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Nonlinear dynamics of topological insulators (Advert Reference: SF18/MPEE/MA)

  • Full or part time
    Dr Y Ma
  • Application Deadline
    Applications accepted all year round
  • Self-Funded PhD Students Only
    Self-Funded PhD Students Only

Project Description

Topological physics is a central branch of modern physics, as evidenced by the Nobel Prize in Physics 2016. In particular, topological insulators have been extensively studied by condensed matter physicists since their discovery about a decade ago. These materials have been touted as a new state of matter since they exhibit robust properties protected by integer topological invariants.
Many quantum phenomena such as topological insulation have proved difficult to observe experimentally in traditional materials. Consequently, there has been significant interest in realising these phenomena in systems governed by classical physics. The earliest and most direct realisations have relied on photonic lattices and Bose-Einstein condensates. More recently, analogues in acoustic systems have also been proposed.

A key feature of optical and mechanical systems is that their governing differential equations are often inherently nonlinear. However, the effect of nonlinearity on topological insulators remains largely unexplored. This PhD project will explore the interplay between topological protection and various coherent structures studied in the mathematical theories of nonlinear waves and pattern formation. A systematic investigation of such nonlinear coherent structures can be useful for diverse industrial applications using photonic and acoustic devices.
The applicant is expected to have a solid background in applied mathematics and scientific computing at the undergraduate level.

Please note eligibility requirement:

* Academic excellence of the proposed student i.e. 2:1 (or equivalent GPA from non-UK universities [preference for 1st class honours]); or a Masters (preference for Merit or above); or APEL evidence of substantial practitioner achievement.
* Appropriate IELTS score, if required

For further details of how to apply, entry requirements and the application form, see

Please note: Applications that do not include a research proposal of approximately 1,000 words (not a copy of the advert), or that do not include the advert reference (e.g. SF18/MPEE/MA) will not be considered.

Start Date: 1 March 2019 or 1 June 2019 or 1 October 2019

Northumbria University takes pride in, and values, the quality and diversity of our staff. We welcome applications from all members of the community. The University hold an Athena SWAN Bronze award in recognition of our commitment to improving employment practices for the advancement of gender equality and is a member of the Euraxess network, which delivers information and support to professional researchers.

Funding Notes

This is an unfunded research project


D. D. J. M. Snee and Y.-P. Ma. Edge Solitons in a Nonlinear Mechanical Topological Insulator. arXiv preprint arXiv:1805.03157 (2018).
C. Chong, P. G. Kevrekidis, M. J. Ablowitz, and Y.-P. Ma. Conical wave propagation and diffraction in two-dimensional hexagonally packed granular lattices. Phys. Rev. E 93, 012909 (2016).
M. J. Ablowitz, C. W. Curtis, and Y.-P. Ma. Adiabatic dynamics of edge waves in photonic graphene. 2D Materials 2 (2), 024003 (2015).
M. J. Ablowitz, C. W. Curtis, and Y.-P. Ma. Linear and nonlinear traveling edge waves in optical honeycomb lattices. Phys. Rev. A 90, 023813 (2014).

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