Our objective it to study important physical and biological processes using mathematical modeling, analysis and computer simulation.
We model interactive population dynamical processes as infinite dimensional dynamical systems.
We work on development of new simulation techniques which
- combine best features of deterministic and stochastic approaches
- remove bottlenecks of existing simulation methods
- are suited to massively parallel computing
- can be used in a wide range of simulation areas, e.g. biosciences, materials science and would eventually contribute to public health and medicine.
Mathematical biology: we model and analyze the dynamics of a variety of populations, such as Daphnia with body size structure and stem cells with maturity structure of individual cells. A wealth of biological information that can be found in nature but cannot be described by standard ODE models can be obtained from curves in a two-parameter space that define stability boundaries of equilibria. Our way to compute these curves employs integral equations, semigroup theory and numerical continuation methods. Collaborators include Prof. Maria dM Vivanco (CIC BioGUNE), Prof. Odo Diekmann (Utrecht), Prof. Andre M. de Roos (Amsterdam) and Dr. Anna Marciniak Czochra (Heidelberg).
Molecular simulation is now a standard tool in the study of many physical processes. Its applications range from nanotechnology to the identification and prediction of biomolecular structure and function. To this day there remain many open challenges and there is a continuing demand for high quality algorithms and supportive theories for molecular modeling.
One of the computational grand challenge problems is the development of a methodology for efficient and accurate sampling of configuration space of complex molecules. If met, a significant progress will be made in understanding many important phenomena, such as protein folding and binding mechanisms.
We are developing, and adopting to a wide range of applications, the conventional methods based on molecular dynamics and Monte Carlo which (i) eliminate the drawbacks of traditional sampling techniques (generalized shadow Hybrid Monte Carlo (HMC) methods), (ii) make use of the multi-scale nature of the macromolecular systems to bridge the time scale gap between simulations and the phenomena of interest (multi-time-stepping HMC methods), (iii) investigate in depth thermodynamic processes that involve the cooperative nature of simulated systems currently outside the time-scale and length-scale range of atomistic simulation techniques (meso-HMC methods).
We closely work with Prof. Sebastian Reich (Potsdam University), Dr. Ross Nobes (Fujitsu Laboratories of Europe), Prof. Mark Sansom (Oxford University) and Prof. Jose Maria Asua (Polymat).
Engineering & Technology
- Biosciences & Health