Exploiting Complexity to Stabilize the Dynamics of Mechanical Systems

Project: Research project

Project Details


The onset of dynamical instabilities has been a problem of longstanding scientific interest in diverse areas of science and engineering, ranging from bridge resonances to fluid turbulence. While progress has been made, the fundamental question of how the properties of a physical system relate to the emergence of instabilities remains largely open. As a result, our ability to control and mitigate such instabilities remains limited. The problem of preventing instabilities is akin to the problem of stabilizing a desired dynamical state. Of special interest are states that have certain symmetries, such as the space-translation symmetry of a simple laminar flow or the time translation symmetry of a motionless structure. Symmetric states are known to exist if the system itself has the same symmetries, but herein lies the rub: sufficient conditions for the existence of a state are usually neither sufficient nor necessary for the state to be stable. In this STIR project, we will propose and explore an innovative approach to prevent, delay, or control the onset of symmetry-breaking instabilities in complex continuous mechanical systems. The approach builds on the recent theoretical discovery that unstable symmetric states may continue to exist and, most importantly, become stable when the symmetry of the system itself is explicitly broken. This novel effect has been established for network systems and shown to emerge from interactions between different parts of the system. This previously unexplored aspect of complexity is thus also expected to occur in continuous media. Demonstrating this possibility is the main goal of this project. Specifically, in this project we plan demonstrate theoretically and experimentally that instabilities in driven pattern-forming systems can be manipulated by breaking the symmetry of the system. As a proof-of-concept study, our theory and experiments will focus on Faraday waves instabilities, which are important in their own right and representative of a large class of instabilities in driven system. The outcomes of this research are expected to provide an important new venue to control instabilities by manipulating system parameters, which should be contrasted with prior progress on preventing instabilities achieved through the explicit control of the system variables, and which is limited precisely by one’s ability to actuate the required variables in real time. This research promises to strongly impact outstanding problems of interest to the Army and potentially illuminate new lines of research. In particular, it can lead to new approaches for the control and mitigation of instabilities in a wide range of contexts, including multi-agent systems, systems subject to resonance-induced instabilities, and consensus algorithms for swarming sensors and infrastructure systems. The proposed research is inherently transdisciplinary and will benefit from Northwestern University tradition in transdisciplinary complex systems research. The project will involve a graduate student and a postdoctoral researcher, and thus will also contribute to the training of the next generation of transdisciplinary scientists.
Effective start/end date6/10/203/9/21


  • Army Research Office (W911NF2010173)


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