Dynamical programming approach for controlling the directed Abelian Dhar-Ramaswamy model

Preventing Instabilities and Inducing Controlled, Slow-Slip in Frictionally Unstable Systems

We propose a theory for preventing instabilities and inducing controlled, slow-slip in frictionally unstable systems, such as the Generalized-Burridge-Knopoff (GBK) model and seismic fault models. We exploit the dependence of friction on pressure and use it as a backdoor for altering the dynamics of the underlying dynamical system. We use the mathematical Theory of Control and, for the first time, we manage to (a) stabilize and restrict chaos in this kind of systems, (b) guarantee slow frictional dissipation and (c) tune the system toward desirable global asymptotic equilibria of lower energy. Our control approach is robust and does not require exact knowledge of the frictional or elastic behavior of the system. Numerical examples of control are given for a Burridge-Knopoff system and a strike-slip fault model obeying rate-and-state friction. GBK models are known to present Self-Organized Critical (SOC) behavior. Therefore, the presented methodology shows an additional example of SOC Control. Even though further developments are necessary before any practical application, we expect our methodology to inspire earthquake mitigation strategies regarding anthropogenic and/or natural seismicity.

Effect of the Adaptive Response on the Wear Behavior of PVD and CVD Coated Cutting Tools during Machining with Built Up Edge Formation

The relationship between the wear process and the adaptive response of the coated cutting tool to external stimuli is demonstrated in this review paper. The goal of the featured case studies is to achieve control over the behavior of the tool/workpiece tribo-system, using an example of severe tribological conditions present under machining with intensive built-up edge (BUE) formation. The built-ups developed during the machining process are dynamic structures with a dual role. On one hand they exhibit protective functions but, on the other hand, the process of built-up edge formation is similar to an avalanche. Periodical growth and breakage of BUE eventually leads to tooltip failure and catastrophe of the entire tribo-system. The process of BUE formation is governed by the stick-slip phenomenon occurring at the chip/tool interface which is associated with the self-organized critical process (SOC). This process could be potentially brought under control through the engineered adaptive response of the tribo-system, with the goal of reducing the scale and frequency of the occurring avalanches (built-ups). A number of multiscale frictional processes could be used to achieve this task. Such processes are associated with the strongly non-equilibrium process of self-organization during friction (nano-scale tribo-films formation) as well as physical-chemical and mechanical processes that develop on a microscopic scale inside the coating layer and the carbide substrate. Various strategies for achieving control over wear behavior are presented in this paper using specific machining case studies of several hard-to-cut materials such as stainless steels, titanium alloy (TiAl6V4), compacted graphitic iron (CGI), each of which typically undergoes strong built-up edge formation. Various categories of hard coatings deposited by different physical vapor deposition (PVD) and chemical vapor deposition (CVD) methods are applied on cutting tools and the results of their tribological and wear performance studies are presented. Future research trends are outlined as well.

Controlling self-organizing dynamics on networks using models that self-organize

Controlling self-organizing systems is challenging because the system responds to the controller. Here, we develop a model that captures the essential self-organizing mechanisms of Bak-Tang-Wiesenfeld (BTW) sandpiles on networks, a self-organized critical (SOC) system. This model enables studying a simple control scheme that determines the frequency of cascades and that shapes systemic risk. We show that optimal strategies exist for generic cost functions and that controlling a subcritical system may drive it to criticality. This approach could enable controlling other self-organizing systems.