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DTSTAMP:20250708T042613Z
DESCRIPTION:Title: An Existence Proof for Fully Localised Planar Patterns\n
 \nAbstract: Spatially localised patterns are known to emerge in a variety 
 of physical settings\, ranging from dryland vegetation to vibrating fluids
  to the buckling of cylinders. While there are a number of mathematical to
 ols for studying localised patterns in one spatial dimension\, developing 
 equivalent approaches in higher spatial dimensions remains a major challen
 ge in the area of pattern formation. In this talk\, we will focus on 2D pa
 tterns that are localised in the radial direction and present a novel form
 al approach to derive radial amplitude equations [D.J. Hill & D.J.B. Lloyd
 \, SIAM J. Appl. Math. (2024)]\, which provides new insight into the emerg
 ence of fully localised planar patterns. As an example\, we formally deriv
 e radial amplitude equations for fully localised hexagons and quasipattern
 s in the Swift--Hohenberg equation (SHE)\, for which we can obtain explici
 t localised solutions. We then present current work on an existence proof 
 for fully localised stripes in the SHE\, using modulation theory from wate
 r waves (e.g. see [B. Buffoni\, M.D. Groves & E. Wahlen\, J. Math. Fluid M
 ech. (2022)]) extended to polar coordinates. To the authors' knowledge\, t
 his would provide the first existence proof of radially-localised non-axis
 ymmetric planar patterns. This work is in collaboration with Mark Groves (
 Universität des Saarlandes).\n\nWhere: Concordia\, room LB 921-4\, and by 
 Zoom (see link below)\n\nhttps://concordia-ca.zoom.us/j/83210406732?pwd=en
 8tvgzKVcul30C4kiXqrEHRA5VaHO.1\n\nMeeting ID: 832 1040 6732\n\nPasscode: 0
 31132\n
DTSTART:20241025T180000Z
DTEND:20241025T190000Z
SUMMARY:Dan Hill (Saarland University)
URL:/mathstat/channels/event/dan-hill-saarland-univers
 ity-360648
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