Noise Induced Phenomena

University Of California-San Diego, La Jolla CA

Investigators

Abstract

Many modern technologies are based on synchronization properties of small spatially or hierarchically extended systems in which complex nonlinear interactions play a crucial role. Of central interest is the observation that on the nano-scale the effects of noise become significant and even crucial. More importantly, far from being a disturbing side effect, it has become clear that noise may actually play an essential role in the mode of operation of small-scale devices. Indeed, some of these devices would not operate at all in the absence of noise. STATEMENT OF OBJECTIVES. This proposal covers a range of interconnected problems involving noise-induced and noise-sustained phenomena in extended nonlinear systems away from equilibrium. The principal foci are: The study of the effects of noise and dimensionality on phase coherence in spatially coupled systems. Issues of interest include the constructive and destructive effects of noise on phase coherence, noise-induced globally chaotic behavior, and noise-induced phase transitions between oscillatory and excitable regimes. The search for coherence resonance properties in coupled excitable units with the possibility of a noise-induced phase transition to a limit cycle behavior at an optimal value of the noise intensity. The design of adaptable coupling mechanisms between excitable units that would lead to a novel information processing system with the ability to store and retrieve spatio-temporal patterns. The further exploration of purely noise-induced spatio-temporal pattern formation and of the newly discovered multistability properties of these patterns that may allow selection based on initial conditions. The study of hypersensitivity in the presence of unstable fixed points and its effects on synchronization and stochastic resonance. This will allow the determination of optimization conditions for coherence resonance as well as the design of new particle separation devices. Furthermore, hypersensitivity in systems that exhibit stochastic resonance and/or noise-induced phase transitions may lead to enormous enhancements in the response of the system to very small external forces, thus laying the groundwork for new extremely sensitive detection devices. The formulation of a model to offer some insight into the long-standing problem of evolutionary biology of the breaking of left-right symmetry and the associated emergence of order. The proposed stochastic model involves a cooperative symmetry-breaking transition. METHODS. A number of analytic methods will be developed, including mean field and modified mean field approaches, discretization-based approaches, and moment hierarchy truncation approaches. Numerical simulations are also essential tools for this research. INTELLECTUAL MERIT. Solution of the problems posed in this proposal will elucidate the constructive and sometimes destructive role of noise in synchronization, coherence, pattern formation and retrieval, and signal detection, and will allow the development of generic rules for the operation of small-scale physical and biophysical systems. BROADER IMPACT. The broader impact of this work will primarily be evident in two directions. One lies in the close and extensive involvement of members of underrepresented groups. The participants in this effort have extensive track records in mentoring undergraduate, graduate, and postgraduate research of members of underrepresented groups, in designing and participating in a variety of institutional initiatives that enhance the participation of underrepresented groups, and a strong commitment to continue and increase these efforts. Another direction lies in the establishment of a large-scale collaboration involving about 50 scientific groups in the European scientific community. This is made possible by the essential role of one of the senior investigators as one of three conveners of a major European Science Foundation effort in statics and dynamics.