Continuum Mechanics

The Continuum Mechanics group consists of two subgroups:

Staff

Dr Joseph Cousins : Research Assistant

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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 staff: Jay MacKenzie, Scott Richardson
    Research students: Andrew Brown, Sathish Kumar, Roxanna Barry, Laura Miller
    Postgraduate opportunities: A coupled cardiovascular-respiration model for mechanical ventilation

  • Personal Website
  • Publications
  • Dr Katarzyna Kowal : Lecturer

    Mathematical modelling and analysis of a broad range of industrial, biological, environmental and geophysical processes involving fluid flow and/or phase change.; Mathematical modelling and analysis of a broad range of industrial, biological, environmental and geophysical processes involving fluid flow and/or phase change.

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

  • Personal Website
  • 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: Liuyang Feng, Hao Gao, Debao Guan, Wenguang Li, Qingying Shu, Xin Zhuan, Jay MacKenzie
    Research students: Ahmed Mostafa Abdelhady Ismaeel, Yingjie Wang

  • Personal Website
  • Publications
  • Dr David MacTaggart : Lecturer

    Theoretical fluid dynamics, Magnetohydrodynamics, Magnetic topology

    Member of other research groups: Continuum Mechanics - Fluid Dynamics and Magnetohydrodynamics
    Research students: Jamie Quinn, Parag Gupta
    Postgraduate opportunities: Observationally-constrained 3D convective spherical models of the solar dynamo (Solar MHD)

  • 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: Multiscale modelling of liquid crystal-filled porous media

  • 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, Andrew Brown
    Postgraduate opportunities: Multiscale modelling of liquid crystal-filled porous media

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

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

  • Dr Scott Richardson : Research Associate

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    Member of other research groups: Mathematical Biology, Continuum Mechanics - Fluid Dynamics and Magnetohydrodynamics
    Supervisors: Andrew Baggaley, Nicholas A Hill

  • 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 students: Bushra Al-Ghabshi, Andrew Brown

  • Personal Website
  • Publications
  • Prof Radostin Simitev : Professor of Applied Mathematics

    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 staff: Peter Mortensen
    Research students: Muhamad Bin Noor Aziz, Parag Gupta, Antesar Mohammed Al Dawoud, Tahani Al Sariri, Jamie Quinn
    Postgraduate opportunities: Observationally-constrained 3D convective spherical models of the solar dynamo (Solar MHD), Fast-slow asymptotic analysis of cardiac excitation models, Numerical simulations of planetary and stellar dynamos

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

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    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 , 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
    Postgraduate opportunities: Observationally-constrained 3D convective spherical models of the solar dynamo (Solar MHD)

  • 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
  • Dr Wei Zhang : Lecturer

    Bayesian data analysis, Ecological statistics, Statistical computing ;

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

  • Dr Xin Zhuan : Research Associate

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


  • Postgraduates

    Bushra Al-Ghabshi : PhD Student

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

  • Andrew Brown : PhD Student

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    Research Topic: Multiscale Modelling of Tissue Tearing
    Member of other research groups: Mathematical Biology, Continuum Mechanics - Fluid Dynamics and Magnetohydrodynamics
    Supervisors: Nicholas A Hill, Raimondo Penta, 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

  • Sathish Kumar : PhD Student

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    Research Topic: Optimisation of stent devices to treat dissected aorta
    Member of other research groups: Mathematical Biology, Continuum Mechanics - Fluid Dynamics and Magnetohydrodynamics
    Supervisor: Nicholas A Hill

  • Parna Mandal : PhD Student

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    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

  • Gordon McNicol : PhD Student

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    Research Topic: A mathematical model for nanokicking
    Member of other research groups: Mathematical Biology, Continuum Mechanics - Fluid Dynamics and Magnetohydrodynamics
    Supervisor: Peter Stewart

  • Laura Miller : PhD Student

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    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


  • 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.

     

    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. 

     

     

    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.

     

    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.

     

    Observationally-constrained 3D convective spherical models of the solar dynamo (Solar MHD) (PhD)

    Supervisors: Radostin Simitev, David MacTaggart, Robert Teed
    Relevant research groups: Continuum Mechanics - Fluid Dynamics and Magnetohydrodynamics

    Solar magnetic fields are produced by a dynamo process in the Solar convection zone by turbulent motions acting against Ohmic dissipation. Solar magnetic activity affects nearEarth space environment and can harm modern technology and endanger human health. Further, Solar magnetism poses fundamental physical and mathematical problems, e.g. about the nature of plasma turbulence and the topology of magnetic field generation. Current models of the global Solar dynamo fall in two classes (a) mean-field dynamos (b) convection-driven dynamos. The mean-field models are only phenomenological as they replace turbulent interactions by ad-hoc source and quenching terms. On the other hand, spherical convection-driven dynamo models are derived from basic principles with minimal assumptions and potentially offer true predictive power; these can also be extended to other stars and giant planets. However, at present, convection driven dynamo models operate in a wrong dynamical regime and have limited success in reproducing a number of important 1 observations including (a) the sunspot cycle period, polarity reversals and the sunspot butterfly diagram, (b) the poleward migration of diffuse surface magnetic fields, (c) the polar field strength and phase relationships between poloidal/toroidal components. The aims of this project are to (a) develop a three-dimensional convection-driven Solar dynamo model constrained by assimilation of helioseismic data, and (b) start to use the model to estimate turbulent properties that determine the internal dynamics and activity cycles of the Sun.

     

    Multiscale modelling of liquid crystal-filled porous media (PhD)

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

    Liquid crystals are scientifically fascinating and visually beautiful liquids that are all around us, forming an integral part of the liquid crystal display (LCD) used in almost every smart phone and computer display, and contained in both the cell wall and internal cytoplasm of all biological cells. The theory of liquid crystal materials that has been developed over the last fifty years has helped to bring about a revolution in display technology and increase the fundamental understanding of this phase of matter. The delicate nature of this phase, which can be disturbed by piconewton forces (about a trillionth of the force I am using to type these words on my keyboard) means that, to be made useful, they often need to be contained between rigid boundaries. In an LCD this is achieved by sandwiching the liquid crystal between to flat plates. However, more complicated structures to contain the liquid crystal have been proposed in recent years, including a polymer matrix or porous solids. By tailoring the porous medium in which the liquid crystal is contained, the optical and electrical properties and the flow of the liquid crystal can be controlled.  

    This PhD project will be focussed on developing a completely new multiscale continuum models of these liquid crystal-solid composites in order to understand and predict the microscopic behaviour of the liquid crystal within the pores, as well as the macroscopic properties of the whole composite system. The new modelling framework, which will be obtained by applying suitable homogenisation techniques (see for instance the reference below), will provide a connection between the composite’s response at the micro- and macro-scale. It is the feedback between the effects at different scales which we aim to understand using this new theory.

    Applicants should have an undergraduate degree in mathematics/applied mathematics and experience in one or more of the following is desirable: continuum mechanics and elasticity; numerical methods for solving differential equations; scientific programming in Matlab; excellent writing and presentation skills.

    During the project the student will benefit from training through the Scottish Mathematical Sciences Training Centre and develop expertise in multiscale continuum models, liquid crystal theory, partial differential equations, and finite element software to perform multi-dimensional numerical simulations related to the implementation of the modelling framework.

    The project will be supervised by Dr Raimondo Penta and Prof. Nigel Mottram, experts in homogenisation theory of porous media and liquid crystals respectively, and the student will join a research group of around fifteen postgraduate and postdoctoral researchers working on liquid crystals and/or porous media and will join the group of over one hundred postgraduate students, in the School of Mathematics and Statistics at Glasgow.   

    Competitive scholarships, for UK and International student, are available and further information can be obtained by contacting Dr Penta (Raimondo.Penta@glasgow.ac.uk) and Prof. Mottram (Nigel.Mottram@glasgow.ac.uk).

    Penta, R., Ramírez-Torres, A., Merodio, J., & Rodríguez-Ramos, R. (2021). Effective governing equations for heterogenous porous media subject to inhomogeneous body forces. Mathematics in Engineering, Vol. 3, No. 4, pp. 1-17, Open Access https://www.aimspress.com/article/id/5584.