Physical systems modelling

We apply a range of analytical and computational techniques to the analysis of problems arising in the modelling of real world systems occurring in the physical and engineering sciences.

Our objective is to provide mathematically-based techniques that provide investigators with the necessary tools to plan, predict and optimise the behaviour of such systems. This may involve analysis of an existing mathematical model for a given system, or the construction of such a model where one is absent.

Current projects

Reactor modelling of anaerobic digester

The objective of the project is to promote sustainability by optimization of the methane production from sewage, vegetable or animal wastes. The basic purpose is to replace the fossil fuel generated methane by the more sustainable methane from wastes.

The modelling of the reactor dynamics is a complex one and suitable models for the chemical reactions for the different bacteria need to be found. The modelling has been simplified to a basic two step reactions involving two species of bacteria: the acidogenic bacteria which consume the initial complex solids substrates to produce volatile fatty acids and the methanogenic bacteria which feed on these volatile fatty acids to produce methane.

The range of stable operating conditions for the reactor in response to different systems variable is being examined.

Researchers: Associate Professor John Shepherd, Dr Andrew Stacey and Dr Ash Khan

Slurry flows

Investigation of slurry flows is important for mineral industry, biomass processing and waste processing. In the design of slurry handling systems such as channel flows, separators with which solids concentrates are separated from the clear liquid, knowledge of the physics underlying slurry flows enables us to optimize the design of systems that handle slurries. 

Slurry flows in channels with settling solids in various geometries are being investigated to determine the time for removal of the settled solids under different flow conditions. The settling solids produce non-Newtonian flows that are modelled using computational fluid dynamic (CFD) methods in RMIT. The flows are generally turbulent multiphase flows.  The problem is to dynamically model this process and determine the optimal time for removal of the solids. The clear liquid solids interface position is needed in order to determine the feasibility of recycling the clear liquid.

Researchers: Dr Yan Ding and Dr Ash Khan

Pollutant gas concentration from combustion

Reaction chemical engineering with multiphase reacting flows provides us tools to investigate problems caused by spread of pollutant from combustion products. In the open terrain with the knowledge of combustion reaction together with the geometry and prevailing conditions, it is possible to predict concentration profiles as functions of time and distances. Combustion of fires from coal or forests produces concentration of noxious gasses which depend on the terrain or geometry for enclosed spaces, and the prevailing winds. The object is to predict the concentration profiles of these pollutants as function of time and geometry.  RMIT  physical modelling group has the CFD tools to predict these concentrations.

Researchers: Dr Yan Ding, Dr John Gear and Dr Ash Khan

Transitions in slowly varying population models

When studying the evolution of populations modelled by differential equations (or systems of same), we are usually faced with equations in which, for mathematical simplicity, the defining model coefficients (parameters) are constants. This simplification makes the mathematical problems within such models relatively straightforward to solve analytically. However, when these models are modified to allow for time variation in the model parameters, such analytic solution is usually not possible, and numerical solution methods must be employed, with the limitations implicit in these.

When the parameter variation is slow, multiscaling methods may be used to construct analytic approximate expressions for the evolving populations. These expressions have proved to be quite accurate, but have been shown to fail in neighbourhoods of points we term transition points, where the model usually undergoes a fundamental change in solution behaviour.

In this ongoing project, we apply the multiscaling process to obtain approximate expressions for solutions away from transition points and seek to show how these may be linked by transition solutions, to provide an approximation for the evolving population right through such points

Researchers: Associate Professor John Shepherd, Dr Andrew Stacey and Dr John Gear

Helical flow of yield-stress fluids

Yield-stress fluids have the property that they remain effectively solid until the local stress in their structure reaches a certain ‘yield’ value, after which they flow as a (generally non-Newtonian) fluid. In the simplest example of such a fluid, the Bingham fluid, the flow, when it occurs, is Newtonian; i.e., the stress versus rate of shearing relationship is linear. Other fluids, such as the Herschel-Bulkley and Casson fluids display more complex stress-rate of shearing relationships upon yielding.

In this investigation, we consider helical flow of such fluids in the gap between infinite concentric cylinders, generated by a combination of axial pressure gradient and rotation of the inner cylinder. We apply a combination of analytic and numerical techniques to study the changes in the boundary of any solid-liquid zones with the flow characteristics.

Researchers: Associate Professor John Shepherd, Dr Andrew Stacey, Fahad Alharbi

Atherosclerosis research projects

Modelling of atherosclerosis formation and growth using computational fluid dynamics (CFD)

Atherosclerosis is a medical terminology meaning artery hardening that lead to Cardio Vascular (CV) diseases mainly from heart disease and stroke. According to the World Health Organization (WHO) fact sheet No. 317 released in March 2013, Cardio Vascular (CV) diseases are the ?rst leading cause of death globally; and the number of death will reach 23.3 million by year 2030. Thus, understanding of the progression of atherosclerosis is of a great importance in saving lives by developing effective disease diagnostic, prognostic and preventive technologies.

This project is focused on the modeling of atherosclerosis initial formation and subsequent growth. We are investigating the accumulation and consumption of lipid-carrying species such as low-density lipoproteins (LDL) in the arterial wall using Computational Fluid Dynamics. A mathematical model has been developed to describe the emergence and progression of atherosclerosis lesions. Lesion growth is defined to be proportional to LDL aggregate, where the inflammatory process is treated as implicit to it. With respect to LDL transporting through endothelium of the artery wall, a simple flux balance boundary condition is implemented. Atherosclerosis growth within the artery wall is then modeled as LDL aggregation beneath the endothelium of the artery wall.

Researchers: Dr Yan Ding, Dr John A. Gear, Mr. Sargon Gabriel (Ph.D student), Dr Yuqing Feng

Hemodynamic and mechanical effects on atherosclerotic lesion morphology

This project is to study the change of the lesion morphology due to the LDL aggregate. The project focuses on the growth of atherosclerotic lesions due to the hemodynamic and mechanical effects on the human arteries impacted by the disturbed blood flow. Since tissue growth is closely related to the state of the wall shear stress, a series of lesion morphologies, as the result of lesion growth, with stenosis severity ranging from 45% to 79% have been investigated using the fluid-structure interaction (FSI) modeling under an idealized sinusoidal input flow profile. Extensive simulation data have been obtained from both the fluid and the solid models using an idealized sinusoidal input blood flow profile, providing insightful data for the stress and strain distribution inside of the elevated lesion, as well as the wall shear stress distribution on the artery inner wall. These data are essential for the modeling of lesion expansion due to biochemical reactions within the lesion and the study of lesion rupture – the ultimate failure resulting fatality.

The current stage of the project is focused on performing further FSI simulations using parameterized lesion geometries and physiology blood flow profiles mimicking the flow conditions of both cardio-healthy and cardio-weak people. The aim of the project is to provide a comprehensive simulation data bank for further analytical and statistical studies of the field.

Researchers: Dr Yan Ding, Dr John A. Gear, Dr Yuqing Feng (CSIRO collaborator).

Influence of HDL and HDL on atherosclerotic lesion growth

A blood stream caries multiple particles, e.g. low density lipoprotein (LDL) and triglycerides, and high-density lipoprotein (HDL), etc. Thus, the blood flow is essentially a multiphase flow. In contrast to the “bad” role of LDL particles that increase the risk of cardio vascular (CV) diseases, the HDL particles are considered to be the “good” ones that help to clean up arteries and reduce the risk of CV. How the LDL and HDL particles interact with each other? And how this interaction affects the growth of an atherosclerotic lesion? These are research questions of the project. In this project, we are modeling a multiphase pulsatile blood flow through axis-asymmetric stenosed artery with different levels of severities, respectively. The blood flow is modelled as non-Newtonian Casson fluid model with LDL particles in suspension and mixing with HDL particles with different volume fractions. The artery is modelled as a rigid vessel. We are aiming to (a) investigate the LDL aggregation around the stenosis and the effect of HDL particles in reducing the LDL accumulation; (2) extend this project to include additional multiphase particles with anti-inflammatory agencies. Thus, the project has a great potential in study and investigation for the effective treatment methodologies of the disease.

Researchers: Dr Yan Ding, Dr John A. Gear, Dr Yuqing Feng (CSIRO collaborator).

Mathematical modeling of biochemical events

The focus of this project is to study the atherosclerotic lesion growth through biochemical interactions within the lesion. Under the endothelial layer of artery wall where LDL particles aggregate, a large amount of white blood cells would be gathered under the command of the body defense system to consume these LDL particles, resulting in a localized inflammatory site. So a lesion is an accumulation of white blood cells, especially macrophages that have taken up oxidized LDL. When these cells die, their contents are released, which attracts more macrophages and creates an extracellular lipid core near the center to inner surface of each atherosclerotic plaque. Conversely, the outer, older portions of the plaque become more calci?c, less metabolically active and more physically sti? over time. This project is to model the inflammatory process due to these biochemical reactions by modeling and solving the system of partial differential equations using numerical methods.

Researchers: Dr Yan Ding, Dr John A. Gear, Dr Yuqing Feng (CSIRO collaborator).

Study of atherosclerotic lesion rupture

Atherosclerotic lesion rupture is the failure of the lesion that closely associated with the fatality. At the very mature stage of the lesion growth, the artery becomes so blocked that the lesion may be ripped open or the outer artery wall becomes severely weakened. At the event of atherosclerotic plaque rupture, a large quantity of thrombogenic cells and lipids can be released into the blood stream in a very short period of time forming deadly blood clots that may result in myocardial infarction or stroke. On the other hand, a severely weakened artery wall can lead to a bulge in the wall called an aneurysm. Aneurysms can break open the artery. This causes bleeding that can be life It has been commonly agreed in the research community that stress and strain fields in the stenosed artery wall were greatly affected by the stenosis severity, lesion morphology including the size and shape of lipid pool and the thickness of the fibrous cap of the plague. In this study, we propose to use the same geometry morphology models developed in Project 2 but include calcification particles with different shape and size. These hard particles are located at the maximum stress locations within the plague based on the simulation results obtained in Project 2. The study is to investigate the rupture failure of the atherosclerotic lesion due to the effect of the local stressors from the calcification particles. The aim of the study is to develop the effective treatment strategy for alleviating the adverse effect from the calcification particles and improve the lesion rupture prediction.

Researchers: Dr Yan Ding, Dr John A. Gear, Dr Yuqing Feng (CSIRO collaborator).

Proposed projects

Population models involving time delays

Many ecosystems are “stressed” when external factors such as pollution, land clearing and sudden shocks to the environment arise. However, most current models that are used by ecologists do not include the changing environment.

Here, we aim to develop mathematical models that directly couple the dynamics of one or two species with a changing environment. This is achieved by treating the carrying capacity, a proxy for the state of the environment, as a state variable in the governing equations of the model. In this way, any changes to the environment can be naturally reflected in the survival, movement and competition of the species within the ecosystem. Further and as important is the impact of the presence of species on the habitat in which they live.

An equally important feature of our models is in the recognition that environments and species do not immediately respond to external shocks.  The effect of a shock on a community and the subsequent response is a dynamical process that involves time-delays from the onset of the shock to the environment’s response. We aim to incorporate such delays and investigate their effects on the evolving population(s).

Researchers: Associate Professor John Shepherd, Dr Andrew Stacey, Associate Professor Harvi Sidhu (UNSW Canberra), Dr Zlatko Jovanovski (UNSW Canberra)


HDR candidates

  • Mr Sargon Gabriel
  • Mr Fahad Alharbi
  • Ms Monika Buljan

Undertake a research degree

Prospective Higher Degree by Research applicants should contact one of our academic or post-doc members to discuss supervision of a research project.

Related research degrees

PhD (Mathematical Sciences)

Master of Science (Mathematical Sciences)


For more information about our research, please contact Associate Professor John Shepherd.

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Acknowledgement of country

RMIT University acknowledges the people of the Woi wurrung and Boon wurrung language groups of the eastern Kulin Nations on whose unceded lands we conduct the business of the University. RMIT University respectfully acknowledges their Ancestors and Elders, past and present. RMIT also acknowledges the Traditional Custodians and their Ancestors of the lands and waters across Australia where we conduct our business.

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