 Australian Mathematical Sciences Institute  Research Publications
Australian Mathematical Sciences Institute  Research Publications
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ItemNo Preview AvailableNumerical and analytical study of undular bores governed by the full water wave equations and bidirectional WhithamBoussinesq equationsVargasMagana, RM ; Marchant, TR ; Smyth, NF (AMER INST PHYSICS, 202106)Undular bores, also termed dispersive shock waves, generated by an initial discontinuity in height as governed by two forms of the Boussinesq system of weakly nonlinear shallow water wave theory, the standard formulation and a Hamiltonian formulation, two related Whitham–Boussinesq equations, and the full water wave equations for gravity surface waves are studied and compared. It is found that the Whitham–Boussinesq systems give solutions in excellent agreement with numerical solutions of the full water wave equations for the positions of the leading and trailing edges of the bore up until the onset on modulational instability. The Whitham–Boussinesq systems, which are far simpler than the full water wave equations, can then be used to accurately model surface water wave undular bores. Finally, comparisons with numerical solutions of the full water wave equations show that the Whitham–Boussinesq systems give a slightly lower threshold for the onset of modulational instability in terms of the height of the initial step generating the undular bore.

Item2D solitary waves in thermal media with nonsymmetric boundary conditionsLouis, SA ; Marchant, TR ; Smyth, NF (WILEY, 201905)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.

ItemConfirmation of Subjective Wellbeing SetPoints: Foundational for Subjective Social IndicatorsCapic, T ; Li, N ; Cummins, RA (SPRINGER, 201805)

ItemMultidimensionality of Longitudinal Data: Unlocking the AgeHappiness PuzzleLi, N (SPRINGER, 201608)

ItemPanel Conditioning and Subjective WellbeingWooden, M ; Li, N (SPRINGER, 201405)

ItemNematic Dispersive Shock Waves from Nonlocal to LocalBaqer, S ; Frantzeskakis, DJ ; Horikis, TP ; Houdeville, C ; Marchant, TR ; Smyth, NF (MDPI, 202106)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.

ItemUnderstanding Motivation behind Mathematics Enrolment Choice in Senior Secondary Schools: Questionnaire DesignLi, 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.

ItemThe Mathematics Enrolment Choice Motivation InstrumentLi, 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 selfconcept, selfefficacy, 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.

ItemA Demonstration of SetPoints for Subjective WellbeingCummins, RA ; Li, N ; Wooden, M ; Stokes, M (Springer Nature, 20140215)This paper presents evidence for the existence of ‘setpoints’ for subjective wellbeing. Our results derive from a 10year 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 setpoints lying between 71 and 90 points, with an average setpointrange of 18–20 points for each person. The implications and limitations of these findings are discussed.