Prof Mulholland has published over 100 papers in applied mathematics, particularly in the modelling of ultrasonic devices and systems. He develops mathematical theorems that provide fundamental insights into wave propagation in heterogeneous media, into sensors that rely on wave propagation, and into the associated inverse problems such as ultrasonic tomography.  He is particularly proud that his theoretical work has led to the manufacture of the world’s first fractal ultrasonic transducer. He was elected as Fellow of the Institute of Mathematics and its Applications in 2011.  In the last five years he has helped to secure over £10 million of external funding. 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. His research is characterised by the many partnerships he has had with industry over the last 34 years. These interactions extend across the Oil and Gas sector (BP, SMS Oilfield), the Energy Sector (Rolls Royce, National Nuclear Laboratory, Doosan Babcock, IHI, GE Power), the Pharmaceutical Industry (GSK, Astra Zeneca, PSE Ltd, Mettler Toledo), Robotics (Vicon, NPL), Medical Technologies (Orthosensor) and Defence (DSTL). His expertise has gained international recognition as evidenced by, for example, the funding from the US based finite element company Onscale, on the use of finite element modelling of piezoelectric materials, and recent funding from the IHI Corporation in Japan to study the inverse problem of constructing material maps of nuclear plant components. The utility of his work was exemplified by the filing of a joint patent with BP in 2016 for his work on ultrasound sensor monitoring of its downstream production plants. In 2022 he filed a patent for an electromagnetic sensor that can sense the curvature of surfaces for use in robotic touch. He has been a member of the UK Research Centre for Non-Destructive Evaluation (RCNDE) since its inception in 2003. This is a collaboration between industry and the Universities of Bristol, Nottingham, Strathclyde, Manchester, Warwick, Liverpool, Southampton and Imperial College London to coordinate the latest research on Non-Destructive Evaluation (NDE) technologies, matching it to the needs of industry. The membership has grown to 14 full industrial members and more than 40 associate industry members. In 2014 Prof Mulholland created the industry consultancy unit within the Mathematics and Statistics department at the University of Strathclyde called SMART (Statistical and Mathematical Advice, Research and Training). From 2013 to 2015 he was a member of the West of Scotland KTP Centre Advisory Board.

Current PhD Students

Alexis Hernandez Arroyo

Oliver (Fangyuan) Wan

Yongxing Cai

Ziwen Yu

Former PhD Students

2018 - 2022       Alistair Ferguson            A Probabilistic Approach to Modelling Ultrasonic Shear Wave Propagation in Locally Anisotropic and Layered Heterogeneous Media

20u16 - 2020       Russell Niven                  Full Waveform Inversion of Ultrasonic Phased Array Data for the Tomographic Reconstruction of Heterogeneous Media for NDT

2016 - 2019       Ainsley Miller                 Reconstructing Spatially Heterogeneous Thermal Maps using Light-based Metrology Sensors

2014 - 2019       Joe Pettigrew                 A Combined Perfectly Matching Layer and Finite Element Formulation for Unbounded Wave Problems

2014 – 2018       Ebrahem Algehyne        Mathematical Modelling of Fractal Ultrasonic Transducers.

2012 – 2016       James Cowley               Modelling the Nonlinear Elasticity and Rupture of Ultrasound Contrast Agents

2011 – 2014       Katy Tant                       Non-destructive Testing using Ultrasound Arrays

2011 – 2014       Laura Cunningham       Ultrasound Wave Propagation in Heterogeneous Materials

2010 – 2014       Aoibhinn Bradley         Ultrasound Waves in Solidifying Foam Materials

2010 - 2012       Natacha Ranariboana    Finite Element Modelling of Electromagnetic Diffraction Gratings

2011 - 2012       Fiona Craig                    Ultrasound Contrast Agents and Localised Drug Delivery for Cancer Treatment

2006 – 2010       Euan Barlow                  Monitoring of Bioprocesses using Non-linear Active Acoustic Methods

2004 – 2008       Gillian Carson                 Particle Sizing using Hertz-Zener Theory and Ultrasonic Measurement of Impact Vibrations

2003 – 2007       Leigh-Ann Orr                 Three-Dimensional Modelling of 1-3 Composite Ultrasonic Transducers

2000 – 2004       Cameron Mackay           Regularisation of Inverse Problems in Electromagnetics

1999 – 2003       Janan Abdulbake            Wave Propagation on Fractal Lattices

1996 – 2000       Sean McDermott            Knotted Reaction-Diffusion Waves

Former Posdoctoral Researchers

2019-2021         Johnathan Singh              Design Optimisation for NDT

2013-2018         Stephen Agimelen         Characterisation of Crystalline Particles in the Manufacturing Processes in the Pharmaceutical Industry

2014-2018         Katy Tant                        Inverse Problems in Ultrasonic Array NDT

2015-2016         Euan Barlow                   Mathematics of Metrology

2013-2015         Claudio Avila                 The use of acoustic technologies for the quantitative analysis of petrochemical and biofuels process streams

2012                   Natacha Lord                Parallel Computing and Ultrasonic Array Systems

2010                   Michael Strauss              MOTHS – Modelling of Insect Tympanal Hearing Systems

2010                   Sean McGinty                Improved Risk Assessment of Carotid Arterial Disease  using Ultrasound Elastography

2010                   Jonathan Murray             MINUET – Musically Inspired Ultrasonic Electrostatic Transducers

2009                   Anna Lishman               An Inverse Problem in Bioprocess Monitoring using Ultrasound

2009                  Kim McCosh                   A Scattering approach to Ultrasonic Waves in Two Phase biological media

2008-2011         Alan Walker                   Theoretical Modelling of Coded Ultrasound Signals

1996-1997         Binoy Manimala              Transport Mechanisms in Combustion Chambers and High Temperature Filters

1996-1997         Thomas Kehl                 Fractal Analysis of Combustion Chambers Fouling

1996-1997         Amardeep Parmar         Simulated Annealing and Local Thermochemical Equilibrium Calculations

1995-1996         Calum MacDonald        Thermal Analysis of Heat Exchanger Fouling

1995-1996         Isobel MacFarlane         High Temperature Filter Deposition in Combustion Chambers.

Recent Grants

2019-2027 EPSRC EP/S023879/1, Centre for Doctoral Training, "Future Ultrasonic Engineering (FUSE)", CI.

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