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SUMMARY:An analytical approach to the effective properties of two-dimensio
 nal random and periodic composites\; designing acoustic meta-materials - D
 avid Abrahams (University of Cambridge)
DTSTART:20230726T090000Z
DTEND:20230726T100000Z
UID:TALK202795@talks.cam.ac.uk
DESCRIPTION:In this talk I shall outline a framework for describing the ef
 fective propagation or scattering response of two-dimensional composite bo
 dies\, or surfaces\, composed of small (subharmonic) inclusions.&nbsp\; We
  shall focus on acoustic waves\, although the methodology is applicable to
  elastic\, electromagnetic or other waves.\nThe presentation will be split
  into two parts\, the first will focus on periodic inclusions (cylinders) 
 which have resonant properties\, and the second will examine randomly dist
 ributed cylinders. Multipole methods will allow both problems to be formul
 ated as systems of equations\, which in the former case are simplified via
  the method of matched asymptotic expansions\, and in the latter case via 
 ensemble averaging and the quasi-crystalline approximation.\nIn the low fr
 equency limit\, methods of complex analysis are shown to be at the heart o
 f obtaining simplified expressions for the dispersion relation and effecti
 ve material properties. Results will be presented as time allows.\nReferen
 ces:1. Michael J. A. Smith and I. David Abrahams\, Tailored acoustic metam
 aterials. Part I. Thin- and thick-walled Helmholtz resonator arrays\, Proc
 eedings of the Royal Society A478\, 20220124\, 2022.2. Michael J. A. Smith
  and I. David Abrahams\, Tailored acoustic metamaterials. Part II. Extreme
 ly thick-walled Helmholtz resonator arrays\, Proceedings of the Royal Soci
 ety A478\, 20220125\, 2022.3. Michael J. A. Smith\, Philip A. Cotterill\, 
 David Nigro\, William J. Parnell and I. David Abrahams\, Asymptotics of th
 e meta-atom: plane wave scattering by a single Helmholtz resonator\, Philo
 sophical Transactions of the Royal Society 380\, 20210383\, 2022.4. Artur 
 L. Gower\, William J. Parnell and I. David Abrahams\, Multiple Waves Propa
 gate in Random Particulate Materials\, SIAM Journal on Applied Mathematics
 \, 79(6)\, 2569-2592\, 2019.5. Artur L. Gower\, I. David Abrahams and Will
 iam J. Parnell\, A proof that multiple waves propagate in ensemble-average
 d particulate materials\, Proceedings of the Royal Society A475\, 20190344
 \, 2019.
LOCATION:Seminar Room 1\, Newton Institute
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