Research in Wave Propagation and Scattering

The history of waves at Manchester

Waves are an important aspect of physics and applied mathematics because they are the fundamental mechanism by which all information is transmitted. Research into wave phenomena at Manchester has a very strong history. Horace Lamb (Beyer Professor 1888-1920) conducted research into waves in elastic media (amongst other aspects) including surface waves, the Rayleigh-Lamb waves in elastic plates that now carry his name and the theory of sound. Sir James Lighthill (Beyer Professor 1950-1959) who is known (amongst other work) for his theory of aeroacoustics and nonlinear acoustics. Together with Gerald Whitham (who obtained his PhD at Manchester in 1953 under the direction of Lighthill) Lighthill developed a comprehensive theory of kinematic waves. The notable contributors to wave theory, DR Bland (viscoelasticity) and D.S. Jones (electromagnetic waves and acoustics) also spent time at Manchester. After Lighthill left Manchester, Fritz Ursell took up the Beyer Chair. Ursell carried out important research into water waves whilst at Manchester, first working with Goldstein and then as Beyer Professor (1961-1990). Ursell had numerous PhD students and postdoctoral assistants at Manchester who went on to do important research in wave mechanics. These include Frank Leppington (1964), David Evans (1966) and Douglas Gregory (1967). Paul Martin worked at Manchester from 1976-1999.

Current research in waves at Manchester

The current focus of wave research at Manchester lies within the Waves in Complex Continua (WICC) Group established in 2010 and led by Prof David Abrahams (Beyer Professor since 1995) and Dr William Parnell. The group is funded by a variety of sources including the EPSRC, the Royal Society, the Leverhulme Trust and industry, perhaps most notably Thales Underwater Systems. It has a thriving group of PhD research students and postdocs working on broad range of research problems in wave mechanics. The group also welcomes research visitors from around the globe.

Of specific importance to the group is the study of waves in heterogeneous media, of which good examples are composite materials and bone. The complex microstructure of such materials gives rise to a complex wave field. Often the interest is how an effective wave propagates through the medium. In order to study problems in this domain, many different types of mathematics are required including the development of fundamental analytical techniques, computational methods, probability theory and the use of many aspects of the theories of acoustics, elasticity and water waves.


bone
Some of the current exciting research projects at Manchester are:
  • Effective propagation of waves in random heterogeneous media, including composite media
  • Waves in periodic heterogeneous media
  • Scattering of waves by multiple obstacles (multiple scattering theory)
  • Hydroacoustics
  • Non-uniqueness of solutions in water wave problems
  • Modelling ultrasound propagation in bone
  • Wave propagation in pre-stressed media
  • Elastodynamic cloaking theory and metamaterials
  • Active cloaking, anti-sound and anti-vibration

water wave
More details of these projects can be found on the WICC website. The image below relates to work done recently on elastodynamic cloaking. This uses pre-stress of rubbery materials in order to guide elastic waves around specific regions of space.
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Contact the Waves Group

If you are interested in research in waves, you can contact the group by sending an email to William.Parnell (@manchester.ac.uk).

Members of staff involved

NAME Title EMAIL @manchester.ac.uk PHONE LOCATION
Abrahams I David Prof. David.Abrahams 0161 27 55901 Alan Turing 2.243
Parnell William Dr William.Parnell 0161 27 55908 Alan Turing 2.238
Simon Mike Dr Mike.J.Simon 0161 27 55827 Alan Turing 2.115