Australian Mathematical Sciences Institute - Research Publications

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    Numerical and analytical study of undular bores governed by the full water wave equations and bidirectional Whitham-Boussinesq equations
    Vargas-Magana, RM ; Marchant, TR ; Smyth, NF (AMER INST PHYSICS, 2021-06-01)
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    2-D solitary waves in thermal media with nonsymmetric boundary conditions
    Louis, SA ; Marchant, TR ; Smyth, NF (WILEY, 2019-05-01)
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    Panel Conditioning and Subjective Well-being
    Wooden, M ; Li, N (SPRINGER, 2014-05-01)
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    Nematic Dispersive Shock Waves from Nonlocal to Local
    Baqer, S ; Frantzeskakis, DJ ; Horikis, TP ; Houdeville, C ; Marchant, TR ; Smyth, NF (MDPI, 2021-06-01)
    The structure of optical dispersive shock waves in nematic liquid crystals is investigated as the power of the optical beam is varied, with six regimes identified, which complements previous work pertinent to low power beams only. It is found that the dispersive shock wave structure depends critically on the input beam power. In addition, it is known that nematic dispersive shock waves are resonant and the structure of this resonance is also critically dependent on the beam power. Whitham modulation theory is used to find solutions for the six regimes with the existence intervals for each identified. These dispersive shock wave solutions are compared with full numerical solutions of the nematic equations, and excellent agreement is found.
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    Understanding Motivation behind Mathematics Enrolment Choice in Senior Secondary Schools: Questionnaire Design
    Li, N ; Koch, I (The University of Melbourne on behalf of the Australian Mathematical Sciences Institute, 2019)
    A theoretical model is proposed as the basis for developing an instrument to investigate factors that may influence mathematics enrolment choice in senior secondary schools in Australia. The rationale for the model construction is explained.
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    The Mathematics Enrolment Choice Motivation Instrument
    Li, N ; Hine, G ; Blackley, S ; Cooke, A (MERGA Inc., 2019)
    The instrument of mathematics enrolment choice motivation (MECM) is designed to measure factors that influence student’s decisions to keep or drop mathematics in Year 11. Using survey responses from 289 Year 11 students, this paper presents the initial form of the instrument, examines its factor structure, internal consistency and discriminant power. The preliminary psychometric evidence supports the proposal of a reduced form with five scales for self-concept, self-efficacy, subjective value, anxiety and learning experience in mathematics. With a clearer factor structure and better item information characteristics, the short form is more practical for use with senior secondary students.
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    A Demonstration of Set-Points for Subjective Wellbeing
    Cummins, RA ; Li, N ; Wooden, M ; Stokes, M (Springer Nature, 2014-02-15)
    This paper presents evidence for the existence of ‘set-points’ for subjective wellbeing. Our results derive from a 10-year longitudinal study in which subjective wellbeing has been measured using a single question of general life satisfaction. The process of data analysis is driven by logic based on the theory of subjective wellbeing homeostasis. This analysis involves the iterative elimination of raw data, from 7,356 individual respondents, based on confidence limits. All results are projected onto a 0–100 point scale. We demonstrate evidence for the existence of set-points lying between 71 and 90 points, with an average set-point-range of 18–20 points for each person. The implications and limitations of these findings are discussed.