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Flows, Waves, and their Asymptotic Stability

Project description

Exploring universal rules that describe common patterns in nature

Waves and flows are central to understanding many physical and biological phenomena, from fluid motion around objects to the collective motion of cells. A key challenge is explaining how wave propagation and concentration emerge from mathematical models. The ERC-funded FloWAS project seeks to advance understanding of these phenomena by studying specific solutions – solutions with self-similarity – that maintain their shape while moving or shrinking. Researchers will explore three areas: how fluid detaches and creates drag forces (using the Prandtl system), how bacteria cluster and interact (using the Keller-Segel system) and how disordered waves organise into travelling patterns (using critical wave equations and nonlinear Schrödinger equations). By connecting these seemingly unrelated phenomena, the proposed research will help uncover universal principles across different areas.

Objective

Equations of waves and flows are used extensively in physics and biology, to describe phenomena ranging from the flow past an airfoil, to the collective motion of cells and to the motion of water surface. A major issue is to explain how the propagation through space and the concentration to various scales can emerge from these mathematical models. Fundamental progress have been made since the beginning of the millenium around the role played by specific solutions that either propagate or shrink while keeping the same shape, such as solitary waves for example. These specific solutions are the key to understand the global dynamics. The goal of this project is to push forward the current knowledge on their stability, their emergence over time, and the dynamics they are responsible in several equations. The FloWAS project will study seemingly unrelated models, whose solutions in fact display remarkably close behaviours.

First, we aim at describing how a thin layer of fluid can detach off a boundary and be ejected away in a stream. This is a key phenomenon to understand the drag exerted on moving objects. For this we will study singular solutions of the unsteady Prandtl system of fluid mechanics. Second, we will study concentration phenomena arising in the movement of bacteria. For that we will consider nonlinear structures appearing in the Keller-Segel system: how they can collapse, and how they can interact. Third, we will consider how, from initially disordered wave packets, order appears over time and traveling waves emerge. This study will be made on the critical wave equation. Applications to weak wave turbulence will be pursued. Describing all these phenomena lies at the frontier of current research, and we expect applications to a wide range of models.

Fields of science (EuroSciVoc)

Keywords

Programme(s)

Topic(s)

Funding Scheme

HORIZON-ERC - HORIZON ERC Grants

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Call for proposal

(opens in new window) ERC-2023-STG

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Host institution

CY CERGY PARIS UNIVERSITE
Net EU contribution
€ 1 310 233,00
Address
33 BOULEVARD DU PORT
95011 Cergy-Pontoise
France
Region
Ile-de-France Ile-de-France Val-d’Oise
Activity type
Higher or Secondary Education Establishments
Links
Total cost
€ 1 310 233,00

Beneficiaries (1)