RP6 (Principal Developer: IMI-BAS)


The intensive development of ICT in recent decades motivated the bright usage of model-based approaches and simulation studies of complex systems and processes in all industrial areas, medicine, ecology etc. Significant part of the activities in this aspect is related to development and application of new techniques for elaboration and investigation of mathematical models, optimization and control of dynamical systems, new advanced computational techniques and software tools for simulation and their implementation in high performance computational environments, development of new services supporting the experimental activities. Many universities and research institutes in Europe work presently on similar projects. The team within this research project has the necessary experience in developing and investigating specific models in engineering and biosciences, elaborating new mathematical approaches, new numerical algorithms and computational techniques for simulation studies, embedded in advanced software environments.

1. Process modeling, control and simulation in bioengineering

The development of model-based systems engineering approach has had a big impact on all industrial processes in the last decade. Dynamic mathematical models are used as a powerful tool to simulate different operating, control and optimization strategies in designing and operating a complex system in order to predict its behaviour long before the physical prototype is built and tested in real life.

The research activities in this task are focused on developing and applying new mathematical techniques and advanced ICT technologies for analysis and control of the dynamic behaviour of models, describing mainly (but not only) biotechnological processes related to food industry and cosmetics, production of modern installations for renewable energy sources (hydrogen and/or methane), of medical substances and products, etc. Smart technologies for dynamic simulation, visualization and data processing like web-based applications and cloud computing will be developed and used. The HPC infrastructure will be involved in investigation of more complex dynamic models.

2. Computational nanomechanics

The computational nanomechanics is concerned with development and study of new smart materials and devices based on them. This involves novel mechanical models based on surface theory taking into consideration the role of the heterogeneity size in nano-scale range, new computational techniques, related innovative software and simulations.

The proposed research is based on the properties of integro-differential equations, and its main directions include: development of new computational tools based on cellular nonlinear/nanoscale network; numerical treatment of boundary integral equation method and its validation; computer simulations of surface stress effects when sizes of the inclusions are in nano-scale range; numerical solutions of wave propagation problems in elastic (anisotropic, piezoelectric, magnetoelectroelastic) solids containing multiple nano-inclusions and nano-cracks. The results will be used to predict the reliable service of nano-heterogeneous multifunctional hi-tech materials, for the dynamic fracture mechanics, as well as to ultrasonic nondestructive testing for evaluation of cracked and fracture state of anisotropic, piezoelectric, magnetoelectroelastic materials. Pilot applications for simulation of processes and devices in mechatronics will be developed. The HPC infrastructure will be needed to simulate processes in real-life 3D media, while the advanced equipment of the digitalization laboratory will be involved in tuning the simulation parameters, validation of the numerical results and further development of the mathematical models.

3. Fractional derivative numerical models in studying complex structures and phenomena

Fractional calculus has drawn increasing attention in mathematical modeling, where derivatives of fractional order appear as a more universal description of complex phenomena. The main advantage of the fractional derivatives is that they more adequately reflect non-local, frequency- and history-dependent properties.

New mathematical models and their numerical implementation involving fractional derivatives will be developed. The related advanced applications include: non-Newtonian fluid dynamics; material rheology; fractal and porous structures; diffusive transport; electrical networks, etc. The newly emerging topics of fractional derivative models for computer simulations of viscoelastic flows, anomalous diffusion, dumped wave propagation, etc. will be studied. In general, non-local interactions mean higer order of the relaetd computational complexity. In this context, the advanced computing (including HPC) technologies are unavoidable to develop high-tech industrial applications and services.