Stochastic dynamics: basic rules and applications

aim of project
Models and methods of stochastic processes are used, to great advantage, as universal interdisciplinary tools in non-linear dynamics, static mechanics, solid-state physics, physical chemistry, biophysics and models of climate dynamics. Stochastic elements in researched models and data represent uncontrolled influence of the environment, heat fluctuations or hidden internal dynamics. In comparison with linear systems or with systems close to the state of balance, noise and fluctuations in non-linear dynamics may have a much greater influence on the system and they may become a source of rare but highamplitude fluctuations leading, for example, to runaway from locally stable states. The aim of the proposed project is to create foundations for many levels of stochastic descriptions in non-linear systems, with a view to future development of analytical and numerical tools and to study typical problems arising in many fields in relation to non-linear stochastic theories. The program will cause an increase of cooperation among specialists in physics, chemistry and biology and it will aim at concentrating European research on stochastic methods used in fundamental issues and practical problems. Existing cooperation will be enhanced and new contacts will be made, with special consideration of dialogue among theoreticians and research used in stochastic non-linear dynamics. The program will also be a forum for young European physicists, who will be able to learn about new areas of interdisciplinary research.

expected results
The proposed research aims at a precise determination of the role of noise and fluctuation in non-linear systems far from the state of balance. On the one hand, the project asks fundamental questions on statistical physics, such as breakdown of detailed balance condition and tunneling of noise in non-linear systems. On the other hand, the aim of the project is to improve techniques and possibilities of creating models by organized exchange of knowledge among specialists studying fluctuations at different levels, ranging from molecular objects to continuous systems. It is also equally important that the program concentrates on research aimed at developing tools used in specific applications. The project also encompasses more detailed studies, such as determining runaway rates and their higher moments, comparison of stochastic models with results of molecular dynamics simulation and analysis of time series.