Mathematical Sciences Research Seminar Series

Solitons in Layered Waveguides: Theory, Results and the Zero-Mass Contradiction

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Seminars

As part of the School of Science and Technology Mathematical Sciences Research Seminar Series, Matthew Tranter NTU presents: Solitons in Layered Waveguides: Theory, Results and the Zero-Mass Contradiction.

  • From: Wednesday 9 October 2019, 1 pm
  • To: Wednesday 9 October 2019, 2 pm
  • Location: 169, Erasmus Darwin, Nottingham Trent University, Clifton Campus, Clifton Lane, Nottingham, NG11 8NS

Event details

As part of the School of Science and Technology Mathematical Sciences Research Seminar Series, Matthew Tranter NTU presents: Solitons in Layered Waveguides: Theory, Results and the Zero-Mass Contradiction.

Abstract

Over the last 20 years a focus of research has been around the existence of solitons within layered waveguides. These waveguides are assumed to have multiple layers with a bonding between each layer and the presence of delamination, namely a region where the bonding is not present. The aim of many recent studies has been to detect and obtain qualitative and quantitative measures for this delaminated region. In this talk we will overview some of the recent results in this area, including theoretical, numerical and experimental results and some conclusions on the detection of delamination.


Firstly we describe the case of a symmetric perfectly bonded layered bar with delamination, obtain theoretical estimates using the Inverse Scattering Transform (IST) and compare direct numerical simulations to the theoretical estimates obtained using the IST, as well as a semi-analytical technique based upon the weakly nonlinear solution. We then extend our approaches to the modelling of a layered bar with a soft bonding layer, described by a system of coupled Boussinesq equations, and again consider the behaviour of the waves in a delaminated region of the waveguide. We also consider the case where we have a delamination of finite length and obtain estimates for the length of the delamination.


Finally, in the limiting case of a soft bond between the layers and the materials in the layers have significantly different properties, Boussinesq-Klein-Gordon (BKG) equations are derived. These equations have been shown to contain the so-called zero-mass contradiction and we will outline the details of this contradiction and how it can be resolved, as well as drawing some conclusions on how this can be used to describe the propagation of solitons in the layered waveguides.

Hosted by Dr David Chappell

All Welcome

For any enquiries please contact Dr David Chappell.

Location details

Room/Building:

169, Erasmus Darwin

Address:

Nottingham Trent University
Clifton Campus
Clifton Lane
Nottingham
NG11 8NS

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