Noise Induced Phenomena

许多现代技术都是基于小的空间或层次扩展系统的同步特性，其中复杂的非线性相互作用起着至关重要的作用。最令人感兴趣的是观察到在纳米尺度上噪声的影响变得显著甚至至关重要。更重要的是，噪声远非一种令人不安的副作用，它实际上可能在小型设备的操作模式中发挥重要作用。事实上，其中一些设备在没有噪音的情况下根本无法工作。保证声明。该建议涵盖了一系列相互关联的问题，涉及噪声引起的和噪声持续的现象，在扩展的非线性系统远离平衡。主要研究方向：空间耦合系统中噪声和维数对相位相干性的影响。感兴趣的问题包括建设性和破坏性的影响，噪声相位相干性，噪声引起的全局混沌行为，和噪声引起的振荡和可兴奋制度之间的相变。研究耦合可激发单元的相干共振性质，在噪声强度的最佳值处，噪声诱导相变到极限环行为的可能性。设计可兴奋单位之间的适应性耦合机制，这将导致一种新的信息处理系统，具有存储和检索时空模式的能力。进一步探索纯粹的噪声引起的时空模式的形成和新发现的多稳定性的这些模式，可以允许基于初始条件的选择。不稳定不动点下的超敏性及其对同步和随机共振的影响的研究。这将允许确定相干共振的优化条件以及新的颗粒分离装置的设计。此外，在系统中，表现出随机共振和/或噪声诱导的相变的超敏性可能会导致系统对非常小的外力的响应的巨大增强，从而为新的极其灵敏的检测设备奠定了基础。一个模型的制定提供了一些洞察进化生物学的左，右对称性的破坏和相关的出现秩序的长期存在的问题。所提出的随机模型涉及一个合作的破坏性的过渡。方法.一些分析方法将被开发，包括平均场和修改的平均场方法，离散化为基础的方法，和时刻层次截断方法。数值模拟也是这项研究的重要工具。智力优势。解决本提案中提出的问题将阐明噪声在同步、连贯性、模式形成和检索以及信号检测中的建设性作用，有时也是破坏性作用，并将允许为小规模物理和生物物理系统的运作制定通用规则。更广泛的影响。这项工作的更广泛影响将主要体现在两个方面。其中之一是代表性不足群体的成员密切和广泛参与。在这项工作的参与者在指导本科生，研究生和研究生的代表性不足的群体的成员的研究，在设计和参与各种机构的举措，提高代表性不足的群体的参与，并坚定地承诺继续和增加这些努力的广泛的跟踪记录。另一个方向是建立一个涉及欧洲科学界约50个科学团体的大规模合作。这是可能的重要作用的一个高级研究人员作为一个主要的欧洲科学基金会的努力在静力学和动力学的三个召集人之一。

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.