MIDAS · Microstructures in Dynamic and Anisotropic Systems
FP7 — People (Marie Curie Actions)
- Duration
- 2013-08-01 → 2015-01-31
- EU contribution
- €231,926
- Participants
- 1
- Scheme
- MC-IEF
Lines connect the coordinator with its partners.
Results in brief
Microstructures in Dynamic and Anisotropic Systems
The project Microstructures in Dynamic and Anisotropic Systems (MIDAS) supported an eighteen-month research fellowship for Nadia Ansini (Sapienza, Rome) at the University of Bath. Microstructures occur in a wide range of materials, including steel and shape memory materials. Over the past decades, experimental and computational advances have revolutionised our understanding of matter on the atomistic (microscopic) scale. The computation of multiscale problems, such as those exhibiting microstructures, however, is difficult and costly at best, and often impossible if very disparate scales have to be resolved simultaneously. Thus scale-bridging has become a central activity in physics, chemistry and biology; a rich mathematical theory underpinning this topic has been developed over the last two decades in particular. This project studied a range of problems with multiple scales. This includes evolutionary problems with “wiggly” energies, where the energy exhibits oscillations on a fine scale, and the evolution seeks to minimize the energy as much as possible – that is, evolve according to an associated gradient flow. Here a new approach of local minimization and variational evolution in connection to the analytic tool of Gamma-convergence was used to understand in detail the intricate range of evolutions depending on an underlying ration of spatial and temporal (discretization) scales. One other aspect of the work undertaken concerns degenerate parabolic equations. Here the motivation is the description of the grain size evolution in steel. Modern analytic tools from the theory of Wasserstein gradient flows could be used to analyse the aforementioned class of parabolic equations with degeneracies.
Data: CORDIS, © European Union
Project objective
Over the past decades, experimental and computational advances have revolutionised our understanding of matter on the atomistic (microscopic) scale. However, a computational analysis of problems involving multiple scales is difficult (often impossible ) and costly at best if very disparate scales have to be resolved simultaneously. Thus scale-bridging has become a central activity in physics, chemistry and biology; a rich mathematical theory underpinning this topic has beendeveloped over the last two decades in particular. However, two challenges which are centralfor technological applications have not been resolved satisfactorily:1) Materials with microstructures are typically anisotropic in a way which is difficult to analyse in detail with existing variational tools such as Gamma-convergence alone;2) Out-of equilibrium effects such as those triggered by dynamics are poorly understood for materials with microstructures.We will address these two challenges, which are linked by the focus on microstructures, by combining the expertise of the applicant, who is from the leading school of Gamma-convergence, with the expertise of the mentors on anisotropic problems and variational approaches for dynamics.The project combines:i) an effective description of oscillatory Hamiltonian systems. Objective: to develop a new approach of deriving effective descriptions of effective Hamiltonians.ii) Analysis of phase transitions with internal microstructure. Objective: to establish new theories suitable to work with Gamma-convergence for problems with anisotropies.""
Original text from CORDIS.
Participants
- UNIVERSITY OF BATH · BATHCoordinatorUnited Kingdom
Links
Data: CORDIS, © European Union