Project description
A unified approach to studying topological singularities
Topological singularities – certain points where continuity breaks down – are intriguing phenomena important for both theory and practical applications. In fields like physics and materials science, they help explain complex structures such as vortices in superconductors, fractures in solids and defects in crystals. Funded by the Marie Skłodowska-Curie Actions programme, the TopSing project will use a new theoretical approach to study certain physical/mechanical problems where singularities appear. Inspired by Ambrosio and Tortorelli’s model, the proposed method seeks a unified way to analyse two main problems involving singularities, making them easier to model and apply in real-world scenarios. In particular, the focus will be on screw dislocations in crystals and their relation with vortices in superconductors, and the non-parametric Plateau problem in codimension-two.
Objective
The exploration of topological singularities is a fascinating task of absolute relevance both from the theoretical and applied point of view.
For example, in physics and materials science they arise from the study of mathematical models for vortices in superconductors, grain boundaries in polycrystals, fractures in solids, and defects in crystals such as disclinations or dislocations. Furthermore, topological singularities play an important role in the study of more geometric problems such as the Plateau problem and the theory of minimal surfaces.
The goal of TopSing is to study some physical/mechanical problems where singularities appear, through a theoretical approach that opens promising directions also for other, apparently unrelated, situations like the non-parametric Plateau problem in higher codimension.
More specifically, we draw our attention to codimension-two singularities and consider two-dimensional models for fields having point singularities which are relevant in the study of two main problems:
1) Screw Dislocations in crystals and their relation with vortices in superconductors;
2) The non-parametric Plateau problem in codimension-two.
The main novelty consists in developing a unified approach, inspired by the classical model by Ambrosio and Tortorelli (AT), that allows to study topological singularities in both contexts listed above. Furthermore this will provide a model which is easier to handle numerically and thus interesting from the point of view of applications.
The project is organised into four main objectives whose common thread is the asymptotic analysis of elliptic functionals á la AT for maps taking values on the unit circle. To our best knowledge there are no similar results in the literature. This is due to the non trivial task of constructing a recovery sequence that takes values on the circle, which we aim at achieving by relying on degree theory and by using techniques developed to study the relaxed area.
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Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Programme(s)
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
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HORIZON.1.2 - Marie Skłodowska-Curie Actions (MSCA)
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Topic(s)
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Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Funding Scheme
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
HORIZON-TMA-MSCA-PF-EF - HORIZON TMA MSCA Postdoctoral Fellowships - European Fellowships
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Call for proposal
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Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
(opens in new window) HORIZON-MSCA-2023-PF-01
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53100 Siena
Italy
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