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Applied Analysis

Current research is concerned with the analytical study of physically motivated systems of partial differential equations. So far it has concentrated on several major directions:

  • The Q-tensor theory describing liquid crystals
  • The Smoluchowski-Doi models describing complex non-Newtonian fluids
  • Aspects of classical Newtonian fluids
  • The nonlinear Schroedinger equations with potential, used in various applications, in particular in nonlinear optics.

An experiment of Oleg D. Lavrentovich (Kent State University) with defect patterns in nematic liquid crystal sample

The main focus is currently on the Q-tensor theory which has developed strongly in the recent years, attracting a significant number of contributors. We will continue working on this and building on it to develop into more general complex materials (especially fluids) and the mathematics needed for their modeling and analysis
We employ analytical methods, based on numerical simulations and study problems inspired by physics considerations.
Eusko Jaurlaritza - Gobierno Vasco ikerbasque - Basque Foundation for Science Bizkaia xede. Bizkaiko Foru Aldundia innobasque - Agencia vasca de la innovación Universidad del País Vasco (UPV/EHU) Ayuntamiento de Bilbao - Bilboko Udala