Harnessing Nonlinearity and Asymmetry for Built-in Control in Mechanical and Fluid Systems

Case, Daniel

doi:https://doi.org/10.21985/n2-5r6t-x202

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Harnessing Nonlinearity and Asymmetry for Built-in Control in Mechanical and Fluid Systems

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Nonlinear systems with many interacting components often exhibit behaviors that cannot be anticipated, even in principle, by only knowing the properties of the constituent parts and thereby emerge as a result of interactions between the parts. Examples of such systems range from power grids and financial markets to food networks and physical materials. Beyond merely understanding the emergent properties of these systems lie the dual goals of developing strategies to control them as well as designing new systems that manifest pre-specified behaviors. In this thesis, we focus on both of these goals. First, we develop an approach for designing microfluidic networks that exhibit an array of programmable flow behaviors. Flows through microfluidic systems typically respond linearly to pressure changes, which hinders the ability to implement built-in flow control mechanisms and results in their dependence on external control devices (e.g., computer-operated pumps). We design microfluidic networks that exhibit a nonlinear relation between the flow rate and applied driving pressure and demonstrate how an array of useful dynamics, such as flow rate oscillations, switching, bistability, and signal amplification may be systematically implemented into larger networks. In another context of harnessing nonlinear effects in a fluid system, we present a new form of dynamical levitation of heavy particles. In this scenario, particles much denser than the fluid can be captured by interacting vortices and, remarkably, be carried against the direction of both the flow and gravity. As a second part of this thesis, we propose new roles for introducing asymmetry into a system. We show new instantiations of the general phenomenon asymmetry-induced symmetry, whereby the stability of the symmetric state(s) of a system is reliant on an asymmetric structure of the system. Specifically, we demonstrate how instabilities that arise in classic mechanical and fluid systems by way of spontaneous symmetry breaking events may be avoided through the systematic introduction of physical system asymmetries. The two particular contexts we consider are optimizing the shape of a column to increase its maximum supported load and suppressing the formation of waves on the surface of a vibrated fluid (i.e., Faraday waves). The results of this thesis present a framework in which systems are designed to exhibit targeted dynamics that arise as emergent phenomena and, thus, provide a new approach for the design of built-in control mechanisms.

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