GRK 2339: 
IntComSin: Interfaces, Complex Structures, and Singular Limits in Continuum Mechanics - Analysis and Numerics

The idea of the research training group Interfaces, Complex Structures, and Singular Limits in Continuum Mechanics: Analysis and Numerics is to combine the expertise at FAU Erlangen-Nürnberg and at University of Regensburg in (S)PDE-analysis, calculus of variations, homogenisation and Gamma-convergence, numerical analysis and scientific computing to set up a unique research and training center to investigate at the highest scientific level selected phenomena and processes, which are related to interfaces, multiple scales/fields, and dimension reduced models arising as singular limits. This way, the research training group responds to the still growing demand for refined mathematical models, their thorough analysis and efficient numerical treatment, which arises in various fields of natural sciences, medicine, and engineering (biology, cardiology and oncology, materials sciences, manufacturing technology). Questions under consideration are currently of major interest both from a mathematical point of view and from an application perspective and lie typically in the following subject areas:i) Interfaces: two-phase flows, free boundaries in tumour growth or population dynamics, fluidic and elastic effects at membranes, shape optimisation, fluid-structure interactions.ii) Complex structures: multiple scales, homogenisation of porous media, micro-macro models for complex fluids, microstructures in elastic media.iii) Singular limits & dimension reduction: thin films, plates/shells and beams, asymptotic limits in phase-field models.The traditionally close collaboration between the groups at FAU and at UR has become even more interlocked during the first funding period through additional elements of online-based cooperation; hence, synergies in research are exploited even more and doctoral candidates are offered a tailor-made training programme. The cornerstones of this programme are specially designed courses in which basic knowledge on the guiding focal topics Interfaces , Complex Structures and Singular Limits is taught or more advanced topics are dealt with. Doctoral projects are generally supervised by two scientists with complementary specializations, and experienced doctoral researchers act as mentors for the new fellows. The training programme is flanked by summer and winter schools as well as by a guest and exchange programme, which is intended to open up access to the international scientific community. Tailor-made training in key qualifications contributes to the autonomy of the doctoral candidates, and their scientific independence is significantly promoted through their involvement in decision-making processes and in the organisation of activities of the research training group.