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Research paper thumbnail of Contents C1466 Contents

Many dierent combustion situations exhibit bifurcations. Some of these are merely artefacts of th... more Many dierent combustion situations exhibit bifurcations. Some of these are merely artefacts of the models constructed, but others are of physical signicance. This paper will discuss the calculation of this behaviour as it occurs in several situations; namely, spontaneous ther-mal ignition in a sphere, propagating flames and microgravity flame

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Research paper thumbnail of Bifurcating combustion behaviour

ANZIAM Journal, 2000

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Research paper thumbnail of Analysing combustion waves in a model with chain branching

ANZIAM Journal, 2007

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Research paper thumbnail of Activated Sludge Wastewater Treatment Process: Performance Comparison between a Two-reactor Cascade and a Single Tank

We investigate a model for the treatment of wastewater in the activated sludge process. The proce... more We investigate a model for the treatment of wastewater in the activated sludge process. The process is based on the aeration of wastewater with flocculating biological growth, followed by the separation of treated wastewater from biological growth. Part of this growth is wasted, and the remainder returned to the system. The biochemical model consists of two types of bacteria, sludge bacteria and sewage bacteria, and two types of ciliated protozoa, free-swimming ciliates and ciliates attached to sludge flocs. A combination of steady-state analysis, path following techniques and numerical integration of the governing equations are used to study the dynamics of this system in a network of two coupled reactors arranged in a series. We compare the treatment efficiency for a single tank system with that of a two-reactor cascade. In the latter scenario the total residence time is fixed and the residence time in the first reactor is taken to be a design parameter. Process parameters that en...

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Research paper thumbnail of Analysing the stability of premixed rich hydrogen–air flame with the use of two-step models

Combustion and Flame, 2013

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Research paper thumbnail of Period doubling and chaotic transient in a model of chain-branching combustion wave propagation

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2010

The propagation of planar combustion waves in an adiabatic model with two-step chain-branching re... more The propagation of planar combustion waves in an adiabatic model with two-step chain-branching reaction mechanism is investigated. The travelling combustion wave becomes unstable with respect to pulsating perturbations as the critical parameter values for the Hopf bifurcation are crossed in the parameter space. The Hopf bifurcation is demonstrated to be of a supercritical nature and it gives rise to periodic pulsating combustion waves as the neutral stability boundary is crossed. The increase of the ambient temperature is found to have a stabilizing effect on the propagation of the combustion waves. However, it does not qualitatively change the behaviour of the travelling combustion waves. Further increase of the bifurcation parameter leads to the period-doubling bifurcation cascade and a chaotic regime of combustion wave propagation. The chaotic regime has a transient nature and the combustion wave extinguishes when the bifurcation parameter becomes sufficiently large. For Lewis nu...

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Research paper thumbnail of Evans function stability of non-adiabatic combustion waves

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2004

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Research paper thumbnail of Mathematics for medical practitioners and patients: Understanding how vaccines work for the community

Australian Journal of General Practice

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Research paper thumbnail of Determining critical conditions for two dimensional compost piles with air flow via numerical simulations

ANZIAM Journal

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Research paper thumbnail of A springs and masses model for determining the lowest risk path in a threat environment

ANZIAM Journal

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Research paper thumbnail of The thermal ignition problem in a cube

ANZIAM Journal

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Research paper thumbnail of Numerical investigation of a reaction in a batch reactor: flammability limits

ANZIAM Journal

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Research paper thumbnail of An economic order quantity model with reverse logistics program

Operations Research Perspectives

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Research paper thumbnail of Two continuous methods for determining a minimal risk path through a minefield

ANZIAM Journal

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Research paper thumbnail of On the route to extinction in non-adiabatic flames from competitive exothermic reactions

Mathematical Modelling of Natural Phenomena

We consider non-adiabatic combustion waves arising from two-step competitive exothermic reaction ... more We consider non-adiabatic combustion waves arising from two-step competitive exothermic reaction schemes. A numerical method is employed to study the behaviour of this system and we show that the inclusion of heat loss can lead to a period-doubling route to the termination of the propagating flame front. The nature of oscillations becomes more complex with increasing loss of heat until the system can no longer sustain a propagating front. In other words, beyond some critical value of heat loss, extinction of the combustion reaction would occur. For the non-adiabatic case, particularly close to the extinction threshold, large excursions in temperature and wave speed above those observed for the adiabatic case can occur. Such behaviour close to extinction may have implications for safety or industrial processes.

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Research paper thumbnail of Analysis of two-dimensional combustion waves arising in the presence of a competitive endothermic reaction

ANZIAM Journal

We consider a system of reaction-diffusion equations describing combustion dynamics. The reaction... more We consider a system of reaction-diffusion equations describing combustion dynamics. The reaction is assumed to undergo two competitive reactions, one which is exothermic and one which is endothermic. The one-dimensional model has been shown to exhibit complex behaviour, from propagating combustion waves with a constant speed to period doubling cascades and the possibility of chaotic wave speeds. In this study, we extend the combustion model from one to two dimensions by exploring a model of an insulated strip with no heat loss and axially symmetric spread. In particular, we compare and contrast the behaviour of the systems in one and two dimensions. References J. D. Buckmaster and G. S. S. Ludford. Theory of Laminar Flames. Cambridge Monographs on Mechanics and Applied Mathematics. Cambridge University Press, 1982. doi:10.1017/CBO9780511569531. V. Gubernov, A. Kolobov, A. Polezhaev, H. Sidhu, and G. Mercer. Period doubling and chaotic transient in a model of chain-branching combust...

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Research paper thumbnail of Combustion meeting in honour of Professor B. F. Gray

The ANZIAM Journal

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Research paper thumbnail of A two dimensional, reaction-diffusion model of compost piles

ANZIAM Journal

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Research paper thumbnail of A mathematical model for heat transfer in fire fighting suits containing phase change materials

Fire Safety Journal

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Research paper thumbnail of A dynamical systems model for fireline growth with suppression

ANZIAM Journal

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Research paper thumbnail of Contents C1466 Contents

Many dierent combustion situations exhibit bifurcations. Some of these are merely artefacts of th... more Many dierent combustion situations exhibit bifurcations. Some of these are merely artefacts of the models constructed, but others are of physical signicance. This paper will discuss the calculation of this behaviour as it occurs in several situations; namely, spontaneous ther-mal ignition in a sphere, propagating flames and microgravity flame

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Bifurcating combustion behaviour

ANZIAM Journal, 2000

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Analysing combustion waves in a model with chain branching

ANZIAM Journal, 2007

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Activated Sludge Wastewater Treatment Process: Performance Comparison between a Two-reactor Cascade and a Single Tank

We investigate a model for the treatment of wastewater in the activated sludge process. The proce... more We investigate a model for the treatment of wastewater in the activated sludge process. The process is based on the aeration of wastewater with flocculating biological growth, followed by the separation of treated wastewater from biological growth. Part of this growth is wasted, and the remainder returned to the system. The biochemical model consists of two types of bacteria, sludge bacteria and sewage bacteria, and two types of ciliated protozoa, free-swimming ciliates and ciliates attached to sludge flocs. A combination of steady-state analysis, path following techniques and numerical integration of the governing equations are used to study the dynamics of this system in a network of two coupled reactors arranged in a series. We compare the treatment efficiency for a single tank system with that of a two-reactor cascade. In the latter scenario the total residence time is fixed and the residence time in the first reactor is taken to be a design parameter. Process parameters that en...

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Research paper thumbnail of Analysing the stability of premixed rich hydrogen–air flame with the use of two-step models

Combustion and Flame, 2013

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Period doubling and chaotic transient in a model of chain-branching combustion wave propagation

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2010

The propagation of planar combustion waves in an adiabatic model with two-step chain-branching re... more The propagation of planar combustion waves in an adiabatic model with two-step chain-branching reaction mechanism is investigated. The travelling combustion wave becomes unstable with respect to pulsating perturbations as the critical parameter values for the Hopf bifurcation are crossed in the parameter space. The Hopf bifurcation is demonstrated to be of a supercritical nature and it gives rise to periodic pulsating combustion waves as the neutral stability boundary is crossed. The increase of the ambient temperature is found to have a stabilizing effect on the propagation of the combustion waves. However, it does not qualitatively change the behaviour of the travelling combustion waves. Further increase of the bifurcation parameter leads to the period-doubling bifurcation cascade and a chaotic regime of combustion wave propagation. The chaotic regime has a transient nature and the combustion wave extinguishes when the bifurcation parameter becomes sufficiently large. For Lewis nu...

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Research paper thumbnail of Evans function stability of non-adiabatic combustion waves

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2004

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Research paper thumbnail of Mathematics for medical practitioners and patients: Understanding how vaccines work for the community

Australian Journal of General Practice

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Research paper thumbnail of Determining critical conditions for two dimensional compost piles with air flow via numerical simulations

ANZIAM Journal

Bookmarks Related papers MentionsView impact

Research paper thumbnail of A springs and masses model for determining the lowest risk path in a threat environment

ANZIAM Journal

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Research paper thumbnail of The thermal ignition problem in a cube

ANZIAM Journal

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Numerical investigation of a reaction in a batch reactor: flammability limits

ANZIAM Journal

Bookmarks Related papers MentionsView impact

Research paper thumbnail of An economic order quantity model with reverse logistics program

Operations Research Perspectives

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Two continuous methods for determining a minimal risk path through a minefield

ANZIAM Journal

Bookmarks Related papers MentionsView impact

Research paper thumbnail of On the route to extinction in non-adiabatic flames from competitive exothermic reactions

Mathematical Modelling of Natural Phenomena

We consider non-adiabatic combustion waves arising from two-step competitive exothermic reaction ... more We consider non-adiabatic combustion waves arising from two-step competitive exothermic reaction schemes. A numerical method is employed to study the behaviour of this system and we show that the inclusion of heat loss can lead to a period-doubling route to the termination of the propagating flame front. The nature of oscillations becomes more complex with increasing loss of heat until the system can no longer sustain a propagating front. In other words, beyond some critical value of heat loss, extinction of the combustion reaction would occur. For the non-adiabatic case, particularly close to the extinction threshold, large excursions in temperature and wave speed above those observed for the adiabatic case can occur. Such behaviour close to extinction may have implications for safety or industrial processes.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Analysis of two-dimensional combustion waves arising in the presence of a competitive endothermic reaction

ANZIAM Journal

We consider a system of reaction-diffusion equations describing combustion dynamics. The reaction... more We consider a system of reaction-diffusion equations describing combustion dynamics. The reaction is assumed to undergo two competitive reactions, one which is exothermic and one which is endothermic. The one-dimensional model has been shown to exhibit complex behaviour, from propagating combustion waves with a constant speed to period doubling cascades and the possibility of chaotic wave speeds. In this study, we extend the combustion model from one to two dimensions by exploring a model of an insulated strip with no heat loss and axially symmetric spread. In particular, we compare and contrast the behaviour of the systems in one and two dimensions. References J. D. Buckmaster and G. S. S. Ludford. Theory of Laminar Flames. Cambridge Monographs on Mechanics and Applied Mathematics. Cambridge University Press, 1982. doi:10.1017/CBO9780511569531. V. Gubernov, A. Kolobov, A. Polezhaev, H. Sidhu, and G. Mercer. Period doubling and chaotic transient in a model of chain-branching combust...

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Research paper thumbnail of Combustion meeting in honour of Professor B. F. Gray

The ANZIAM Journal

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Research paper thumbnail of A two dimensional, reaction-diffusion model of compost piles

ANZIAM Journal

Bookmarks Related papers MentionsView impact

Research paper thumbnail of A mathematical model for heat transfer in fire fighting suits containing phase change materials

Fire Safety Journal

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Research paper thumbnail of A dynamical systems model for fireline growth with suppression

ANZIAM Journal

Bookmarks Related papers MentionsView impact