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: Magnetic helicity as the key to dynamo bistability , Observationally-constrained 3D convective spherical models of the solar dynamo (Solar MHD), Stellar atmospheres and their magnetic helicity fluxes

  • 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, Mathematical Modelling of Active Fluids, 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, Stellar atmospheres and their magnetic helicity fluxes, Magnetic helicity as the key to dynamo bistability , 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

  • 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: Force balances in planetary cores and atmospheres, Observationally-constrained 3D convective spherical models of the solar dynamo (Solar MHD), Stellar atmospheres and their magnetic helicity fluxes

  • 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

    Ecological modelling; hierarchical models; likelihood approximation methods;

    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

    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.

     

    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

     

     

    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

     

    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.

     

    Force balances in planetary cores and atmospheres (PhD)

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

    Current dynamo simulations are run, not under the conditions of planetary cores and atmospheres, but in a regime idealised for computations. To forecast changes in planetary magnetic fields such as reversals and dynamo collapse, it is vital to understand the actual fluid dynamics of these regions.

    The aim of this project is to produce simulations of planetary cores and atmospheres with realistic force balances and, in doing so, understand how such force balances arise and affect the dynamics of the flow. Force balances control many aspects of the fluid dynamics, and hence the dynamo process itself, including the size of flow structure, the buoyancy flux and zonal flows, so an understanding of the force balance available in various planetary cores and atmospheres is vital for understanding their dynamo processes. To achieve this the project will use a different technique to that typically used in dynamo simulations. The approach is to perform global simulations in a spherical shell with a magnetic field imposed by explicitly setting a component (or components) of the field at one of the boundaries. Within the interior the field is evaluated as normal using the induction equation. This set-up amounts to a model of magnetoconvection where the dynamics of the flow and magnetic field can be studied independently of the dynamo mechanism.

     

    Magnetic helicity as the key to dynamo bistability (PhD)

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

    The planets in the solar system exhibit very different types of large-scale magnetic field.The Earth has a strongly dipolar field, whereas the fields of other solar system planets, such as Uranus and Neptune, are far more irregular. Although the different physical compositions of the planets of the solar system will influence the behaviour of the large-scale magnetic fields that they generate, the morphology of planetary magnetic fields can depend on properties of dynamos common to all planets. Here, we refer to an important and recent discovery from dynamo simulations. Remarkably, two very different types of chaotic dipolar dynamo solutions have been found to exist over identical values of the basic parameters of a generic model of convection-driven dynamos in rotating spherical shells. The two solutions mentioned above can be characterised as ‘mean dynamos’, MD, where a strong poloidal field dominates and ‘fluctuating dynamos’, FD, where the poloidal component is weaker and the large-scale field can be described as multipolar. Although these two states have been shown to be bistable (co-exist) for a wide range of identical parameters, it is not clear how a particular state, MD or FD, is chosen and how/when one state can change to the other. Some of the bifurcations of such states has been investigated, but a deep understanding of the dynamics that cause the bifurcations remains to be developed. Since the magnetic topology of MD and FD states are fundamentally different, an important part of this project will be to probe the nature of MD and FD states by studying magnetic helicity, a magnetohydrodynamic invariant that combines information on the topology of the magnetic field with the magnetic flux. The role of magnetic helicity and other helicities (e.g. cross helicity) is currently not well understood in relation to MD and FD states, but these quantities are conjectured to be very important in the development of MD and FD states.  

    Bistability is also related to a very important phenomenon in dynamos - global field reversal. A strongly dipolar (MD) field can change to a transitional multipolar (FD) state before a reversal and then settle into another dipolar equilibrium (of opposite polarity) again after the reversal.This project aims to develop a coherent picture of how bistability operates in spherical dynamos. Since bistability is a fundamental property of dynamos, a characterisation of how bistable solutions form and develop is key for any deep understanding of planetary dynamos and, in particular, could be crucial for understanding magnetic field reversals.

     

    Stellar atmospheres and their magnetic helicity fluxes (PhD)

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

    Our Sun and many other stars have a strong large-scale magnetic field with a characteristic time variation. We know that this field is being generated via a dynamo mechanism driven by the turbulent convective motions inside the stars. The magnetic helicity, a quantifier of the field’s topology, is and essential ingredient in this process. In turbulent environments it is responsible for the inverse cascade that leads to the large-scale field, while the build up of its small-scale component can quench the dynamo.
    In this project, the student will study the effects of magnetic helicity fluxes that happen below the stellar surface (photosphere), within the stellar atmosphere (chromosphere and corona) and between these two layers. This will be done using two-dimensional mean field simulations that allow parameter studies for different physical parameters. A fully three-dimensional model of a convective stellar wedge will then be used to provide a more detailed picture of the helicity fluxes and their effect on the dynamo. Using recent advancements that allow us to extract surface helicity fluxes from solar observations, the student will make use of observations to verify the simulation results. Other recent observational results on the stellar magnetic helicity will be used to benchmark the findings.

     

    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.