Analysis of the effective long time-behaviour of molecular systems

分子系统的有效长期行为分析

• 批准号: EP/K027743/1
• 负责人: Johannes Zimmer
• 金额: $ 28.31万
• 依托单位: University of Bath
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2013
• 资助国家: 英国
• 起止时间: 2013 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FK027743%2F1
• 关键词: Analysis; effective; long; time; behaviour

Playing golf means: moving the golf ball from the given initial position on the tee through a landscape of hills and valleys to the hole as the final location. Somewhat simplified, the aim of this project is to understand how to play golf not in the three-dimensional space we are accustomed to, but in a complicated landscape with hundreds of dimensions.While this sounds like a mathematical folly, this is what in fact happens in many complex systems, such as molecules or DNA. For example, molecules can exist in several distinctly different states, sometimes called conformations. These states can be pictured as wells of a complex energy landscape. Let us say that the molecule consists of N atoms, each described by 3 space coordinates and 3 momentum coordinates. Then the wells are in a 6N dimensional space. Starting with one conformation of the molecule (one of the wells, as the chemical equivalent of the tee), the atoms will then spend most of the time jostling around in that well before a rare spontaneous fluctuation occurs that lifts the atoms of the reactant over the barrier into the next valley, the well of the other conformation (corresponding to the hole in the golf analogy). This is an example of a so-called rare event. And while these events are indeed rare, they normally carry crucial information on the system in question. So one would like to understand and predict these transitions and rare events. However, a direct molecular simulation would need to resolve the atomistic timescale, while rare events take place on timescales which can be larger by many orders of magnitude; this renders direct simulations unfeasible even on the largest supercomputers.Instead, the aim of this project is to derive rigorously reduced models that capture the effective long-time behaviour ofhigh-dimensional complex systems. A particular focus will be on rare events and transition states. A variety of model problems will be investigated, chosen to capture key challenges present in a number of more complicated problems in various application areas.

打高尔夫意味着：将高尔夫球从球座上的给定初始位置移动通过丘陵和山谷的景观到达作为最终位置的球洞。这个项目的目的是了解如何在我们所熟悉的三维空间中打高尔夫球，而不是在数百维的复杂景观中打高尔夫球。虽然这听起来像是一个数学上的愚蠢，但这实际上是在许多复杂系统中发生的事情，例如分子或DNA。例如，分子可以以几种截然不同的状态存在，有时称为构象。这些状态可以被描绘成一个复杂的能源景观的威尔斯井。假设分子由N个原子组成，每个原子由3个空间坐标和3个动量坐标描述。那么威尔斯在6 N维空间中。从分子的一种构象开始（其中一个威尔斯，就像球座的化学等价物），原子将在该阱中度过大部分时间，然后发生罕见的自发波动，将反应物的原子提升到下一个山谷，另一种构象的阱（对应于高尔夫球比喻中的洞）。这就是所谓的罕见事件。虽然这些事件确实很罕见，但它们通常携带有关系统的关键信息。因此，人们希望了解和预测这些转变和罕见事件。然而，直接的分子模拟需要解决原子的时间尺度，而罕见的事件发生在时间尺度上，可以大许多数量级;这使得直接模拟甚至在最大的超级计算机上也不可行。相反，这个项目的目的是导出严格简化的模型，以捕捉高维复杂系统的有效长时间行为。一个特别的重点将是罕见事件和过渡状态。各种模型问题将被调查，选择捕捉关键的挑战，目前在一些更复杂的问题，在各个应用领域。

项目成果

Travelling waves for a Frenkel-Kontorova chain

Frenkel-Kontorova 链的行波

• DOI: 10.1016/j.jde.2017.03.046
• 发表时间: 2017
• 期刊: Journal of Differential Equations
• 影响因子: 2.4
• 作者: Buffoni B

Hydrodynamic limit of condensing two-species zero range processes with sub-critical initial profiles

亚临界初始剖面冷凝两种物质零范围过程的流体力学极限

• DOI: 10.48550/arxiv.1610.04358
• 发表时间: 2016
• 作者: Dirr N

Hydrodynamic Limit of Condensing Two-Species Zero Range Processes with Sub-critical Initial Profiles.

具有亚临界初始剖面的两种物质零程过程的流体动力学极限。

• DOI: 10.1007/s10955-017-1827-6
• 发表时间: 2017
• 期刊: Journal of statistical physics
• 影响因子: 1.6
• 作者: Dirr N

Entropic and gradient flow formulations for nonlinear diffusion

• DOI: 10.1063/1.4960748
• 发表时间: 2016-08-01
• 期刊: JOURNAL OF MATHEMATICAL PHYSICS
• 影响因子: 1.3
• 作者: Dirr, Nicolas;Stamatakis, Marios;Zimmer, Johannes
• 通讯作者: Zimmer, Johannes

The Semi-infinite Asymmetric Exclusion Process: Large Deviations via Matrix Products

半无限不对称排除过程：通过矩阵乘积产生大偏差

• DOI: 10.1007/s11118-017-9635-9
• 发表时间: 2017
• 期刊: Potential Analysis
• 影响因子: 1.1
• 作者: Duhart H