Professor Anthony Mulholland

Research Professor

Mathematics and Statistics

Personal statement

Prof Mulholland has published over 100 papers in applied mathematics, particularly in the modelling of ultrasonic devices and systems. In the last five years he has helped to secure over £10 million of external funding and this has allowed him to create a research group in the Department of Mathematics and Statistics. He has been funded by EPSRC on several grants (EP/K028049/1, EP/K014250/1, EP/I019731, EP/F017421, EP/E018858, GR/S31235, GR/N27644, GR/N02207, EP/L022125/1) and by industry partners such as the National Nuclear Laboratory, Rolls-Royce, Serco Assurance (Risley), Shell, Weidlinger Associates, BP, GSK, Astra Zeneca and Doosan Power Systems. He plays the leading role in the modelling developments in the Centre for Ultrasonic Engineering (CUE) at Strathclyde University ( CUE has world class facilities and a vibrant research environment, including around 90 researchers with backgrounds in engineering, chemistry, biology, mathematics and statistics, physics, material science and computing. CUE is a leading partner in the UK National Centre for Research in Non-Destructive Evaluation (RCNDE), the other founder members being the universities of Imperial, Bath, Bristol, Manchester, Nottingham and Warwick ( He was elected as Fellow of the Institute of Mathematics and its Applications in 2011. He has undertaken various leadership roles within the academic community, was the Vice Dean for Knowledge Exchange in the Faculty of Science from 2010 to 2015, and is currently Head of the Department of Mathematics and Statistics. He now has a substantial portfolio of management responsibilities and led the development of the Knowledge Exchange arm of the University’s Strategic Plan in 2010. During this period the university has been recognised for its engagement with industry firstly by the THES award for the University of the Year in 2012 and subsequently as the THES Entrepreneurial University of the Year in 2013.  He has collaborations throughout the US and Europe, and is a member of a French GDR network in Ultrasonics.    He was elected on to the council of the European Consortium for Mathematics in Industry in 2016.  He was the first person to conceive of a fractal ultrasonic transducer and, after producing a series of mathematical papers that showed the potential in such technology, these devices are now being manufactured. 

Current PhD Students

Russel Niven

Joe Pettigrew

Ebrahem Algehyne

Jamie Cowley

Majid Alharbi

Marcus Ingram

Haoyu Fang

Ainsley Miller

Current Postdoctoral Researchers

Katy Tant

Stephen Agimelen

Euan Barlow

Recent Grants

2016-2020  EPSRC EP/P005268/1, £516K, “iNEED (including Non-destructive Evaluation in Engineered Design).” PI.

2017-2018  Wellcome Trust £41.5K, “Marchenko medical ultrasound imaging: translating Geophysical imaging to Medical Science.” CI.

2014-2020 EPSRC Grant EP/L022125/1, £10.8M "UK Research Centre in Non-Destructive Testing (RCNDE)" CI.

2012-2015  EPSRC Grant EP/K014250/1    £3.1M "Intelligent Decision Support and Control Technologies for Continuous Manufacturing of Pharmaceuticals and Fine
Chemicals" CI.

2011-2014    EPSRC Grant EP/1019731/1 £263,700 “New Methods for Ultrasonic NDE of Difficult Materials.” CI.

2008 – 2012    EPSRC Grant EP/F017421/1  £947,712 “Generation, Detection and Analysis of Optimally Coded Ultrasonic  Waveform systems.” CI.

2007 – 2010    EPSRC Grant EP/E018858/1   £458,463“Systems risks in information-rich environments.” CI.

2005 – 2008    EPSRC Grant EP/C540387/1 £84,835    “Real-time monitoring of bioprocesses using in situ non-linear active acoustic methods.” CI.

2003 – 2007    EPSRC Grant GR/S31235/01   £424,396 “A New Range of Ultrasonic Transducers using Dispersed Phase Materials.” CI.

2001 – 2005    EPSRC Grant GR/N27644/01   £480,862 “New Generation of Ultrasonic Systems.'' CI.

 2001 – 2004    EPSRC Grant GR/N02207  £149,379 “Realising the Potential of the Dielectric Approach to Non-Destructive  Examination of Adhesive Bonded Structures.” CI.



Effective grain orientation mapping of complex and locally anisotropic media for improved imaging in ultrasonic non-destructive testing
Tant K M M, Galetti E, Mulholland A J, Curtis A, Gachagan A
Inverse Problems in Science and Engineering Vol 28, pp. 1694-1718 (2020)
Determination of bubble size distribution using ultrasound array imaging
Ingram Marcus, Mineo Carmelo, Gachagan Anthony, Mulholland Anthony J, Nordon Alison, Hegarty Martin
IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control Vol 67, pp. 1424-1437 (2020)
Analysis of a fractal ultrasonic transducer with a range of piezoelectric length scales
Algehyne Ebrahem A, Mulholland Anthony J
IMA Journal of Applied Mathematics Vol 84, pp. 605-631 (2019)
Enhanced phased array imaging through reverberating interfaces
Ingram Marcus, Gachagan Anthony, Mulholland Anthony J, Nordon Alison, Dziewierz Jerzy, Hegarty Martin
45th Annual Review Of Progress In Quantitative Nondestructive Evaluation 45th Annual Review of Progress in Quantitative Nondestructive Evaluation, QNDE 2018 AIP Conference Proceedings (2019)
Multi-sensor inline measurements of crystal size and shape distributions during high shear wet milling of crystal slurries
Agimelen Okpeafoh S, Svoboda Vaclav, Ahmed Bilal, Cardona Javier, Dziewierz Jerzy, Brown Cameron J, McGlone Thomas, Cleary Alison, Tachtatzis Christos, Michie Craig, Florence Alastair J, Andonovic Ivan, Mulholland Anthony J, Sefcik Jan
Advanced Powder Technology Vol 29, pp. 2987-2995 (2018)
Broadband 1-3 piezoelectric composite transducer design using Sierpinski Gasket fractal geometry
Fang Haoyu, Qiu Zhen, Mulholland Anthony J, O'Leary Richard L, Gachagan Anthony
IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control Vol 65, pp. 2429-2439 (2018)

More publications

Professional activities

Invited Talk: The Life and Works of Lewis Fry Richardson
Invited Talk: Inverse Problems in Manufacturing, Robotics, and the Nuclear Industry
PhD Examination: University of Leeds: Huntul
PhD Examination: Imperial: Zhang
Symposium on implementation of articulation programme between Strathclyde and SCAU
Invited Talk: Mathematical Modelling of Ultrasonic Systems

More professional activities


EPSRC Centre for Doctoral Training in Future Ultrasonic Engineering (FUSE)
Gachagan, Anthony (Principal Investigator) Mulholland, Anthony (Co-investigator) Windmill, James (Co-investigator)
01-Jan-2019 - 31-Jan-2027
Multi-Sensor Solid Monitoring Acoustic System
Gachagan, Anthony (Principal Investigator) Mulholland, Anthony (Co-investigator) Nordon, Alison (Co-investigator)
12-Jan-2018 - 12-Jan-2020
Acoustic Based Characterisation of arc fusion process control parameters
MacLeod, Charles Norman (Principal Investigator) Dobie, Gordon (Co-investigator) Gachagan, Anthony (Co-investigator) Mulholland, Anthony (Co-investigator) Pierce, Gareth (Co-investigator) Stratoudaki, Theodosia (Co-investigator) Tant, Katherine Margaret Mary (Co-investigator)
Acoustic based characterisation of arc fusion process control parameters and their effect on long-term defect initiation
02-Jan-2018 - 31-Jan-2023
MECAWAVE: A French CNRS Funded Network
Mulholland, Anthony (Principal Investigator)
I was a co-author of a successful funding bid to the CNRS to fund a 4 year, network in France to run events on research into Mechanical Waves. The
01-Jan-2018 - 31-Jan-2021
iNEED (including Nondestructive Evaluation in Engineered Design)
Mulholland, Anthony (Principal Investigator) Ijomah, Winifred (Co-investigator) Illes, Tibor (Co-investigator) Windmill, James (Co-investigator)
"Many high-value manufactured components that are made in the UK are used in safety critical structures such as nuclear plants and aircraft engines. Such components must be checked periodically for the presence of flaws and other precursors to the component failing. This is performed at various stages in the lifetime of the component: at the manufacturing stage, periodically while the component is in service, and to assess the component for remanufacturing at the end of its lifetime.

Components must be checked non-destructively, which is challenging; normally the component's design is not optimised to maximise the probability of detecting a flaw using non-destructive evaluation (NDE). The Engineering Design Challenge is to bring NDE considerations into the design engineer's virtual design toolbox.

This project aims to enable design engineers to optimise the design of a given component such that they maximise their ability thereafter to test this component non-destructively for the presence of any flaws. Thus flaw-detectability will used as an additional design criterion. This will also help in remanufacturing as we will be more able to assess the integrity of used components. In this way we will improve society by having safer aircraft, nuclear plants and oil pipelines, improve the environment by having fewer wasted components and using less energy, and improve the UK economy by developing the UK's expertise in these high value sectors.

The most common modality in non-destructive evaluation of these safety critical structures is ultrasound transducer imaging. The Centre for Ultrasonic Engineering (CUE) at the University of Strathclyde has extensive experience in the computer simulation and mathematical modelling of ultrasonic transducers and in their use in NDE. They are ideally placed to develop such a software platform. The University of Strathclyde also hosts the Scottish Institute for Remanufacture (SIR), so the project will utilise the research expertise in this area in conjunction with that of CUE. This project will enable CUE and SIR to form a new alliance with experimental design and tomographic imaging experts from the School of Geosciences at the University of Edinburgh. In the Geosciences, sophisticated imaging methods are used to image the Earth's subsurface, and design theory is developed to optimise imaging array geometries and methods. This combined capability will enable the joint project team to develop a virtual environment where techniques for designing and imaging the internal structures of safety critical components can be assessed and optimised."
01-Jan-2016 - 31-Jan-2021
PSE Ltd - IAA - CMAC: Sizing of Crystal Particles using Sensor Data (IAA secondment)
Mulholland, Anthony (Principal Investigator) Agimelen, Okpeafoh Stephen (Co-investigator)
01-Jan-2016 - 31-Jan-2016

More projects