Noise Induced Phenomena

许多现代技术都是基于小型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。人们最感兴趣的是观察到，在纳米尺度上，噪音的影响变得显著甚至至关重要。更重要的是，噪音远不是一种令人不安的副作用，很明显，噪音实际上可能在小型设备的操作模式中起着至关重要的作用。事实上，在没有噪音的情况下，其中一些设备根本无法工作。目标说明。这一建议涵盖了一系列相互关联的问题，涉及扩展非线性系统中远离平衡的噪声诱导和噪声持续现象。主要研究了空间耦合系统中噪声和维数对相位相干性的影响。感兴趣的问题包括噪声对相位相干性的建设性和破坏性影响，噪声引起的全局混沌行为，以及振荡和可激态之间的噪声引起的相变。在耦合可激单元中寻找相干共振特性，在噪声强度的最优值处噪声诱导相变到极限环行为的可能性。设计可激发单元之间的自适应耦合机制，从而形成具有时空模式存储和检索能力的新型信息处理系统。进一步探索纯噪声诱导的时空模式形成和新发现的这些模式的多稳定性特性，这些特性可能允许基于初始条件的选择。不稳定不动点存在下的超敏性及其对同步和随机共振的影响。这将允许确定相干共振的优化条件以及设计新的粒子分离装置。此外，在表现出随机共振和/或噪声诱导相变的系统中，超敏性可能导致系统对非常小的外力的响应大大增强，从而为新的极灵敏检测设备奠定基础。提出一个模型，以提供对进化生物学中长期存在的问题的一些见解，即左右对称的打破和相关的秩序的出现。所提出的随机模型涉及一个合作的对称破缺过渡。方法。许多分析方法将被开发，包括平均场和修正平均场方法，基于离散化的方法，和矩层次截断方法。数值模拟也是本研究的重要工具。知识价值。解决本建议中提出的问题将阐明噪声在同步、相干、模式形成和检索以及信号检测方面的建设性和有时破坏性作用，并将允许为小规模物理和生物物理系统的操作制定一般规则。更广泛的影响。这项工作的广泛影响主要体现在两个方面。一个是代表人数不足的群体成员的密切和广泛参与。这项工作的参与者在指导未被充分代表的群体成员的本科生、研究生和研究生研究方面有着广泛的记录，在设计和参与各种加强未被充分代表的群体参与的机构倡议方面，以及对继续和增加这些努力的坚定承诺方面。另一个方向是建立涉及欧洲科学界约50个科学小组的大规模合作。作为欧洲科学基金会在静力学和动力学方面的主要工作的三个召集人之一，一位高级研究员的重要作用使这一切成为可能。

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.