Australian Mathematical Sciences Institute - Research Publications

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    2-D solitary waves in thermal media with nonsymmetric boundary conditions
    Louis, SA ; Marchant, TR ; Smyth, NF (WILEY, 2019-05)
    Abstract Optical solitary waves and their stability in focusing thermal optical media, such as lead glasses, are studied numerically and theoretically in (2 + 1) dimensions. The optical medium is a square cell and mixed boundary conditions of Newton cooling and fixed temperature on different sides of the cell are used. Nonlinear thermal optical media have a refractive index which depends on temperature, so that heating from the optical beam and heat flow across the boundaries can change the refractive index of the medium. Solitary wave solutions are found numerically using the Newton conjugate‐gradient method, while their stability is studied using a linearized stability analysis and also via numerical simulations. It is found that the position of the solitary wave is dependent on the boundary conditions, with the center of the beam moving toward the warmer boundaries, as the parameters are varied. The stability of the solitary waves depends on the symmetry of the boundary conditions and the amplitude of the solitary waves.
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    Panel Conditioning and Subjective Well-being
    Wooden, M ; Li, N (SPRINGER, 2014-05)
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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.