| title: | Colored-noise-induced phase transitions and transport phenomena in nonlinear systems |
|---|---|
| reg no: | ETF5943 |
| project type: | Estonian Science Foundation research grant |
| subject: |
1.1. Mathematics 1.3. Physics |
| status: | accepted |
| institution: | TPU Faculty of Mathematics and Natural Sciences |
| head of project: | Romi Mankin |
| duration: | 01.01.2004 - 31.12.2007 |
| description: | The planned investigation addresses the effect of the flatness parameter of a three-level telegraph noise modelling environmental fluctuations on the behavior of non-linear systems. The research will be focused on two basic problems. First, noise-induced phase transitions in self-regulating ecological model systems as described by Compertz and Verhulst, will be studied in order to find out (1) those regions in the space of system parameters, where phase transitions can be expected to occur, and (2) the critical noise parameters corresponding to abrupt (catastrophic) shifts in the state of the model system. Second, the combined effect of the telegraph process and the white noise modelling equilibrium thermal motion on the transport of generalized Brownian particles in a fluctuating spatially periodic field of force will be studied in order to determine (1) the factors contributing to the amplification of the particle flux (current); (2) the regions of system parameters characterized by anomalously high mobility of the particles; (3) the necessary and sufficient conditions for current reversals in the studied motion. Expected results. The mean-field method will be used to demonstrate that in model systems with a generalized Verhulst self-regulation, where population interaction can be either symbiotic or competitive, it may happen that noise with a finite correlation time may induce a transition from a monostable into a bistable state. The accompanying phase transitions may be of interest for different fields of research such as, e.g. theory of populations, ecology, economics, information theory etc. We hope to be able to demonstrate that at sufficiently low temperature the flatness of a nonequilibrium noise may induce an anomalously high mobility of Brownian particles in a force field with a spatially periodic potential. The expected effect may appear useful in the separation of macroscopic molecules as well as in the planning of experiments aimed at the detection of weak signals against a noisy background. |
| project group | ||||
|---|---|---|---|---|
| no | name | institution | position | |
| 1. | Ain Ainsaar | Tallinn University of Educational Sciences | dotsent | |
| 2. | Tõnu Laas | Tallinn University of Educational Sciences | dotsent | |
| 3. | Romi Mankin | TPU Faculty of Mathematics and Natural Sciences | Professor | |
| 4. | Eerik Reiter | Tallinn Technical University | dotsent | |
| 5. | Astrid Rekker | University of Tartu | doktorant | |
| 6. | Ako Sauga | Tallinn University of Educational Sciences | lektor | |