Research Network: Analysis on Graphs
Lead Research Organisation:
CARDIFF UNIVERSITY
Department Name: Computer Science
Abstract
Many important physical systems have been modelled with the aid of graph like structures.
A number of groups in the UK are working on these problems and the proposed network will be a means where
they can meet fellow research workers to discuss problems and present new ideas with the goal of creating synergy.
As well as facilitating interaction between UK mathematicians working in these areas the network will also bring in
outside experts to contribute to the meetings and also provide funds for these experts to vist members of the network.
A number of groups in the UK are working on these problems and the proposed network will be a means where
they can meet fellow research workers to discuss problems and present new ideas with the goal of creating synergy.
As well as facilitating interaction between UK mathematicians working in these areas the network will also bring in
outside experts to contribute to the meetings and also provide funds for these experts to vist members of the network.
Planned Impact
The network will be built from research groups with interests in mathematical aspects of graphs, with skills in
mathematical analysis through to physics.
Initialy the impact of this research will, be felt by researchers in mathematics and physics working in these and closely-related
fields. As quantun graphs are used to model physical and engenerring problems (e.g thin mesoscopic structures).
in a longer time scale and impact could be made in these more applied areas.
Recently the study of complex networks (e.g. world wide web) has shown that they may be are scale free with all the inherent implications for failure. Our study of non-linear problems, although motivated by non-linear optics, could have an impact in this area as well.
mathematical analysis through to physics.
Initialy the impact of this research will, be felt by researchers in mathematics and physics working in these and closely-related
fields. As quantun graphs are used to model physical and engenerring problems (e.g thin mesoscopic structures).
in a longer time scale and impact could be made in these more applied areas.
Recently the study of complex networks (e.g. world wide web) has shown that they may be are scale free with all the inherent implications for failure. Our study of non-linear problems, although motivated by non-linear optics, could have an impact in this area as well.
Organisations
People |
ORCID iD |
| B Brown (Principal Investigator) |
Publications
Brammall M
(2015)
Quantum Ergodicity for Quantum Graphs without Back-Scattering
in Annales Henri Poincaré
Brown B
(2018)
Compressed Resolvents and Reduction of Spectral Problems on Star Graphs
in Complex Analysis and Operator Theory
Brown B
(2017)
Gap localization of TE-modes by arbitrarily weak defects
in Journal of the London Mathematical Society
Brown B
(2017)
Gap localization of TE-modes by arbitrarily weak defects
Brown B
(2020)
Gap localization of multiple TE-Modes by arbitrarily weak defects
in Journal of the London Mathematical Society
Brown M
(2015)
Gap localization of TE-Modes by arbitrarily weak defects
Foulger I
(2013)
Quantum search on graphene lattices
Foulger I
(2014)
Quantum search on graphene lattices.
in Physical review letters
Waltner D
(2013)
Subdeterminant approach for pseudo-orbit expansions of spectral determinants in quantum maps and quantum graphs.
in Physical review. E, Statistical, nonlinear, and soft matter physics
| Description | This was a researcy network, with the aim of getting different people in different universitites working together. This happened and some new colaborations were established and others strengthened. Most of the projects have been academic based. |
| Sector | Education |
| Impact Types | Economic |