Statistical Physics of Complex systems

复杂系统是由许多相互作用的实体组成的系统，在这些实体中，从微观层面的相互作用中产生了有趣的全系统行为。这些新出现的现象不能仅用个体构成来解释，而是整个系统的本质属性。复杂的行为可以在物理系统(如湍流、电子输运、超导、等离子体物理)中找到，但也可以在许多其他学科中找到。因此，复杂系统的组成部分可以是物理学中的电子或粒子，也可以是金融市场中的交易者，生物系统中的基因或蛋白质，或者语言进化模型中的演讲者。在这个项目中，我们将使用统计物理学的思想和方法来研究随机复杂系统。这项工作将侧重于所谓的相互作用的“以个人为基础的系统”。我们将从理论的角度研究这类系统，识别它们的特征行为，并开发表征这类系统的方法。这包括近似方法和模拟工具。最初的一个特别重点将是所谓的“选民模式”类别中的模式。它描述了多个特征的传播和空间排序，类似于生物进化的模型。其目的是描述空间秩序和无序的方法。学生将使用数值模拟和统计物理中的工具来做这件事。在项目的后期阶段，我们将把它扩展到语言动力学和生物进化(例如，抗微生物耐药性、进化博弈论)等方面的应用。该项目将随着我们的发展以及新的应用程序和想法的出现而扩展和调整。该项目将始终专注于随机过程、统计物理、非线性动力学以及复杂系统的建模和分析。该项目坚定地位于EPSRC的职权范围内，因为其主要目标是为研究复杂系统开发新的数学和计算方法。本论文将推进非平衡统计物理和涌现领域的研究。

Complex systems are systems composed of many interacting entities in which interesting system-wide behaviour emerges from the interaction at the micro-level. These emergent phenomena cannot be explained by looking at individuals constituents alone, but are intrinsically a property of the system as a whole. Complex behaviour can be found in physical systems (e.g. turbulence, electronic transport, superconductivity, plasma physics), but also in a number of other disciplines. The constituents of a complex systems can therefore be electrons or particles in physics, but also traders in a financial market, genes or proteins in a biological system, or speakers in a model of language evolution.In this project we will use ideas and methods from statistical physics to investigate stochastic complex systems. The work will focus on so-called `individual-based systems' of interacting agents. We will study such systems from a theoretical point of view, identify their characteristic behavior, and we will develop methods for the characterization of such systems. This includes approximation methods and simulation tools. One particular initial focus will be on models in the class of the so-called `voter model'. This describes the spreading and spatial ordering of multiple traits, similar to models of biological evolution. The objective is to characterize the approach to spatial order and disorder. The student will use numerical simulations and tools from statistical physics to do this. In later stages of the project we will expand this to applications for example in language dynamics and biological evolution (e.g. anti-microbial resistance, evolutionary game theory). The project will branch out and be adapted as we go along and as new applications and ideas arise. The focus will always remain on stochastic processes, statistical physics, nonlinear dynamics, and the modelling and analysis of complex systems.The project sits firmly in the EPSRC remit, as the main objective is to develop new mathematical and computational methods for the study of complex systems. The thesis will advance the field of non-equilibrium statistical physics and emergence.