title: Characterisation and prediction of state of health of rechargeable batteries

authors: Dunn, Christopher

subjects: electrochemical impedance spectroscopy (EIS)

abstract: Electrochemical impedance spectroscopy (EIS) is used extensively in battery research, but usually at frequencies that do not reflect real-world usage patterns. This has resulted in equivalent circuit models (ECMs) that are over-complicated, and suboptimal battery management systems. It is logical to measure batteries at frequencies reflecting their daily or weekly charge-discharge cycles, i.e., of the order of microhertz. This is generally not done, however, because of difficulties that include extreme measurement durations and the need for care to avoid issues such as charge distribution problems, charge drift, and the risk of overcharging or flattening the battery. This research demonstrates the feasibility of extra-low frequency (ELF) EIS measurement using standard, non-specialised measurement equipment, and the optimisation of frequency domain data through the superimposition of small-signal measurement tones on larger square wave currents.

Study of charge movement rates in the frequency domain and voltage responses in the time domain in batteries indicates connections between voltage sweep rate in cyclic voltammetry (CV) and current magnitude in incremental capacity analysis (ICA). The key factor determining what the investigator sees, e.g., reversibility  of electrode processes or evidence of individual electrochemical reactions, is rate of movement of charge. Thus, controlled current can be used to obtain CV-type data from a battery, something that would be hazardous if done conventionally using a voltage ramp.

Repeatable, low-error EIS measurements at ELFs are essential for inferring battery ECM components, including constant phase elements (CPEs). The fractional order of a CPE is linked to battery state of health (SoH) and energy efficiency. This thesis shows that efficiency measurements with waveforms representative of real battery usage can be used to track battery SoH accurately.

text: Characterisation and prediction of state of health of rechargeable batteries Electrochemical impedance spectroscopy (EIS) is used extensively in battery research, but usually at frequencies that do not reflect real-world usage patterns. This has resulted in equivalent circuit models (ECMs) that are over-complicated, and suboptimal battery management systems. It is logical to measure batteries at frequencies reflecting their daily or weekly charge-discharge cycles, i.e., of the order of microhertz. This is generally not done, however, because of difficulties that include extreme measurement durations and the need for care to avoid issues such as charge distribution problems, charge drift, and the risk of overcharging or flattening the battery. This research demonstrates the feasibility of extra-low frequency (ELF) EIS measurement using standard, non-specialised measurement equipment, and the optimisation of frequency domain data through the superimposition of small-signal measurement tones on larger square wave currents.

Study of charge movement rates in the frequency domain and voltage responses in the time domain in batteries indicates connections between voltage sweep rate in cyclic voltammetry (CV) and current magnitude in incremental capacity analysis (ICA). The key factor determining what the investigator sees, e.g., reversibility  of electrode processes or evidence of individual electrochemical reactions, is rate of movement of charge. Thus, controlled current can be used to obtain CV-type data from a battery, something that would be hazardous if done conventionally using a voltage ramp.

Repeatable, low-error EIS measurements at ELFs are essential for inferring battery ECM components, including constant phase elements (CPEs). The fractional order of a CPE is linked to battery state of health (SoH) and energy efficiency. This thesis shows that efficiency measurements with waveforms representative of real battery usage can be used to track battery SoH accurately.

year: 2024

title: Lie theory and separation of variables. 8. Semisubgroup coordinates for Ψtt - ∆2Ψ = 0

authors: Kalnins, Ernie G.

subjects: Mathematics

abstract: We classify and study all coordinate systems which permit R-separation of variables for the wave equation in three space–time variables and such that at least one of the variables corresponds to a one-parameter symmetry group of the wave equation. We discuss 33 such systems and relate them to orbits of commuting operators in the enveloping algebra of the conformal group SO (3,2).

text: Lie theory and separation of variables. 8. Semisubgroup coordinates for Ψtt - ∆2Ψ = 0 We classify and study all coordinate systems which permit R-separation of variables for the wave equation in three space–time variables and such that at least one of the variables corresponds to a one-parameter symmetry group of the wave equation. We discuss 33 such systems and relate them to orbits of commuting operators in the enveloping algebra of the conformal group SO (3,2).

year: 1975-12

title: Secular schools, spirituality and Maori values

authors: Fraser, Deborah

abstract: New Zealand has had free, state, secular education since 1877, but just what is meant by secularism is changing. Since the 1980s the growth of Maori education initiatives has mushroomed and these place emphasis on Maori values and beliefs, including spirituality. In addition, in 1999 a definition and statement on spirituality appeared in the health and physical education national curriculum document. This statement referred to values, beliefs, meaning and purpose. It also incorporated a Maori model of well‐being which places the spiritual alongside other dimensions of humanity. This article explores the concept of spirituality in secular schooling in New Zealand. Some influences from Maori culture are explored with particular reference to values, ethical decision‐making and spirituality. Interviews with Maori teachers highlight how moral decisions often reflect spiritual beliefs and practices. It is argued that schooling has a moral obligation to reflect indigenous values if understanding, respect and cultural identity are to be promoted and cherished. It is also suggested that spirituality challenges what we have traditionally considered as learning at school.

text: Secular schools, spirituality and Maori values New Zealand has had free, state, secular education since 1877, but just what is meant by secularism is changing. Since the 1980s the growth of Maori education initiatives has mushroomed and these place emphasis on Maori values and beliefs, including spirituality. In addition, in 1999 a definition and statement on spirituality appeared in the health and physical education national curriculum document. This statement referred to values, beliefs, meaning and purpose. It also incorporated a Maori model of well‐being which places the spiritual alongside other dimensions of humanity. This article explores the concept of spirituality in secular schooling in New Zealand. Some influences from Maori culture are explored with particular reference to values, ethical decision‐making and spirituality. Interviews with Maori teachers highlight how moral decisions often reflect spiritual beliefs and practices. It is argued that schooling has a moral obligation to reflect indigenous values if understanding, respect and cultural identity are to be promoted and cherished. It is also suggested that spirituality challenges what we have traditionally considered as learning at school.

year: 2004