Controlling self-organized criticality in sandpile models

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.

Greedy control of cascading failures in interdependent networks

Complex systems are challenging to control because the system responds to the controller in a nonlinear fashion, often incorporating feedback mechanisms. Interdependence of systems poses additional difficulties, as cross-system connections enable malicious activity to spread between layers, increasing systemic risk. In this paper we explore the conditions for an optimal control of cascading failures in a system of interdependent networks. Specifically, we study the Bak-Tang-Wiesenfeld sandpile model incorporating a control mechanism, which affects the frequency of cascades occurring in individual layers. This modification allows us to explore sandpile-like dynamics near the critical state, with supercritical region corresponding to infrequent large cascades and subcritical zone being characterized by frequent small avalanches. Topological coupling between networks introduces dependence of control settings adopted in respective layers, causing the control strategy of a given layer to be influenced by choices made in other connected networks. We find that the optimal control strategy for a layer operating in a supercritical regime is to be coupled to a layer operating in a subcritical zone, since such condition corresponds to reduced probability of inflicted avalanches. However this condition describes a parasitic relation, in which only one layer benefits. Second optimal configuration is a mutualistic one, where both layers adopt the same control strategy. Our results provide valuable insights into dynamics of cascading failures and and its control in interdependent complex systems.

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.

Cascading failures in scale-free interdependent networks

Large cascades are a common occurrence in many natural and engineered complex systems. In this paper we explore the propagation of cascades across networks using realistic network topologies, such as heterogeneous degree distributions, as well as intra- and interlayer degree correlations. We find that three properties, scale-free degree distribution, internal network assortativity, and cross-network hub-to-hub connections, are all necessary components to significantly reduce the size of large cascades in the Bak-Tang-Wiesenfeld sandpile model. We demonstrate that correlations present in the structure of the multilayer network influence the dynamical cascading process and can prevent failures from spreading across connected layers. These findings highlight the importance of internal and cross-network topology in optimizing robustness of interconnected systems.

Self-organization of dragon king failures

The mechanisms underlying cascading failures are often modeled via the paradigm of self-organized criticality. Here we introduce a simple network model where nodes self-organize to be either weakly or strongly protected against failure in a manner that captures the trade-off between degradation and reinforcement of nodes inherent in many network systems. If strong nodes cannot fail, any failure is contained to a single, isolated cluster of weak nodes and the model produces power-law distributions of failure sizes. We classify the large, rare events that involve the failure of only a single cluster as "black swans." In contrast, if strong nodes fail once a sufficient fraction of their neighbors fail, then failure can cascade across multiple clusters of weak nodes. If over 99.9% of the nodes fail due to this cluster hopping mechanism, we classify this as a "dragon king," which are massive failures caused by mechanisms distinct from smaller failures. The dragon kings observed are self-organized, existing over a wide range of reinforcement rates and system sizes. We find that once an initial cluster of failing weak nodes is above a critical size, the dragon king mechanism kicks in, leading to piggybacking system-wide failures. We demonstrate that the size of the initial failed weak cluster predicts the likelihood of a dragon king event with high accuracy and we develop a simple control strategy that can dramatically reduce dragon kings and other large failures.

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.

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

A dynamical programming approach is used to deal with the problem of controlling the directed abelian Dhar-Ramaswamy model on two-dimensional square lattice. Two strategies are considered to obtain explicit results to this task. First, the optimal solution of the problem is characterized by the solution of the Bellman equation obtained by numerical algorithms. Second, the solution is used as a benchmark to value how far from the optimum other heuristics that can be applied to larger systems are. This approach is the first attempt on the direction of schemes for controlling self-organized criticality that are based on optimization principles that consider explicitly a tradeoff between the size of the avalanches and the cost of intervention.