Objectives of the project

The general goal of the project is to establish a significant scientific team in the field of mathematical properties of models in continuum mechanics and thermodynamics, developed by an intensive collaboration of five important research teams at three Prague affiliations and their goal-directed collaboration with top experts from abroad.

Mechanics and thermodynamics of the continuum, or the continuum physics, describes the behaviour of substances from one-component gases, water and scarcely deformed elastic substances to medleys of gases and liquids, granular substances such as avalanches or food to substances immensely rheologically complicated which are however extremely important such as tar or biosubstances in human body. Even this quite sketchy list shows the wide spectrum of fields in which models of the continuum physics can be applied to understanding of complicated procedures and to their forecasting. To give just a few examples, let us name meteorology, biomedicine, astrophysics, plasma physics or food industry. The mathematical description is based on the so-called balance equations for matter, momentum, impetus, energy and entropy. These balance equations described by a system of evolution partial differential equations involve quantities such as stress tensor, heat flow, inner energy and entropy, whose specific form or equation characterizes the specific substance. Since often it is not even possible to carry out a test that would describe a given phenomenon, the numerical treatment of a corresponding model (that is, the designation of an appropriate numerical structure, algorithmization and subsequent computer output and its comparison with the initial goal) presents the only possible way to the understanding of the process. However, an ability to propose a good numerical structure requires a deep knowledge of physical properties of the model as well as the knowledge of its analytic properties or properties of similar models. One of the goals of the project is a rigorous mathematical and numerical analysis of complete systems describing flux and deformations of compressible gases, noncompressible fluids or elastic or visco-elastic matters. The purpose of the center is to concentrate experts (from five departments at three institutions) whose research is connected with basic questions studied by the center, aimed at a better understanding of processes described by the models.

The main goal is to establish the center which would be able to interact with similar teams or individuals working in applied areas home and abroad. The role of the center will be at least two-fold: first, it will act as a counseling center in questions which approach to a given problem should be taken, and second, as an acceptor of new stimulations to further development.

The center will become a natural partner for collaboration with similar scientific centers in Europe and overseas or with individuals with broad fields of interest. This would be the case for example if the center would participate in the HYKEII project under the Marie Curie Actions, Marie Curie Research Training Networks (RTN) (the application that has been just submitted involves 16 members of the scientific team).

The Jindřich Nečas center will become a base for long-time working post-doc stays and research visits of top world experts (of duration from one month to one term), aimed at supporting the research in areas which have been so far neglected due to capacitary reasons.

Our next aim is the numerical analysis concentrated at the development of new and improvement of existing algorithms for the above-mentioned class of models and computer simulation for comparison of mathematical results with the original model.

The center concentrates research fellows which are internationally respected experts in their research fields, which are closely connected to the scientific program of the center. The existing team however does not cover all the important topics. This fact is a consequence of a high degree of specialization, characteristic for the contemporary research. The aim of the concentration of individuals into the center team is to develop a powerful tool for filling such gaps in the Czech science. For this purpose, top experts will be invited to Prague to extend knowledge in many particular areas but also to initialize research of Czech scientists in these fields; this should be done by term-long lecture courses and by the everyday interaction with PhD. students, diploma students and members of the center.