were to demonstrate that there are closed orbits in the corresponding classical system if k is rational, and for a number of examples there are generating quantum symmetries that are higher order differential operators than two. Indeed they conjectured that for a general class of potentials of this type, quantum constants of higher order should exist. We give credence to this conjecture by showing that for an even more general class of potentials in classicalmechanics, there are higher-order constants of the motion as polynomials in the momenta. Thus these systems are all superintegrable.

text: Superintegrability and higher-order constants for classical and quantum systems We extend recent work by Tremblay, Turbiner, and Winternitz which analyzes an infinite family of solvable and integrable quantum systems in the plane, indexed by the positive parameter k. Key components of their analysis were to demonstrate that there are closed orbits in the corresponding classical system if k is rational, and for a number of examples there are generating quantum symmetries that are higher order differential operators than two. Indeed they conjectured that for a general class of potentials of this type, quantum constants of higher order should exist. We give credence to this conjecture by showing that for an even more general class of potentials in classicalmechanics, there are higher-order constants of the motion as polynomials in the momenta. Thus these systems are all superintegrable.

year: 2011

title: Structural characterisation of pre-processed thermoplastic protein derived from bloodmeal

authors: Bier, James Michael

abstract: Additives are required to convert bloodmeal powder into an extrudable thermoplastic protein-based bioplastic. These include a protein denaturant, a surfactant, a reducing agent and plasticisers. The objective of this work was to assess the structural changes induced in bloodmeal by these additives prior to extrusion. Structure was investigated using Fourier transform infrared (FT-IR) spectroscopy, wide angle X-ray scattering (WAXS) and synchrotron light based FT-IR microspectroscopy. 
FT-IR results suggested the additives reduced α-helical content. The shape of the amide I region (1600 – 1700 cm⁻¹, representing carbonyl group stretching in the protein backbone) is known to depend on protein secondary structures. Bloodmeal showed a broad, convoluted peak in this region, with a maximum in the range 1648 – 1658 cm⁻¹, associated with α-helices. With processing additives, a dip was seen in the α-helix region, with twin peaks emerging either side of it. Urea, one of the additives, also absorbs in the amide I region and may also contribute to a change in its shape. Analysis of the amide 3 region supported a reduction in the ratio of α helices to β sheets. Further support of structural changes was shown by WAXS. The additives decreased the sharpness of peaks corresponding to 4.8 Å and 10 Å, thought to represent intra-helix spacing and inter-helix packing respectively.
FT-IR microspectroscopy at the Australian Synchrotron enabled spatial variations in secondary structure to be explored using peaks in the amide 3 region. Spatial distribution of secondary structure was detected in bloodmeal and thermoplastically modified bloodmeal prior to extrusion (PPM-TEG). Bloodmeal showed domain separation on the approximate order of 10 μm, whilst PPM-TEG appeared to have larger phases and overall reduced α-helical content, relative to beta sheets.

text: Structural characterisation of pre-processed thermoplastic protein derived from bloodmeal Additives are required to convert bloodmeal powder into an extrudable thermoplastic protein-based bioplastic. These include a protein denaturant, a surfactant, a reducing agent and plasticisers. The objective of this work was to assess the structural changes induced in bloodmeal by these additives prior to extrusion. Structure was investigated using Fourier transform infrared (FT-IR) spectroscopy, wide angle X-ray scattering (WAXS) and synchrotron light based FT-IR microspectroscopy. 
FT-IR results suggested the additives reduced α-helical content. The shape of the amide I region (1600 – 1700 cm⁻¹, representing carbonyl group stretching in the protein backbone) is known to depend on protein secondary structures. Bloodmeal showed a broad, convoluted peak in this region, with a maximum in the range 1648 – 1658 cm⁻¹, associated with α-helices. With processing additives, a dip was seen in the α-helix region, with twin peaks emerging either side of it. Urea, one of the additives, also absorbs in the amide I region and may also contribute to a change in its shape. Analysis of the amide 3 region supported a reduction in the ratio of α helices to β sheets. Further support of structural changes was shown by WAXS. The additives decreased the sharpness of peaks corresponding to 4.8 Å and 10 Å, thought to represent intra-helix spacing and inter-helix packing respectively.
FT-IR microspectroscopy at the Australian Synchrotron enabled spatial variations in secondary structure to be explored using peaks in the amide 3 region. Spatial distribution of secondary structure was detected in bloodmeal and thermoplastically modified bloodmeal prior to extrusion (PPM-TEG). Bloodmeal showed domain separation on the approximate order of 10 μm, whilst PPM-TEG appeared to have larger phases and overall reduced α-helical content, relative to beta sheets.

year: 2012

title: Tephras and New Zealand archaeology

authors: Lowe, David J.

subjects: tephrochronology

abstract: Establishing an accurate date for earliest Polynesian settlement in New Zealand is essential for understanding patterns of settlement and associated environmental impacts, and the processes and rates of cultural change in Eastern Polynesia. Tephra deposits from five volcanic centres, together with exotic sea-rafted pumice, provide isochronous constraints on the timing of earliest settlement and human impacts in northern New Zealand. A local basaltic tephra from Rangitoto Island (Auckland) and locally distributed andesitic tephras from Egmont volcano directly date human occupation to c. AD 1400–1450. Distal andesitic tephras (Tufa Trig Formation) from Mt Ruapehu, Tongariro volcanic centre, help constrain the timing of earliest anthropogenic deforestation signals in Hawke's Bay. Sea-rafted Loisels Pumice(s), although of uncertain stratigraphic reliability in places, overlies cultural remains that can be no younger than c. AD 1350 along the east coast, North Island. The regionally extensive rhyolitic Kaharoa Tephra, which erupted from Okataina volcano between c. AD  1300–1390, is the critical “settlement layer” datum for dating prehistory in the North Island: no human artefacts are recorded beneath it and the earliest inferred environmental impacts by humans are dated to c. AD  1280, just prior to its deposition. This maximum date matches the earliest radiocarbon dates derived for both settlement and human impacts from archaeological and natural sites (c. AD 1250), and implies that the onset of deforestation was essentially contemporaneous with initial settlement.
The widespread rhyolitic Taupo Tephra, which erupted from Taupo volcano c. AD 200, provides an isochronous benchmark well before earliest settlement. The tephra may coincide approximately with a putative earlier transient contact in New Zealand based on Pacific rat-bone (Rattus exulans) dates. More precise calendrical dates on the tephras—via dendrochronology or ice-core records or other dating methods—would help refine assessment of the timing of earliest settlement, while extending the distributional range of critical tephra layers, through application of crypto-tephra analysis, could lead to a greater understanding of settlement patterns.

text: Tephras and New Zealand archaeology Establishing an accurate date for earliest Polynesian settlement in New Zealand is essential for understanding patterns of settlement and associated environmental impacts, and the processes and rates of cultural change in Eastern Polynesia. Tephra deposits from five volcanic centres, together with exotic sea-rafted pumice, provide isochronous constraints on the timing of earliest settlement and human impacts in northern New Zealand. A local basaltic tephra from Rangitoto Island (Auckland) and locally distributed andesitic tephras from Egmont volcano directly date human occupation to c. AD 1400–1450. Distal andesitic tephras (Tufa Trig Formation) from Mt Ruapehu, Tongariro volcanic centre, help constrain the timing of earliest anthropogenic deforestation signals in Hawke's Bay. Sea-rafted Loisels Pumice(s), although of uncertain stratigraphic reliability in places, overlies cultural remains that can be no younger than c. AD 1350 along the east coast, North Island. The regionally extensive rhyolitic Kaharoa Tephra, which erupted from Okataina volcano between c. AD  1300–1390, is the critical “settlement layer” datum for dating prehistory in the North Island: no human artefacts are recorded beneath it and the earliest inferred environmental impacts by humans are dated to c. AD  1280, just prior to its deposition. This maximum date matches the earliest radiocarbon dates derived for both settlement and human impacts from archaeological and natural sites (c. AD 1250), and implies that the onset of deforestation was essentially contemporaneous with initial settlement.
The widespread rhyolitic Taupo Tephra, which erupted from Taupo volcano c. AD 200, provides an isochronous benchmark well before earliest settlement. The tephra may coincide approximately with a putative earlier transient contact in New Zealand based on Pacific rat-bone (Rattus exulans) dates. More precise calendrical dates on the tephras—via dendrochronology or ice-core records or other dating methods—would help refine assessment of the timing of earliest settlement, while extending the distributional range of critical tephra layers, through application of crypto-tephra analysis, could lead to a greater understanding of settlement patterns.

year: 2000