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URL;TYPE=URI:https://www.wpi.edu/news/calendar/events/mathematical-sciences
 -department-applied-math-seminar-binan-gu-wpi
SUMMARY:Mathematical Sciences Department Applied Math Seminar - Binan Gu, W
 PI
DESCRIPTION:Applied Math Seminar\nBinan Gu, WPI\nThursday, September 3\n1-2
 pm\nSH 313\nTitle: Shallow-Water Wave Scattering in Channel Networks: From
  Two-Dimensional Junctions to Quantum GraphsAbstract: Consider shallow-wat
 er waves propagating through a two-dimensional network of channels. At a j
 unction, an incoming wave divides into reflected and transmitted component
 s. We ask how this division depends on channel widths and branching angles
 . An idealized model-reduction replaces each channel by its centreline, pr
 oducing a 1D metric graph; a wave differential operator together with vert
 ex conditions define what is known as aquantum graph. We study the lineari
 zed shallow-water equations, where (quantum-graphs-like) Neumann--Kirchhof
 f vertex conditions lead to ascattering matrix. This matrix maps incoming 
 waves onto outgoing waves, revealing the roles of geometric channel parame
 ters.The 1D graph reduction is ultimately a modelling hypothesis whose reg
 ime of validity must be determined, in particular regarding the role of th
 e 2Dbranching angles. For wave propagation, the relevant small parameter i
 s the channel widthrelativeto wavelength, κ. We examine the limit κ → 0, c
 orresponding to long waves. We explore different scenarios, varying the ch
 annel-width ratios, the branching angles, and thejunction symmetryin order
  to determine when the two-dimensional results are close to the reduced/si
 mplified 1D scattering predictions.\n
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