Active-dissipative nonlinear spatially extended media: Complexity, coarse-graining, multiscale analysis and numerical methods

主动耗散非线性空间扩展介质：复杂性、粗粒度、多尺度分析和数值方法

• 批准号: EP/H034587/1
• 负责人: Serafim Kalliadasis
• 金额: $ 49.71万
• 依托单位: Imperial College London
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2010
• 资助国家: 英国
• 起止时间: 2010 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FH034587%2F1
• 关键词: Active; dissipative; nonlinear; spatially; extended

Spatially extended systems (SES), i.e. infinite dimensional dynamical systems described through partial differential equations deterministic or stochastic in large or unbounded domains, are typically characterized by the presence of a wide range of characteristic length and time scales which often leads to complex spatio-temporal behavior. SES arise frequently as mathematical models of a large variety of natural phenomena and technological applications. The complexity of SES and their dynamics is such that it is very difficult, if not impossible to analyze them directly, either mathematically or, in several cases, numerically. It is imperative, therefore, to seek a low-dimensional description of SES, i.e. to produce coarse grained models that capture most, if not all of the essential dynamic features of the particular applications and which are much easier to study analytically and numerically. The primary aim of the proposed research is the development of state-of-the-art efficient methods for mode reduction and coarse-graining of SES, both deterministic and stochastic.

空间扩展系统（Spatially extended systems，SES）是通过确定性或随机性的偏微分方程描述的无限维动力系统，其特征在于存在大范围的特征长度和时间尺度，这往往导致复杂的时空行为。社会经济学经常作为各种自然现象和技术应用的数学模型出现。SES及其动态的复杂性是这样的，它是非常困难的，如果不是不可能直接分析它们，无论是在数学上，或在某些情况下，数字。因此，必须寻求一个低维的描述SES，即产生粗粒度的模型，捕捉大多数，如果不是所有的基本动态特性的特定应用程序，这是更容易研究分析和数值。所提出的研究的主要目的是国家的最先进的有效方法的发展模式减少和粗粒度的SES，确定性和随机。

项目成果

THE OVERDAMPED LIMIT OF DYNAMIC DENSITY FUNCTIONAL THEORY: RIGOROUS RESULTS

• DOI: 10.1137/110844659
• 发表时间: 2012-01-01
• 期刊: MULTISCALE MODELING & SIMULATION
• 影响因子: 1.6
• 作者: Goddard, B. D.;Pavliotis, G. A.;Kalliadasis, S.
• 通讯作者: Kalliadasis, S.

A Multiscale Analysis of Diffusions on Rapidly Varying Surfaces

快速变化表面扩散的多尺度分析

• DOI: 10.1007/s00332-015-9237-x
• 发表时间: 2015
• 期刊: Journal of Nonlinear Science
• 影响因子: 3
• 作者: Duncan A

Controlling roughening processes in the stochastic Kuramoto-Sivashinsky equation

• DOI: 10.1016/j.physd.2017.02.011
• 发表时间: 2017-06-01
• 期刊: PHYSICA D-NONLINEAR PHENOMENA
• 影响因子: 4
• 作者: Gomes, S. N.;Kalliadasis, S.;Pradas, M.
• 通讯作者: Pradas, M.

Langevin Dynamics with Space-Time Periodic Nonequilibrium Forcing

具有时空周期性非平衡强迫的朗之万动力学

• DOI: 10.1007/s10955-014-1118-4
• 发表时间: 2014
• 期刊: Journal of Statistical Physics
• 影响因子: 1.6
• 作者: Joubaud R

Controlling spatiotemporal chaos in active dissipative-dispersive nonlinear systems.

• DOI: 10.1103/physreve.92.022912
• 发表时间: 2015-08
• 期刊: Physical review. E, Statistical, nonlinear, and soft matter physics
• 作者: S. Gomes;M. Pradas;S. Kalliadasis;Demetrios T. Papageorgiou;G. Pavliotis