title: Indeterminacy and instability in Petschek reconnection

authors: Forbes, Terry G.

subjects: magnetic reconnection

abstract: We explain two puzzling aspects of Petschek's model for fast reconnection. One is its failure to occur in plasma simulations with uniform resistivity. The other is its inability to provide anything more than an upper limit for the reconnection rate. We have found that previously published analytical solutions based on Petschek's model are structurally unstable if the electrical resistivity is uniform. The structural instability is associated with the presence of an essential singularity at the X-line that is unphysical. By requiring that such a singularity does not exist, we obtain a formula that predicts a specific rate of reconnection. For uniform resistivity, reconnection can only occur at the slow, Sweet-Parker rate. For nonuniform resistivity, reconnection can occur at a much faster rate provided that the resistivity profile is not too flat near the X-line. If this condition is satisfied, then the scale length of the nonuniformity determines the reconnection rate.

text: Indeterminacy and instability in Petschek reconnection We explain two puzzling aspects of Petschek's model for fast reconnection. One is its failure to occur in plasma simulations with uniform resistivity. The other is its inability to provide anything more than an upper limit for the reconnection rate. We have found that previously published analytical solutions based on Petschek's model are structurally unstable if the electrical resistivity is uniform. The structural instability is associated with the presence of an essential singularity at the X-line that is unphysical. By requiring that such a singularity does not exist, we obtain a formula that predicts a specific rate of reconnection. For uniform resistivity, reconnection can only occur at the slow, Sweet-Parker rate. For nonuniform resistivity, reconnection can occur at a much faster rate provided that the resistivity profile is not too flat near the X-line. If this condition is satisfied, then the scale length of the nonuniformity determines the reconnection rate.

year: 2013

title: Influence of ageing heating rates on the microstructure and mechanical properties of Ti-5553 alloy

authors: Jia, Mengqi

subjects: fatigue

abstract: The Ti-5553 alloy, a high-strength β-titanium alloy, is increasingly recognised for its exceptional mechanical properties, making it a preferred material for critical aerospace applications. This thesis examines the effects of varying ageing heating rates on the microstructure and mechanical properties of the forged Ti-5553 alloy, focusing on hardness, tensile properties, and fatigue performance. Following solution treatment at 810°C, the alloy was aged at 610°C with heating rates of 1°C/min, 5°C/min, 10°C/min, and 15°C/min. Detailed microstructural analysis was conducted using Scanning Electron Microscopy (SEM) and Energy Dispersive X ray Spectroscopy (EDX). The microstructural examination revealed that different ageing heating rates caused only minor variations in the alloy's bimodal microstructure. Slower ageing heating rates produced a relatively fine, homogeneously distributed primary α phase within the β grains, while faster rates resulted in a slightly coarser bimodal microstructure. Chemical homogeneity analysis confirmed a consistent distribution of critical elements, with α stabilisers concentrated in the primary α phase and β stabilisers in the β phase, ensuring stable phase compositions across all samples. The observed slight microstructural changes were reflected in the alloy's mechanical properties. Hardness across different ageing heating rates varied between 357.4 HV and 372.6 HV. The ultimate tensile strength (UTS) declined from 1307.2 MPa at 1°C/min to 1264.5 MPa at 15°C/min, while ductility improved from 15.6% to 17.1% over the same range. The alloy demonstrated good fatigue resistance at lower stress amplitudes and ageing heating rates, enduring over 10 million cycles at 337.5 MPa under the 1°C/min condition. However, fatigue life decreased with higher stress amplitudes and ageing heating rates, highlighting the alloy's sensitivity to more extreme conditions. In summary, while the varying ageing heating rates resulted in only minor changes to the microstructure, these alterations had some impact on the mechanical properties of the Ti-5553 alloy. These findings highlight the importance of precise microstructural control in optimising the alloy's performance, especially in applications where achieving a balance between strength, ductility, and fatigue resistance is crucial.

text: Influence of ageing heating rates on the microstructure and mechanical properties of Ti-5553 alloy The Ti-5553 alloy, a high-strength β-titanium alloy, is increasingly recognised for its exceptional mechanical properties, making it a preferred material for critical aerospace applications. This thesis examines the effects of varying ageing heating rates on the microstructure and mechanical properties of the forged Ti-5553 alloy, focusing on hardness, tensile properties, and fatigue performance. Following solution treatment at 810°C, the alloy was aged at 610°C with heating rates of 1°C/min, 5°C/min, 10°C/min, and 15°C/min. Detailed microstructural analysis was conducted using Scanning Electron Microscopy (SEM) and Energy Dispersive X ray Spectroscopy (EDX). The microstructural examination revealed that different ageing heating rates caused only minor variations in the alloy's bimodal microstructure. Slower ageing heating rates produced a relatively fine, homogeneously distributed primary α phase within the β grains, while faster rates resulted in a slightly coarser bimodal microstructure. Chemical homogeneity analysis confirmed a consistent distribution of critical elements, with α stabilisers concentrated in the primary α phase and β stabilisers in the β phase, ensuring stable phase compositions across all samples. The observed slight microstructural changes were reflected in the alloy's mechanical properties. Hardness across different ageing heating rates varied between 357.4 HV and 372.6 HV. The ultimate tensile strength (UTS) declined from 1307.2 MPa at 1°C/min to 1264.5 MPa at 15°C/min, while ductility improved from 15.6% to 17.1% over the same range. The alloy demonstrated good fatigue resistance at lower stress amplitudes and ageing heating rates, enduring over 10 million cycles at 337.5 MPa under the 1°C/min condition. However, fatigue life decreased with higher stress amplitudes and ageing heating rates, highlighting the alloy's sensitivity to more extreme conditions. In summary, while the varying ageing heating rates resulted in only minor changes to the microstructure, these alterations had some impact on the mechanical properties of the Ti-5553 alloy. These findings highlight the importance of precise microstructural control in optimising the alloy's performance, especially in applications where achieving a balance between strength, ductility, and fatigue resistance is crucial.

year: 2024-09-15

title: Rauaroha: He tohu Aroha rau i te akoranga

authors: Paringatai, Karyn

subjects: huarahi ako

abstract: Nö te tau 2001 i whakatüria ai e Ako Aotearoa (National Centre for Tertiary Teaching Excellence) tëtahi tohu hei whakanui i ngä mahi a te tangata e whakaako ana i te taumata takiura. Me whakaatu te kaiwhiwhi tohu i tana ü roa ki ngä taumata tiketike rawa i tana mahi whakaako. Tekau mä rua ngä kaiwhiwhi toa i ia tau, kätahi ka whiriwhirihia ai e tëtahi kömiti kaiwhakawä kia kotahi te tangata e whiwhi nei i te Tohu Tiketike o te Pirimia. Mö ngä tau e whä kua hipa ake nei i riro i ngä kaiako Mäori te tohu tiketike nei. Ko te aronga o tënei tuhinga he whakaatu i ngä ähuatanga o ënei kaiako kia märama pai atu ai te whakaaro tiketike o te Mäori ki tënei mea te ako.

text: Rauaroha: He tohu Aroha rau i te akoranga Nö te tau 2001 i whakatüria ai e Ako Aotearoa (National Centre for Tertiary Teaching Excellence) tëtahi tohu hei whakanui i ngä mahi a te tangata e whakaako ana i te taumata takiura. Me whakaatu te kaiwhiwhi tohu i tana ü roa ki ngä taumata tiketike rawa i tana mahi whakaako. Tekau mä rua ngä kaiwhiwhi toa i ia tau, kätahi ka whiriwhirihia ai e tëtahi kömiti kaiwhakawä kia kotahi te tangata e whiwhi nei i te Tohu Tiketike o te Pirimia. Mö ngä tau e whä kua hipa ake nei i riro i ngä kaiako Mäori te tohu tiketike nei. Ko te aronga o tënei tuhinga he whakaatu i ngä ähuatanga o ënei kaiako kia märama pai atu ai te whakaaro tiketike o te Mäori ki tënei mea te ako.

year: 2017