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Near-field scattering by the method of locally subsonic waves (2024)
Journal Article
Chapman, C. J., & Hawkins, S. C. (2024). Near-field scattering by the method of locally subsonic waves. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 480(2292), 1 - 26. https://doi.org/10.1098/rspa.2023.0720

A technique is developed for determining the sound field scattered by a compact body when it is close enough to an acoustic source to be in its near field. Our approach is based on the fact that large regions of many near fields may be well approxima... Read More about Near-field scattering by the method of locally subsonic waves.

Uniform approximations and effective boundary conditions for a high-contrast elastic interface (2023)
Journal Article
Chapman, C. J., & Mogilevskaya, S. G. (2023). Uniform approximations and effective boundary conditions for a high-contrast elastic interface. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 479(2277), 1 - 22. https://doi.org/10.1098/rspa.2023.0140

A difficulty in the theory of a thin elastic interface is that series expansions in its thickness become disordered in the high-contrast limit, i.e. when the interface is much softer or much stiffer than the media on either side. We provide a mathema... Read More about Uniform approximations and effective boundary conditions for a high-contrast elastic interface.

A Poisson scaling approach to backward wave propagation in a tube (2022)
Journal Article
Chapman, & Sorokin, S. (2022). A Poisson scaling approach to backward wave propagation in a tube. Philosophical Transactions A: Mathematical, Physical and Engineering Sciences, https://doi.org/10.1098/rsta.2021.0386

A mathematical analysis of wave propagation along an elastic cylindrical tube is presented, with the aim of determining the range of Poisson’s ratio for which backward wave propagation (i.e. at negative group velocity) can occur near the ring frequen... Read More about A Poisson scaling approach to backward wave propagation in a tube.

A Wronskian method for elastic waves propagating along a tube (2021)
Journal Article
Chapman, & Sorokin, S. (2021). A Wronskian method for elastic waves propagating along a tube. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 1-19. https://doi.org/10.1098/rspa.2021.0202

A technique involving the higher Wronskians of a differential equation is presented for analysing the dispersion relation in a class of wave propagation problems. The technique shows that the complicated transcendental-function expressions which occu... Read More about A Wronskian method for elastic waves propagating along a tube.

Fractional power series and the method of dominant balances (2021)
Journal Article
Chapman, H., & Wynn, H. (2021). Fractional power series and the method of dominant balances. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 20200646 - 20200646

This paper derives an explicit formula for a type of fractional power series, known as a Puiseux series, arising in a wide class of applied problems in the physical sciences and engineering. Detailed consideration is given to the gaps which occur in... Read More about Fractional power series and the method of dominant balances.

Canonical sound fields in the frequency-domain theory of supersonic leading-edge noise (2019)
Journal Article
Chapman, C., & Powles, C. (2019). Canonical sound fields in the frequency-domain theory of supersonic leading-edge noise. Wave Motion, 1 - 12 (12). https://doi.org/10.1016/j.wavemoti.2019.01.003

This paper determines the three-dimensional structure of certain single-frequency canonical sound fields occurring in the theory of blade–vortex interaction when the flow velocity relative to the blade is supersonic. A relative velocity of this magni... Read More about Canonical sound fields in the frequency-domain theory of supersonic leading-edge noise.

A class of reduced-order models in the theory of waves and stability (2016)
Journal Article
Chapman, C., & Sorokin, S. (2016). A class of reduced-order models in the theory of waves and stability. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, https://doi.org/10.1098/rspa.2015.0703

This paper presents a class of approximations to a type of wave field for which the dispersion relation is transcendental. The approximations have two defining characteristics: (i) they give the field shape exactly when the frequency and wavenumber l... Read More about A class of reduced-order models in the theory of waves and stability.