General Description
Proposed theme: One of the research areas of applied nonlinear dynamics mathematics is the analysis of certain process.
Research Subjects Since the middle of the last century more advanced theory have been studied experimentally in the field of electrorheological fluids. The first major discovery in electrorheological fluids was due to Willis Winslow in 1949. These fluids have the interesting property that their viscosity depends on the electric field in the fluid. Winslow noticed that in such fluids (for instance lithium polymethachrylate) viscosity in an electrical field is inversely proportional to the strength of the field. The field induces string-like formations in the fluid, which are parallel to the field. They can raise the viscosity by as much as five orders of magnitude. This phenomenon is known as the Winslow effect. Electrorheological fluids have been used in robotics and space technology. The experimental research has been done mainly in the USA, for instance in NASA laboratories. In this project we intend to continue our research and results in the field of combining the qualitative analysis of described problems by nonhomogeneous differential with numerical analysis of a wide classes of such nonlinear systems. The research project theme is at the interface between pure and applied nonlinear analysis, mathematical physics and numerical analysis. We use refined mathematical techniques wich combine topology, variational calculus, nonlinear differential equations and with partial derivates, differential geometry, functional and harmonic analysis and numerical analysis. This heady mix of ideas has produced a vast body of work and a seemingly endless supply of open problems which are closely related to practical models of applied sciences. Our team has already results in the field and intend to extend the domain substantiation and the aplicability in the area of diferential cryptography and physics.
Young Researchers
By his structure, the project focus on development of research capacities of young people and their training in areas of high importance of theoretical and applied mathematics. Fulfilling this goal is apparent in the articles described in section results, which were accepted in publications of international circulation.
All the project's objectives, according with the schedule, were fullfield, more than that, were overcounted. Beside these, were created new research lines. All of these can be shown from Rezults section