Abstract: This paper numerically investigates the nonlinear dynamics of the unstable convection regime of the thermal convection loop, an experimental analogue of the Lorenz model. The lower half of the toroidal loop is heated and maintained at a constant high temperature, while the upper half is cooled at a constant low temperature. Subject to the proper boundary conditions, the system of governing equations is solved using a finite volume method. The numerical simulations are performed for water corresponding to Pr = 5.83 and Rayleigh number varying from 1000 to 150,000. In the case of a loop heated from below and cooled from above, it has been demonstrated theoretically and experimentally in the literature that multiple flow regimes are possible. Numerical results in terms of streamlines, isotherms, and local heat flux distributions along the walls are presented for each flow regime. Although several studies have investigated the chaotic regime of convection loops, there have been no detailed numerical simulations of the dynamics of flow reversals. Fine-scale flow behavior during the transition from one flow direction to another is illustrated by the temporal evolution of temperature distribution, mass flow rate, and local heat flux at selected locations in the system. Issues related to the observed Kelvin–Helmholtz instabilities are discussed.
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Bongard's work focuses on understanding the general nature of cognition, regardless of whether it is found in humans, animals or robots. This unique approach focuses on the role that morphology and evolution plays in cognition. Addressing these questions has taken him into the fields of biology, psychology, engineering and computer science.
Danforth is an applied mathematician interested in modeling a variety of physical, biological, and social phenomenon. He has applied principles of chaos theory to improve weather forecasts as a member of the Mathematics and Climate Research Network, and developed a real-time remote sensor of global happiness using messages from Twitter: the Hedonometer. Danforth co-runs the Computational Story Lab with Peter Dodds, and helps run UVM's reading group on complexity.
Laurent studies the interaction of structure and dynamics. His research involves network theory, statistical physics and nonlinear dynamics along with their applications in epidemiology, ecology, biology, and sociology. Recent projects include comparing complex networks of different nature, the coevolution of human behavior and infectious diseases, understanding the role of forest shape in determining stability of tropical forests, as well as the impact of echo chambers in political discussions.
Hines' work broadly focuses on finding ways to make electric energy more reliable, more affordable, with less environmental impact. Particular topics of interest include understanding the mechanisms by which small problems in the power grid become large blackouts, identifying and mitigating the stresses caused by large amounts of electric vehicle charging, and quantifying the impact of high penetrations of wind/solar on electricity systems.
Bagrow's interests include: Complex Networks (community detection, social modeling and human dynamics, statistical phenomena, graph similarity and isomorphism), Statistical Physics (non-equilibrium methods, phase transitions, percolation, interacting particle systems, spin glasses), and Optimization(glassy techniques such as simulated/quantum annealing, (non-gradient) minimization of noisy objective functions).