MaPSS: Maths Postgraduate Seminar Series: Sidney Holden -- Fundamental eigenmodes of the wave equation on a membrane and on a disc-shaped graph

Hello all, 

The next MaPSS talk of this semester will be at 17:00 on Mon 12th of August in Carslaw
535.  It’s a great opportunity to meet fellow postgrads, listen to an interesting talk,
and of course get some free pizza! 

************************************************************************************** 

Speaker: Sidney Holden 

Title: Fundamental eigenmodes of the wave equation on a membrane and on a disc-shaped
graph 

Abstract: We aim to determine which collections of 1D structures most closely reproduce
the behaviour of ’equivalent’ 2D structures when subjected to the wave equation.  We
solve the wave equation on a star graph and find that though the fundamental eigenmode
exhibits similar behaviour to that on the 2D membrane, the speeds at which this
behaviour occurs differ significantly.  We attempt to approximate the fundamental
eigenmode of the wave equation on the membrane by increasing the density of vertices on
a random disc-shaped graph.  We expect that as the density of vertices increases, the
resulting collection of edges approximates 2D continuous space to the extent that the
fundamental eigenvalue of the random disc-shaped graph approaches that of the wave
equation on the membrane.  

************************************************************************************** 

See you there! 

Details can also be found on the school’s Postgraduate Society website:
http://www.maths.usyd.edu.au/u/MaPS/mapss.2019.html 

Cheers, Wenqi