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Numerical studies and applications of mobile nonlinear lattice modes in 2-dhexagonal and cubic lattices


Research objectives and content
The project focuses on the study of localized, highly nonlinear excitations in lattices, using realistic models of crystals. In particular we plan to deepen the study of a recent striking discovery that of moving longitudinal 'breathers' in 2D lattices (this work was initiated by host researcher Prof. J C Eilbeck and the applicant during a 3-month stay). The phenomenon belongs to the field of 'intrinsic nonlinear localization', which is attracting enormous interest in nonlinear science. Part of their novelty lies in the presence of high discreteness. The motivation for the study of 2D lattices comes from the experiments performed by Prof. F M Russell on mica crystals.
Our aim is to obtain a characterization of breathers in different 2D lattices, by means of numerical computations in nonlinear models. Then we will apply the results to real systems. The phenomenon of track formation in mica is the main candidate to be interpreted in terms of moving breathers, but we propose to extend the results to other systems where nonlinearity and discreteness play a fundamental role, among which is High Tc superconductivity.
Training content (objective, benefit and expected impact)
The applicant expects to gain a substantial research experience at the leading edge of nolinear science, working under the direction of Prof J C Eilbeck. The collaboration with visiting Prof. F M Russell ensure that the research will be in direct contact with experiments in real systems. Some preliminary work has been done, and the results look most encouraging; a successful interpretation of track formation in mica i terms of breathers would open the door to a great number of applications in Condensed Matter and Material Science.
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EH14 4AS Edinburgh

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