ABSTRACT

NONTECHNICAL SUMMARY

This award supports theoretical research and education to investigate emergent phenomena in condensed-matter, ecological, and biological systems, with a specific emphasis on the brain. Training in these fundamental topics will also help advance the careers of junior researchers in the physical, mathematical, and biological sciences. The overarching goal is to understand phenomena that emerge in systems with many particles or components that interact with each other. These phenomena are a reflection of the components acting in concert and are distinct from the properties associated from an individual particle or component of the system.

In ferromagnetic materials, with the prototypical example being a bar magnet, magnetism arises at low temperatures, where the tendency for magnetism overwhelms thermal fluctuations. However, if such a material is suddenly cooled to low temperature, barriers to ferromagnetism arise, leading to the formation of a glassy state rather than the perfect alignment of microscopic magnets across the material which leads to the ferromagnetic state. A goal of the research is to determine the conditions under which magnetic or glassy behavior arises. A major focus of the research is the study of dense networks, in which the number of links is much larger than the number of nodes. An important example is the human brain, which typically has 100 billion neurons and 100 trillion connections. The connectivity patterns of these neurons contain a rich spectrum of local motifs that may underlie the wondrous functionality of the brain. An important goal is to elucidate these fascinating structures. Another focus is to understand the ecological interplay between depletion of an environment by foraging, the nourishment of the forager by resource consumption, and environmental replenishment by resource growth. An important aim is to determine the conditions under which the forager and resource densities remain in balance and when boom and bust cycles arise.

This award also supports the PI's efforts to develop a massive open online course on topics related to statistical physics.

TECHNICAL SUMMARY

This award supports theoretical research and education that involve applying the techniques of non-equilibrium statistical physics to emergent phenomena in condensed-matter, ecological, and biological systems, with a focus on the brain. While ostensibly disparate, these projects all rely on common investigative tools, including analysis of master equations, scaling theories, and large-scale numerical simulations. Training in using these essential tools will also help advance the careers of junior researchers in the physical, mathematical, and biological sciences.

The first project is to understand the dynamics of kinetic ferromagnetic systems that do not conform to conventional power-law coarsening. Such systems may get stuck in complex metastable states that consist of multiple "breathing" domains. Long-time properties are controlled domain merging - either as isolated events or part of a macroscopic cascade. The resulting ultraslow dynamics resembles that of glassy materials and should provide new insights into glassy behavior.

A second focus is dense networks in which the average node degree increases with the number of nodes N. An important example is the brain. Human brains typically have 100 billion neurons, each of which is connected to roughly 1000 other neurons. The structural connectivity of the brain reveals a rich spectrum of motifs in which small sets of nodes are densely interconnected; such structures may underlie the wondrous functionality of the brain. These and related features, such as multiple phase transitions in the density of fixed-size cliques will be elucidated by the master equation applied to dense networks.

Finally, a principled model of foraging, which is based on the starving random walk model, will be investigated. Here the forager consumes food upon encountering it, thereby depleting the resource locally. Moreover, the forager starves if it wanders for too long without encountering food. When regeneration and reproduction are also incorporated, an even richer phenomenology arises - the dynamics can be steady or oscillatory, with a large-scale spatial organization of foragers and resources. These features will be elucidated by exploiting first-passage and stochastic processes and by large-scale simulations.

This award also supports the PI's efforts to develop a massive open online course on topics related to statistical physics.

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