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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Sound absorption by perforated walls along boundar
ies - Agnes Lamacz-Keymling (Universität Duisburg-
Essen)
DTSTART;TZID=Europe/London:20230322T120000
DTEND;TZID=Europe/London:20230322T123000
UID:TALK195745AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/195745
DESCRIPTION:Asymptotic analysis of multiscale models with peri
odically heterogeneous coefficients became possibl
e with the development of the method of homogeniza
tion in the 1970s. \;If the periodicity length
is small compared to the size of the sample of th
e medium it turns out that the original equation i
s approximated well by an effective model with con
stant coefficients. \;\nIn this talk our inte
rest lies in the mathematical analysis of a sound
absorbing perforated plate\, e.g. along the wall o
r ceiling of a room.To this end we analyze the Hel
mholtz equation in a complex domain where a sound
absorbing structure at a part of the boundary is m
odelled by a periodic geometry with periodicity $\
\varepsilon>0$. A resonator volume of thickness $\
\varepsilon$ is connected with the main part of th
e macroscopic domain by thin channels (opening $\\
varepsilon^3$). \;We analyze solutions in the
limit $\\varepsilon\\to 0$ to find that while the
lowest order approximation is trivial the effectiv
e system at order $\\varepsilon$ indeed describes
sound absorption.\nThe talk is based on a joint wo
rk with P. Donato and B. Schweizer. \;
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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