Machine-Aided General Framework for Fluctuating Dynamic Density Functional Theory (MAGFFDDFT)

波动动态密度泛函理论的机器辅助通用框架 (MAGFFDDFT)

• 批准号: EP/X038645/1
• 负责人: Serafim Kalliadasis
• 金额: $ 195.56万
• 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: 2023
• 资助国家: 英国
• 起止时间: 2023 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FX038645%2F1
• 关键词: Machine; Aided; General; Framework; Fluctuating

Many-body systems are ubiquitous in nature, ranging from stellar clusters to soft matter and down to the quantum scale of electrons. Classical fluids are many-body systems at sufficiently high temperatures that quantum effects can be neglected, and which can be easily deformed or structurally altered by external forces and thermal fluctuations. Hence, classical fluids encompass a wide spectrum of simple and complex systems often inherently multiscale. As a result, fluids often exhibit complex behaviour characterised by phase transitions, critical phenomena and emergent properties. Apart from the purely theoretical interest, fluids are central in a wide spectrum of natural phenomena and applications. Not surprisingly, they have been an active topic of both fundamental and applied research for several decades. Major advances, often from statistical mechanics, include the development of coarse-grained models for the evolution of observables by averaging out the microscopic properties and retaining the main effects at the macroscale. However, despite the considerable attention a large number of problems remain unresolved. In particular, existing models suffer from serious limitations including unknown functions-parameters and assumptions-simplifications, e.g. close-to-equilibrium conditions, which often restrict their applicability to largely idealised systems. The aim of the proposed research is to develop a machine-aided generic theoretical-numerical framework that would overcome existing limitations and shortcomings and would allow us to obtain rationally and systematically optimal low-dimensional general laws governing the dynamics of observables, which in turn can be used for the accurate, efficient and systematic analysis of classical fluids and complex multiscale systems in general. This in turn would allow us to advance our understanding of observable dynamics in a wide spectrum of areas, from engineering and physics which so far lack a formal unified framework.

多体系统在自然界中无处不在，从星团到软物质，再到电子的量子尺度。经典流体是在足够高的温度下的多体系统，量子效应可以忽略不计，并且可以很容易地被外力和热波动变形或结构改变。因此，经典流体包含广泛的简单和复杂系统，通常固有地多尺度。因此，流体往往表现出复杂的行为，其特征是相变，临界现象和涌现特性。除了纯理论的兴趣，流体在广泛的自然现象和应用中也是中心。毫不奇怪，几十年来，它们一直是基础研究和应用研究的活跃主题。主要的进展，通常来自统计力学，包括通过平均微观属性并保留宏观尺度的主要影响来发展可观测量演化的粗粒度模型。然而，尽管受到了相当大的关注，但大量问题仍未得到解决。特别是，现有的模型遭受严重的限制，包括未知的功能参数和简化，例如接近平衡的条件，这往往限制了它们的适用性，主要是理想化的系统。拟议的研究的目的是开发一个机器辅助的通用理论-数值框架，克服现有的局限性和缺点，并使我们能够获得合理和系统的最佳低维的一般法律管理的动态观测，这反过来又可以用于准确，有效和系统的分析经典流体和复杂的多尺度系统一般。这反过来又将使我们能够在广泛的领域中推进我们对可观察动力学的理解，从迄今为止缺乏正式统一框架的工程和物理学。