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CIRM – Centre International de Rencontres Mathématiques

The properties of heterogenous materials are governed by the arrangement of their nanoscale constituents. This is especially true for hierarchically organized biomaterials such as bone, tendon, wood but also for technical materials such as steel, concrete or ceramics. In particular, the understanding of orientations in 3D is a key factor to predict the physical properties of current materials, model their properties more faithfully and to propose ways to improve future materials for fields such as medicine, energy storage, composite structures or low carbon construction materials. The aim of this workshop is to assemble the communities of Material Scientists, Physicists and Mathematicians working on methods to determine orientation distributions on the nano- and crystal scale in 2D and 3D, and to stimulate a discussion on existing techniques, their computational limitations and ways to improve them, with a particular focus on their mathematical underpinnings.

CIRM – Centre International de Rencontres Mathématiques

This project focuses on the development of unconditionally stable conforming space—time methods for the linear time‑dependent Schrödinger equation. The main challenge is to overcome the lack of inf‑sup stability in the standard Petrov‑Galerkin formulation for this equation. In fact, the conforming space—time finite element discretization requires a restrictive CFL condition. To address this issue, we propose two approaches. ‑The first one is to augment the sesquilinear form of the standard scheme by adding a carefully chosen inconsistent penalty term to improve the discrete properties of the scheme. By introducing this term, we aim to improve stability without compromising convergence order. ‑The second approach involves the composition of the continuous sesquilinear form with an appropriate transform of the test functions. This modification aims to endow the new sesquilinear form with higher stability properties than its unmodified counterpart.

Applied Mathematics (in general),    Mathematical Physics

CIRM – Centre International de Rencontres Mathématiques

Our project focuses on understanding the interplay between elasticity and the classical Hele-Shaw model, with the long-term of simplifying the model and improving its suitability for numerical applications and algorithmic development. Our first aim is to show existence of solutions via the convergence of an implicit time-discretization using the Wasserstain distance. We expect the limit to satisfy the equation in a distributional sense as well as an optimal energy-dissipation relation. Similarly, we construct weak solutions to the Cahn-Hilliard equation with degenerate mobility and elastic misfits. Finally, we aim to prove that the sharp interface limit is a distributional solution to the elastically modified Hele–Shaw flow with optimal energy-dissipation rate.

CIRM – Centre International de Rencontres Mathématiques

The school will introduce participants to several hot research topics at the frontier between geophysical fluid dynamics, fundamental physics and mathematics. The main themes will be spontaneous stochasticity, waves in geophysical and astrophysical fluids and fundamental challenges in hydrodynamic and wave turbulence. The school will consist of several lecture series, plus a number of research seminars, covering mathematical, theoretical and experimental aspects. The school is organized in the framework of an international collaboration which started in 2019 and which is financially supported by the Simons Foundation (https://cims.nyu.edu/wave-turbulence/people/). This “Simons Collaboration on Wave Turbulence” brings together physicists and mathematicians with the aim of addressing fundamental questions about the Wave Turbulence theory and its applicability to real systems and especially to the Earth climate system.

Courses and Events for Math Students and Early Career Researchers,    Applied Mathematics (in general)