RandSCALES
Financiado
Bridging Scales in Random Materials
The identification and justification of scaling limits is a central theme in modern PDE theory, reflected for instance in the theories of homogenization and singular limits. In many multiscale PDE models, randomness plays a crucia...
The identification and justification of scaling limits is a central theme in modern PDE theory, reflected for instance in the theories of homogenization and singular limits. In many multiscale PDE models, randomness plays a crucial role: In random media, the quantitative homogenization process is driven by decorrelation and concentration of measure; for ill-posed evolution problems like many interface evolution equations, random noise may provide a regularization, potentially restoring well-posedness and hence approximability by numerical schemes. In the present project, we pursue a program to achieve a deeper understanding of the role of randomness in multiscale PDEs. We focus on three important, yet largely unexplored, aspects:
A) We develop a quantitative stochastic homogenization theory for nonlinear material models, ranging from variational models for brittle fracture over models from statistical mechanics to the motion of interfaces in random media. A key challenge is posed by the non-convex structure of the models, giving rise to rough energy landscapes and the emergence of complex physical phenomena.
B) We establish generalizations of homogenization in the absence of scale separation, a problem naturally posed in the framework of random media. By developing new high-dimensional approximability results, we will contribute to uncertainty quantification and the design of numerical homogenization schemes with lower computational complexity.
C) We develop a theory of stability and approximability of interface evolution problems past topology changes, a setting in which randomness may lead to the regularization of ill-posed evolutions and thereby allow for the derivation of error estimates for numerical approximation schemes. By relying on energy methods, we avoid the use of comparison principles, greatly enhancing the scope of applicability of our theory.
ver más
Duración del proyecto: 66 meses
Fecha Inicio: 2020-08-20
Fecha Fin: 2026-02-28
Fecha Fin: 2026-02-28
Línea de financiación: concedida
El organismo H2020 notifico la concesión del proyecto el día 2020-08-20
Línea de financiación objetivo
El proyecto se financió a través de la siguiente ayuda:
ERC-2020-STG:
ERC STARTING GRANTS
Cerrada
hace 5 años
Presupuesto
El presupuesto total del proyecto asciende a
1M€
Líder del proyecto
INSTITUTE OF SCIENCE AND TECHNOLOGY AUSTRIA
No se ha especificado una descripción o un objeto social para esta compañía.
Perfil tecnológico
TRL
4-5
Perfil tecnológico
TRL
4-5
308.00K€ |
Participante