Continuum Mechanics

The Continuum Mechanics group consists of two subgroups:

Staff

Joseph Cousins : Research Assistant

;

Member of other research groups: Continuum Mechanics - Modelling and Analysis of Material Systems, Continuum Mechanics - Fluid Dynamics and Magnetohydrodynamics

  • Prof Nicholas A Hill : Simson Chair

    Biological and physiological fluid dynamics; bioconvection; physiological pulse propagation;; Soft tissue mechanics; aneurysms; aortic dissection; gall bladder pain; upscaling; Random walk models for movement of micro-organisms and animals; spatial point processes in plant ecology

    Member of other research groups: Mathematical Biology, Continuum Mechanics - Modelling and Analysis of Material Systems, Continuum Mechanics - Fluid Dynamics and Magnetohydrodynamics
    Research students: Jay MacKenzie, Roxanna Barry, Laura Miller
    Postgraduate opportunities: A coupled cardiovascular-respiration model for mechanical ventilation

  • Personal Website
  • Publications
  • Dr Wenguang Li : Postdoctoral Research Fellow

    Biomechanics; modelling of gallbladder; non-linear finite strain modelling

    Member of other research groups: Continuum Mechanics - Modelling and Analysis of Material Systems
    Supervisor: Xiaoyu Luo

  • Publications
  • Prof Xiaoyu Luo : Professor of Applied Mathematics

    Biomechanics; fluid-structure interactions; mathematical biology ; solid mechanics

    Member of other research groups: Mathematical Biology, Continuum Mechanics - Modelling and Analysis of Material Systems, Continuum Mechanics - Fluid Dynamics and Magnetohydrodynamics
    Research staff: Hao Gao, Wenguang Li, Qingying Shu
    Research students: Debao Guan, Xin Zhuan, Ahmed Mostafa Abdelhady Ismaeel, Jay MacKenzie, Yingjie Wang
    Postgraduate opportunities: Assessing risk of heart failure with cardiac modelling and statistical inference

  • Personal Website
  • Publications
  • Dr David MacTaggart : Lecturer

    Theoretical fluid dynamics, Magnetohydrodynamics

    Member of other research groups: Continuum Mechanics - Fluid Dynamics and Magnetohydrodynamics
    Research students: Jamie Quinn, Parag Gupta

  • Personal Website
  • Publications
  • Prof Nigel Mottram : Professor of Applied Mathematics

    My research interests are in the mathematical modelling of real-world systems, generally focussing on those that include the dynamics of non-Newtonian fluids. I am particularly interested in anisotropic fluids such as liquid crystals, where viscoelasticity is an important consideration, as is their behaviour under electric fields.

    Member of other research groups: Mathematical Biology, Continuum Mechanics - Modelling and Analysis of Material Systems, Continuum Mechanics - Fluid Dynamics and Magnetohydrodynamics
    Research student: Parna Mandal
    Postgraduate opportunities: Mathematical Modelling of Liquid Crystal Displays, Flow of groundwater in soils with vegetation and variable surface influx, Mathematical Modelling of Active Fluids, Flow of glacial ice sheets over deformable material, Viscous fingering instabilities: control and flow-structure interaction

  • Dr Raymond W Ogden : George Sinclair Chair

    Nonlinear elasticity; biomechanics

    Member of other research groups: Continuum Mechanics - Modelling and Analysis of Material Systems
    Research staff: Andrey Melnik

  • Personal Website
  • Publications
  • Dr Raimondo Penta : Lecturer

    Member of other research groups: Mathematical Biology, Continuum Mechanics - Modelling and Analysis of Material Systems, Continuum Mechanics - Fluid Dynamics and Magnetohydrodynamics
    Research students: Tahani Al Sariri, Laura Miller

  • Personal Website
  • Publications
  • Dr Ariel Ramirez Torres : Lecturer

    My scientific interests range several fields, including multi-scale expansions, non-linear mechanics, composite materials and non-local phenomena, and my research addresses problems of current interest in Homogenisation Theory, Continuum Mechanics, Mathematical Biology and Fractional Calculus. In particular, the focus of my investigations is on the mathematical modelling of biological media and processes that are of importance in real-world problems.

    Member of other research groups: Mathematical Biology, Continuum Mechanics - Modelling and Analysis of Material Systems, Continuum Mechanics - Fluid Dynamics and Magnetohydrodynamics

  • Dr Steven Roper : Lecturer

    I am interested in applications of continuum mechanics to phenomena in materials science. In particular problems involving solid mechanics and surface science (the combined chemical and mechanical equilibrium of droplets of fluid in contact with soluble substrates); crystal growth; pattern formation (block co-polymers).; I am interested in applications of fluid mechanics to industrial and geophysical problems. In particular in fluid-driven fracture (the interaction of flow fluid with fracture mechanics); porous media (particularly the reactive porous media found in the solidification of pure and alloyed materials - mushy layers); compositional convection; low Reynolds number flow (thin films and free surface flows); the behaviour of foams.

    Member of other research groups: Continuum Mechanics - Modelling and Analysis of Material Systems, Continuum Mechanics - Fluid Dynamics and Magnetohydrodynamics
    Research student: Bushra Al-Ghabshi

  • Personal Website
  • Publications
  • Dr Radostin Simitev : Reader

    Reaction-diffusion equations; Excitable systems; Mathematical models of cardiac electrical excitation; Thermal convection in rotating systems; MHD and dynamo theory

    Member of other research groups: Mathematical Biology, Continuum Mechanics - Fluid Dynamics and Magnetohydrodynamics
    Research students: Muhamad Bin Noor Aziz, Parag Gupta, Antesar Mohammed Al Dawoud, Peter Mortensen, Tahani Al Sariri, Jamie Quinn
    Postgraduate opportunities: Electrophysiological modelling of hearts with diseases, Fast-slow asymptotic analysis of cardiac excitation models, Numerical simulations of planetary and stellar dynamos

  • Personal Website
  • Publications
  • Dr Peter Stewart : Senior lecturer

    ; ;

    Member of other research groups: Mathematical Biology, Continuum Mechanics - Modelling and Analysis of Material Systems, Continuum Mechanics - Fluid Dynamics and Magnetohydrodynamics
    Research students: Roxanna Barry, Ahmed Mostafa Abdelhady Ismaeel, Gordon McNicol, Ifeanyi Onah Sunday
    Postgraduate opportunities: Mathematical models of vasculogenesis, A coupled cardiovascular-respiration model for mechanical ventilation , Predicting patterns of retinal haemorrhage, Theoretical modelling of cell response to external cues, Radial foam fracture, Continuous production of solid metal foams

  • Personal Website
  • Publications
  • Dr Robert Teed : Lecturer

    Magnetohydrodynamics; Dynamo theory; Convection in astrophysical and geophysical bodies; the geodynamo; planetary dynamos; the solar dynamo and solar cycle.

    Member of other research groups: Continuum Mechanics - Fluid Dynamics and Magnetohydrodynamics

  • Personal Website
  • Publications
  • Dr Stephen J Watson : Lecturer

    ; The application of new mathematical ideas and new computational paradigms to material science, with an emphasis on self-assembling nano-materials; analysis and numerical analysis of partial differential equations arising in Continuum Physics; Material Science and Geometry.

    Member of other research groups: Continuum Mechanics - Modelling and Analysis of Material Systems, Analysis

  • Publications

  • Postgraduates

    Bushra Al-Ghabshi : PhD Student

    Member of other research groups: Continuum Mechanics - Modelling and Analysis of Material Systems
    Supervisor: Steven Roper

  • Parag Gupta : PhD Student

    Research Topic: Modelling of stellar differential rotation and related dynamo properties
    Member of other research groups: Continuum Mechanics - Fluid Dynamics and Magnetohydrodynamics
    Supervisors: Radostin Simitev, David MacTaggart

  • Parna Mandal : PhD Student

    ;

    Research Topic: Optimising antibiotic release from medical implants to counteract biofilm formation
    Member of other research groups: Continuum Mechanics - Modelling and Analysis of Material Systems, Continuum Mechanics - Fluid Dynamics and Magnetohydrodynamics
    Supervisor: Nigel Mottram

  • Laura Miller : PhD Student

    ;

    Member of other research groups: Mathematical Biology, Continuum Mechanics - Modelling and Analysis of Material Systems
    Supervisors: Raimondo Penta, Nicholas A Hill

  • Jamie Quinn : PhD Student

    Member of other research groups: Continuum Mechanics - Fluid Dynamics and Magnetohydrodynamics
    Supervisors: David MacTaggart, Radostin Simitev

  • Xin Zhuan : PhD Student

    ;

    Research Topic: Heart tissue remodelling under stress
    Member of other research groups: Mathematical Biology, Continuum Mechanics - Modelling and Analysis of Material Systems
    Supervisor: Xiaoyu Luo


  • Postgraduate opportunities

    Continuous production of solid metal foams (PhD)

    Supervisors: Peter Stewart
    Relevant research groups: Continuum Mechanics - Fluid Dynamics and Magnetohydrodynamics, Continuum Mechanics - Modelling and Analysis of Material Systems

    Porous metallic solids, or solid metal foams, are exceedingly useful in many engineering applications, as they can be manufactured to be strong yet exceedingly lightweight. However, industrial processing methods for producing such foams are problematic and unreliable, and it is not currently possible to control the porosity distribution of the final product a priori.


    This project will consider a new method of solid foam production, where bubbles of gas are introduced continuously into a molten metal flowing through a heat exchanger; foaming and solidification then occur almost simulatanously, allowing the foam structure to be controlled pointwise. The aim of this project is to construct a simple mathematical model for a gas bubble moving in a liquid filled channel ahead of a solidification front, to predict optimal conditions whereby the gas bubble is drawn toward the phase boundary, hence forming a porous solid.


    This project will require some background in fluid mechanics and a combination of analytical and numerical techniques for solving partial differential equations.

     

    Radial foam fracture (PhD)

    Supervisors: Peter Stewart
    Relevant research groups: Continuum Mechanics - Fluid Dynamics and Magnetohydrodynamics, Continuum Mechanics - Modelling and Analysis of Material Systems

    Gas-liquid foams are a useful analgoue of crystalline atomic solids. 2D foam fracture has been used to study the mechanisms of fracture in metals. A two-dimenisonal network model (formed from a large system of differential equations) has recently been produced to study foam fracture in a rectangular channel which is pressurised along one edge. This model has helped to explain the origin of the velocity gap (a range of inadmissable steady fracture velocities), observed both in foam fracture experiments and in atomistic simulations of brittle fracture. This project will apply this network modelling approach to study radial foam fracture in a Hele-Shaw cell, to mimick recent experiments. This system has strong similarity to radial Saffmann-Taylor fingering, where fingering has been observed when a less viscous fluid displaces a more viscous fluid in a confined geometry. This project will involve studying systems of ordinary and partial differential equations using both numerical and analytical methods.

     

    Predicting patterns of retinal haemorrhage (PhD)

    Supervisors: Peter Stewart
    Relevant research groups: Continuum Mechanics - Fluid Dynamics and Magnetohydrodynamics, Continuum Mechanics - Modelling and Analysis of Material Systems, Mathematical Biology, Statistics and Data Analytics

    Retinal haemorrhage (bleeding of the blood vessels in the retina) often accompanies traumatic brain injury and is one of the clinical indicators of `shaken baby syndrome'. This PhD project will give you the opportunity to develop a combination of mathematical and statistical models to help explain the onset of retinal haemorrhage. You will devise and implement image processing algorithms to quantify the pattern of bleeding in clinical images of haemorrhaged retinas. In addition, you will develop a mathematical model for pressure wave propagation through the retinal circulation in response to an acute rise in intracranial pressure, to predict the pattern of retinal bleeding and correlate to the images. Cutting-edge pattern recognition methods from Machine Learning and Bayesian modelling will be used to infer characteristic signatures of different types of brain trauma. These will be used to help clinicians in characterising the origin of traumatic brain injury and diagnosing its severity. This is an ideal project for a postgraduate student with an interest in applying mathematical modelling, image analysis and machine learning to predictive healthcare. The project will give you the opportunity to join a cross-disciplinary Research Hub that aims to push the boundaries of quantitative medicine and improve clinical decision making in cases of suspected non-accidental head injury using innovative mathematical and statistical modelling.

     

    Numerical simulations of planetary and stellar dynamos (PhD)

    Supervisors: Radostin Simitev
    Relevant research groups: Continuum Mechanics - Fluid Dynamics and Magnetohydrodynamics

    Using Fluid Dynamics and Magnetohydrodynamics to model the magnetic fields of the Earth, planets, the Sun and stars. Involves high-performance computing. 

     

     

    Theoretical modelling of cell response to external cues (PhD)

    Supervisors: Peter Stewart
    Relevant research groups: Continuum Mechanics - Fluid Dynamics and Magnetohydrodynamics, Continuum Mechanics - Modelling and Analysis of Material Systems, Mathematical Biology

    Cells and tissues respond to mechanotransductive and biochemical cues. These external cues interact with protein signaling pathways within the cell and can trigger changes in size, structure, binding and differentiation. This project will use theoretical modelling to examine the response of an array of cells to various external mechanical and biochemical cues, considering how these cues can be tailored to optimize a particular outcome. The model will couple the mechanical components of the cell (nucleus, cytoskeleton,…) to internal protein expression pathways (Myosin II, MLCK,…) and the properties of the external stimuli. The model will take the form of coupled differential equations which will be solved using both analytical and numerical methods.

    This model will be validated against experimental data in two main ways, including examining the response of the array to small amplitude mechanical vibration (‘nanokicking’) to predict its influence on the behavior of the array over long timescales. The model will also be used to understand growth factor delivery using PODS® technology developed by Cell Guidance Systems to predict the optimal spatial arrangement of PODS® relative to the array and the resulting temporal and spatial profiles of both the growth factor and the cell growth and proliferation.

    This project involves collaboration with Prof Matt Dalby (Institute of Molecular, Cell and Systems Biology).

     

    Mathematical models of vasculogenesis (PhD)

    Supervisors: Peter Stewart
    Relevant research groups: Continuum Mechanics - Fluid Dynamics and Magnetohydrodynamics, Continuum Mechanics - Modelling and Analysis of Material Systems, Mathematical Biology

    Vasculogenesis is the process of forming new blood vessels from endothelial cells, which occurs during embryonic development. Viable blood vessels facilitate tissue perfusion, allowing the tissue to grow beyond the diffusion-limited size. However, in the absence of vasculogenesis, efforts to engineer functional tissues (eg for implantation) are restricted to this diffusion-limited size. This project will investigate mathematical models for vasculogenesis and explore mechanisms to stimulate blood vessel formation for in vitro tissues. The project will involve collaboration with Department of Biological Engineering at MIT, as part of the SofTMechMP project.

     

    Mathematical Modelling of Active Fluids (PhD)

    Supervisors: Nigel Mottram
    Relevant research groups: Continuum Mechanics - Fluid Dynamics and Magnetohydrodynamics, Mathematical Biology

     

    The area of active fluids is currently a “hot topic” in biological, physical and mathematical research circles. Such fluids contain active organisms which can be influenced by the flow of fluid around them but, crucially, also influence the flow themselves, i.e. by swimming. When the organisms are anisotropic (as is often the case) a model of such a system must include these inherent symmetries. Models of bacteria and even larger organisms such as fish have started to be developed over the last ten years in order to examine the order, self-organisation and pattern formation within these systems, although direct correlation and comparison to real-world situations has been limited.

    This project will use the theories and modelling techniques of liquid crystal systems and apply such modelling techniques to the area of anisotropy and self-organisation derived from active agents. The research will involve a continuum description of the fluid, using equations similar to the classical Navier-Stokes equations, as well as both the analytical and numerical solution of ordinary and partial differential equations.

    Contact nigel.mottram@glasgow.ac.uk for more details

     

     

    Flow of groundwater in soils with vegetation and variable surface influx (PhD)

    Supervisors: Nigel Mottram
    Relevant research groups: Continuum Mechanics - Fluid Dynamics and Magnetohydrodynamics, Mathematical Biology

    Groundwater is the water underneath the surface of the earth, which fills the small spaces in the soil and rock, and is extremely important as a water supply in many areas of the world. In the UK, groundwater sources, or aquifers, make up over 30% of the water used, and a single borehole can provide up to 10 million litres of water every day (enough for 70,000 people).

    The flow of water into and out of these aquifers is clearly an important issue, more so since current extraction rates are using up this groundwater at a faster rate than it is being replenished. In any specific location the fluxes of water occur from precipitation infiltrating from the surface, evaporation from the surface, influx from surrounding areas under the surface, the flow of surface water (e.g. rivers) into the area, and the transpiration of water from underground directly into the atmosphere by the action of rooted plants.

    This complicated system can be modelled using various models and combined into a single system of differential equations. This project will consider single site depth-only models where, even for systems which include complicated rooting profiles, analytical solutions are possible, but also two- and three-dimensional models in which the relatively shallow depth compared to the plan area of the aquifer can be utilised to make certain "thin-film" approximations to the governing equations.

    Contact nigel.mottram@glasgow.ac.uk for more details

     

     

    Mathematical Modelling of Liquid Crystal Displays (PhD)

    Supervisors: Nigel Mottram
    Relevant research groups: Continuum Mechanics - Fluid Dynamics and Magnetohydrodynamics, Continuum Mechanics - Modelling and Analysis of Material Systems

    In the modern world, Liquid Crystal Displays are all around us - from your TV and mobile phone, to the small display on your washing machine. Within these displays are thin layers of liquid, which react to an applied electric field to switch between different states. These states have different molecular configurations, and it is how these molecular arrangements interact with liqht that make them crucial to display technologies. The mathematical modelling of these molecular arrangements, using a continuum mechanics approach, has been essential to the development of LCDs over the last thirty years.

    In this project we will consider the mathematical modelling of novel types of displays, based on confined regions of liquid crystal and effects such as flexoelectricity and defect latching. As well as the development of these models, and the derivation of the resulting partial differential equations, this project will involve analytic and numerical methods for solving the equations.

    The results of this project will lead to a deeper understanding of liquid crystals in confinement but will also help display device manufacturers understand how to improve current and new displays.

    Contact nigel.mottram@glasgow.ac.uk for more details

     

    Viscous fingering instabilities: control and flow-structure interaction (PhD)

    Supervisors: Katarzyna Kowal, Nigel Mottram
    Relevant research groups: Continuum Mechanics - Fluid Dynamics and Magnetohydrodynamics, Continuum Mechanics - Modelling and Analysis of Material Systems

    The interface between two fluids can be made morphologically unstable, resulting in complex pattern formation frequently encountered in porous media and biological systems. Such phenomena are widespread in nature and industry, ranging from crude oil recovery, hydrology, and filtration, to the self-organisation of collective biological systems and medical applications. In most cases, these instabilities occur when a less viscous fluid displaces a more viscous one, for example water displacing syrup, either by injection or by gravity when the interface separates two fluids of different densities. Initially small disturbances to the liquid-liquid interface may result in the formation of a single finger or multiple fingers that can undergo successive tip-splitting, and may involve complex, multiple finger interactions resulting in interesting fluid-dynamical patterns. In industrial processes, it is often desirable to suppress these instabilities and to control their late-time dynamics. The aim of the project is to investigate suppression techniques involving flow-structure interaction. The project involves mathematical modelling and numerical computation. Informal enquiries: katarzyna.kowal@glasgow.ac.uk / nigel.mottram@glasgow.ac.uk

     

    Flow of glacial ice sheets over deformable material (PhD)

    Supervisors: Katarzyna Kowal, Nigel Mottram
    Relevant research groups: Continuum Mechanics - Fluid Dynamics and Magnetohydrodynamics, Continuum Mechanics - Modelling and Analysis of Material Systems

    Ice sheets are large bodies of ice, such those of Greenland and Antarctica, that slowly deform, or spread, under their own weight. Glacial ice appears to behave as a solid on small length and time scales; however, over large scales and under substantial pressure due to their own weight, ice sheets begin to flow as a viscous fluid, much like the viscous fluids we regularly see and eat, like honey and syrup. As such, understanding the flow of thin films of viscous fluids helps us to understand large-scale ice-sheet dynamics. These dynamics are also strongly affected by what is going on beneath ice sheets. The presence of meltwater and glacial till greatly accelerates the flow and results in rapid ice discharge towards the oceans. The project seeks to explore the dependence of the flow of viscous fluids, such as glacial ice sheets on the large scale, on what lubricates it from below and on the accumulation of the underlying material. The project involves mathematical modelling and numerical computation, but depending on the candidate’s interests, there will also be the opportunity for designing and conducting small-scale fluid-dynamical laboratory experiments involving viscous fluids, such as syrup (after COVID). Informal enquiries: katarzyna.kowal@glasgow.ac.uk / nigel.mottram@glasgow.ac.uk

     

    A coupled cardiovascular-respiration model for mechanical ventilation (PhD)

    Supervisors: Peter Stewart, Nicholas A Hill
    Relevant research groups: Continuum Mechanics - Fluid Dynamics and Magnetohydrodynamics, Mathematical Biology

    Mechanical ventilation is a clinical treatment used to draw air into the lungs to facilitate breathing, used in treatment of premature babies with respiratory distress syndrome and in the treatment of severe Covid pneumonia. The aim is to oxygenate the blood while simultaneously removing unwanted by-products. However, over-inflation of the lungs can reduce the blood supply to the gas exchange surfaces, leading to a ventilation-perfusion mis-match. This PhD project will give you the opportunity to develop a mathematical model to describe the coupling between blood flow in the pulmonary circulation and air flow in the lungs (during both inspiration and expiration). You will devise a coupled computational framework, capable of testing patient-specific ventilation protocols. This is an ideal project for a postgraduate student with an interest in applying mathematical modelling and image analysis to predictive healthcare. The project will give you the opportunity to join a cross-disciplinary Research Hub that aims to push the boundaries of quantitative medicine and improve clinical decision making using innovative mathematical and statistical modelling.