title: Lie theory and the wave equation in space–time. 5. R-separable solutions of the wave equation ψtt-∆3ψ=0

authors: Kalnins, Ernie G.

subjects: Mathematics

abstract: A detailed classification is made of all orthogonal coordinate systems for which the wave equation ψtt-∆3ψ=0 admits an R-separable solution. Only those coordinate systems are given which are not conformally equivalent to coordinate systems that have already been found in previous articles. We find 106 coordinates to given a total of 368 conformally inequivalent orthogonal coordinates for which the wave equation admits an R separation of variables.

text: Lie theory and the wave equation in space–time. 5. R-separable solutions of the wave equation ψtt-∆3ψ=0 A detailed classification is made of all orthogonal coordinate systems for which the wave equation ψtt-∆3ψ=0 admits an R-separable solution. Only those coordinate systems are given which are not conformally equivalent to coordinate systems that have already been found in previous articles. We find 106 coordinates to given a total of 368 conformally inequivalent orthogonal coordinates for which the wave equation admits an R separation of variables.

year: 1978-06

title: Design of SCALDO based high-current DC power supply

authors: Ariyarathna, Thilanga

subjects: Supercapacitor

abstract: Supercapacitor assisted (SCA) techniques are primarily based on supercapacitors having in the order of one million times more capacitance, together with one to two orders of magnitude smaller equivalent series resistance (ESR), compared with conventional capacitors. In the first successful SCA technique, the supercapacitor-assisted low dropout regulator (SCALDO) combined a linear regulator in series with a supercapacitor to act as a lossless voltage dropper. SCALDO created the opportunity to develop an entirely new family of highly efficient, interference-free, very-low-frequency DC-DC converters, which have evolved further into several branches over the last 6 years.

Leading data centre operators such as Google have announced their intention to move toward 48 V server rack architecture to minimise power losses in distribution lines and to improve overall operating efficiency. This thesis investigated the potential of the SCALDO technique to develop a high-current DC power supply suitable for Google server racks, meeting requirements such as electrical isolation, fast transient response, high efficiency and DC-UPS capability within the converter.

Work related to this thesis proved that by creatively extending the SCALDO technique to achieve higher current at high voltage and further developing a bulk DC-rail from AC input by extending the previously proven fast supercapacitor charger technique, a SCALDO-assisted high-current DC power supply can be achieved. As a proof-of-concept project with a DC output of 12 V (one fourth scale) at 10 A load current capability, several key circuit blocks were developed including: (i) high current discrete LDO of 10 A; (ii) four switch implementation of a SCALDO stage; and (iii) a transformer-isolated input DC stage to feed the output SCALDO stage based on a hybrid-type medium frequency switch mode. This overall implementation is expected to overcome the limitations of a direct-SCALDO stage, maintaining high end-to-end efficiency. Matlab and LTspice simulation models were developed to observe the behaviour of these new power converter techniques.

The thesis discusses the significance of this work, related techniques, the loss-circumventing principle in the RC charging loop, which is the theoretical basis of SCALDO, and the design and simulation details of a novel power conversion technology. It also presents the implementation details of the prototypes built to verify this approach.

text: Design of SCALDO based high-current DC power supply Supercapacitor assisted (SCA) techniques are primarily based on supercapacitors having in the order of one million times more capacitance, together with one to two orders of magnitude smaller equivalent series resistance (ESR), compared with conventional capacitors. In the first successful SCA technique, the supercapacitor-assisted low dropout regulator (SCALDO) combined a linear regulator in series with a supercapacitor to act as a lossless voltage dropper. SCALDO created the opportunity to develop an entirely new family of highly efficient, interference-free, very-low-frequency DC-DC converters, which have evolved further into several branches over the last 6 years.

Leading data centre operators such as Google have announced their intention to move toward 48 V server rack architecture to minimise power losses in distribution lines and to improve overall operating efficiency. This thesis investigated the potential of the SCALDO technique to develop a high-current DC power supply suitable for Google server racks, meeting requirements such as electrical isolation, fast transient response, high efficiency and DC-UPS capability within the converter.

Work related to this thesis proved that by creatively extending the SCALDO technique to achieve higher current at high voltage and further developing a bulk DC-rail from AC input by extending the previously proven fast supercapacitor charger technique, a SCALDO-assisted high-current DC power supply can be achieved. As a proof-of-concept project with a DC output of 12 V (one fourth scale) at 10 A load current capability, several key circuit blocks were developed including: (i) high current discrete LDO of 10 A; (ii) four switch implementation of a SCALDO stage; and (iii) a transformer-isolated input DC stage to feed the output SCALDO stage based on a hybrid-type medium frequency switch mode. This overall implementation is expected to overcome the limitations of a direct-SCALDO stage, maintaining high end-to-end efficiency. Matlab and LTspice simulation models were developed to observe the behaviour of these new power converter techniques.

The thesis discusses the significance of this work, related techniques, the loss-circumventing principle in the RC charging loop, which is the theoretical basis of SCALDO, and the design and simulation details of a novel power conversion technology. It also presents the implementation details of the prototypes built to verify this approach.

year: 2021

title: "He taketake, he hurumanu te moana i rōhia ai": Mā te Māori ngā toronga o te motu ki whenua kē e taurima?

authors: Dewes, Kaneihana

subjects: Iwi taketake

abstract: Kai te tino ia o te tuhinga rangahau nei, he whakatōmene i te āhua kaiārahi o te Māori i ngā tūāhua hono ki ahurea kē. Mā konei e whakatau ai, e whakatūwherahia rānei ngā āhuatanga e mea ana mā te Māori ngā toronga o te motu ki whenua kē e taurima. He momo tēnei nā te Māori, i takea mai i ngā mahi pokai moana, me ngā waka i whakaterea i ngā rohenga moana o Te Moana-nui-a-Kiwa, ā, puta noa. Waihoki, he taonga tonu wā tātau kai ngā tauira o ngā tūhononga ahurea o ngā iwi taketake o te ao; he taonga anō kai waenganui i a tātau ngā whenua maha i pakanga ki rāwāhi, he tohu nui nā te ‘price of citizenship’. He momo nā te Māori te tātaki i ngā mahi whakarauora reo, waihoki, he rite tonu te noho tahi ki whenua kē i roto i te kōingo ki te whakatipu i te reo o te whenua. Mā konei, ka marohi ai te hiranga o Te Reo Māori me ngā Tikanga Māori, tēnei hiranga e tohu ana i te hua o ngā hononga ahurea ki ngā iwi taketake huri noa, kia whai hua mō Niu Tireni i ngā toronga ki whenua kē.

text: "He taketake, he hurumanu te moana i rōhia ai": Mā te Māori ngā toronga o te motu ki whenua kē e taurima? Kai te tino ia o te tuhinga rangahau nei, he whakatōmene i te āhua kaiārahi o te Māori i ngā tūāhua hono ki ahurea kē. Mā konei e whakatau ai, e whakatūwherahia rānei ngā āhuatanga e mea ana mā te Māori ngā toronga o te motu ki whenua kē e taurima. He momo tēnei nā te Māori, i takea mai i ngā mahi pokai moana, me ngā waka i whakaterea i ngā rohenga moana o Te Moana-nui-a-Kiwa, ā, puta noa. Waihoki, he taonga tonu wā tātau kai ngā tauira o ngā tūhononga ahurea o ngā iwi taketake o te ao; he taonga anō kai waenganui i a tātau ngā whenua maha i pakanga ki rāwāhi, he tohu nui nā te ‘price of citizenship’. He momo nā te Māori te tātaki i ngā mahi whakarauora reo, waihoki, he rite tonu te noho tahi ki whenua kē i roto i te kōingo ki te whakatipu i te reo o te whenua. Mā konei, ka marohi ai te hiranga o Te Reo Māori me ngā Tikanga Māori, tēnei hiranga e tohu ana i te hua o ngā hononga ahurea ki ngā iwi taketake huri noa, kia whai hua mō Niu Tireni i ngā toronga ki whenua kē.

year: 2022