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

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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.***