Project description
Multi-scale analysis of wave propagation in random media
Random media greatly perturb the propagation of waves triggering undesired effects such as the trapping of seismic waves or desired effects such as the trapping of sound waves by noise abatement walls. These phenomena are well-understood from a physical point of view but much less understood in mathematical terms. The goal of the EU-funded COR-RAND project is to understand the interplay between differential operators and randomness to explain the rich variety of wave propagation modes. Researchers will use corrector equations to characterise the solutions of partial differential equations with random coefficients at multiple time and spatial scales.
Objective
"Consider a partial differential equation (PDE) with random coefficients as in engineering or applied physics: When combined with a spatial scale separation, the randomness and the differential operator interact to give rise to some effective behavior. The recent growing mathematical activity in this domain has led to a ``seemingly'' complete theory of stochastic homogenization of linear elliptic operators. Central to this theory is the so-called corrector equation, a degenerate elliptic equation posed on the (infinite-dimensional) probability space. The context of linear elliptic operators yields the simplest such equation. Time-dependent and/or nonlinear PDEs also involve corrector equations (or a family thereof), albeit with a significantly more complex structure. Their study and use to characterize the large-scale/time behavior of solutions of PDEs with random coefficients are at the heart of this project. Whereas the relevance of corrector equations is clear in problems such as diffusion in random media, sedimentation of randomly placed particles in a fluid, or water waves on a rough bottom, it is less obvious for the long-time behavior of waves in disordered media. The latter is related to the spectrum of the associated random elliptic operator, the characterization of which still remains a largely open question today. We propose to relate the long-time behavior of waves to the properties of a family of corrector equations. These corrector equations are widely unstudied and offer many analytical challenges. They constitute the first half of the project. Even in the ``well-understood'' setting of linear elliptic operators, this requires to revisit the corrector equation in the light of much weaker topologies than considered before. The second half of the project aims at using correctors to establish the large-scale behavior of solutions as random objects. This may involve surprising quantities such as the recently introduced ``homogenization commutator""."
Fields of science (EuroSciVoc)
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
- natural sciences earth and related environmental sciences geology sedimentology
- natural sciences mathematics pure mathematics topology
- natural sciences mathematics pure mathematics mathematical analysis differential equations partial differential equations
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Keywords
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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H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC)
MAIN PROGRAMME
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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.
ERC-COG - Consolidator Grant
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Call for proposal
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
(opens in new window) ERC-2019-COG
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Net EU financial contribution. The sum of money that the participant receives, deducted by the EU contribution to its linked third party. It considers the distribution of the EU financial contribution between direct beneficiaries of the project and other types of participants, like third-party participants.
75006 PARIS
France
The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.