RUI: Fragmentation, Dispersal, and Coalescence in Nonequilibrium Statistical Mechanics

这项研究得到了本科生机构研究计划的支持。这项研究将探索如何使用统计力学概念、模型、工具和哲学来更好地了解基于主体的、随机的、远离平衡的意见动力学、合作和竞争(Spin-Flip)模型中的动态相变现象和时空格局的形成。共同的主线涉及到社会经济人口的统计机械方法，重点是随着相互作用的因素在多维意识形态、观点或战略空间内演变和形成群体时的碎片化、分散和结合动力学。对于这些复杂的、自组织的非平衡系统，依赖于网络拓扑和维度、序参数性质(连续和离散)和对称性、共识和共存动力学之间的差异，以及普适性类的健壮性和范围，是许多基本问题的核心。除了主题本身，这项研究的学术价值坚定地建立在它公开的跨学科特征上，将不同的学科联系在一起；为基于社会经济主体的建模提供统计物理方法，即少数群体游戏；以及对本科生研究人员的指导。更广泛的影响包括巴纳德学院的本科生女性参与；该统计物理项目与哥伦比亚大学正在进行的补充研究的互动；以及与莱顿和牛津的国际合作。%本理论研究将探索统计物理概念和工具在社会和经济系统中的应用。特别是，将探索所谓的基于代理的系统。这些系统类似于投票人群，在那里，独立实体(选民)受到代理人(广告、同行压力)的影响。这项工作将与包括英国和荷兰在内的一些团体一起进行。这将为巴纳德学院的本科生创造机会。

This research is supported under the Research at Undergraduate Institutions program. The research will explore how statistical mechanical concepts, models, tools and philosophy can be used to better inform our understanding of dynamical phase transition phenomena and spatiotemporal pattern formation in agent-based, stochastic, far-from-equilibrium (spin-flip) models of opinion dynamics, cooperation and competition. The common thread concerns a statistical mechanical approach to socioeconomic populations, focusing on fragmentation, dispersal and coalescence dynamics, as interacting agents evolve and form groups within a multidimensional ideological, opinion, or strategy space. Dependence upon network topology and dimensionality, order parameter nature (continuous vs. discrete) and symmetry, differences between consensus vs. coexistence dynamics, as well as the robustness and scope of universality classes lie at the heart of many fundamental questions yet to be answered for these complex, self-organized non-equilibrium systems. Beyond the topics themselves, the intellectual merit of this research is firmly based upon its overtly interdisciplinary character, tying together various disciplines; providing a statistical physics approach to socioeconomic agent-based modeling, i.e., the Minority Game; and the mentoring of undergraduate researchers.Broader impacts include the involvement of undergraduate women from Barnard College; the interaction of this statistical physics program with complementary research being done at Columbia; and international collaborations with Leiden and Oxford.%%%This theoretical research will explore the applications of statistical physics concepts and tools to social and economic systems. In particular, so-called agent-based systems will be explored. These systems are similar to voting populations where independent entities (voters) are being influenced by agents (advertising, peer pressure). The work will be performed with a number of groups including ones in England and the Netherlands. This will create opportunities for undergraduates at Barnard College.***