Formation and Properties of Spatially Localized States

提案ID：0605238 PI：埃德加诺布洛奇机构：加州大学伯克利分校题目：空间局域态的形成和性质摘要这是一个研究一维和二维空间局域态的形成和稳定性的建议。这样的状态可以被看作是相空间中的同宿或异宿连接，其中一个空间坐标扮演时间的角色。在许多情况下，这种状态的存在与一种叫做同宿蛇形的现象有关。在这个建议中，我们将调查不同的机制，导致形成的空间局域化结构和它们的稳定性方面的一个和两个维的扰动。这项研究将采用可逆系统的空间动力学技术，再加上详细的数值，并将集中在几个四阶偏微分方程的重要性，在物理科学。该理论将被扩展到可逆性弱破缺的系统中。该建议侧重于物理科学中重要的偏微分方程中空间局域结构的起源和性质。这种结构在光学实验、均匀磁场中的铁磁流体和对流中观察到，并且在其他均匀背景中采取孤立凸起的形式，或者连接两个不同均匀状态的前面。 空间局域振荡，称为微扰子，在振动的颗粒介质和化学反应中观察到。技术将被开发来解释这些状态的起源，以及它们的稳定性。该理论将被扩展到研究系统中的相关状态的形成放在一个轻微的倾斜。

Proposal ID: 0605238PI: Edgar KnoblochInstitution: University of California, BerkeleyTitle: Formation and Properties of Spatially Localized StatesAbstractThis is a proposal to study the formation and stability properties of spatially localized states in one and two spatial dimensions. Such states can be viewed in terms of homoclinic or heteroclinic connections in phase space, with one spatial coordinate playing the role of time. In many cases the presence of such states is related to a phemenon called homoclinic snaking. In this proposal we shall investigate different mechanisms leading to the formation of spatially localized structures and their stability with respect to both one and two-dimensional perturbations. The study will employ the techniques of spatial dynamics for reversible systems coupled with detailed numerics, and will focus on several fourth order partial differential equations of importance in the physical sciences. The theory will be extended to systems in which reversibility is weakly broken.This proposal focuses on the origin and properties of spatially localized structures in partial differential equations of importance in the physical sciences. Such structures are observed in experiments in optics, ferrofluids in a uniform magnetic field and in convection, and take the form of isolated bumps in an otherwise uniform background, or a front connecting two different uniform states. Spatially localized oscillations, called oscillons, are observed in vibrating granular media and in chemical reactions. Techniques will be developed to explain the origin of these states, and their stability properties. The theory will be extended to study the formation of related states in systems placed on a slight incline.