No abstract

We report the discovery of a discrete hierarchy of micro-transitions occurring in models of continuous and discontinuous percolation. The precursory micro-transitions allow us to target almost deterministically the location of the transition point to global connectivity. This extends to the class of intrinsically stochastic processes the possibility to use warning signals anticipating phase transitions in complex systems.

Finding conditions that support synchronization is a fertile and active area of research with applications across multiple disciplines. Here we present and analyze a scheme for synchronizing chaotic dynamical systems by transiently uncoupling them. Specifically, systems coupled only in a fraction of their state space may synchronize even if fully coupled they do not. Although, for many standard systems, coupling strengths need to be bounded to ensure synchrony, transient uncoupling removes this bound and thus enables synchronization in an infinite range of effective coupling strengths. The presented coupling scheme thus opens up the possibility to induce synchrony in (biological or technical) systems whose parameters are fixed and cannot be modified continuously.Synchronization is one of the most prevalent collective phenomena in coupled dynamical systems [1]. Synchronization and related consensus phenomena have been frequently found in biological, ecological, physical, engineering and social systems such as in predator-prey dynamics, the spread of epidemics, the migration of large populations, systems of self-driven particles and systems of social or technical dynamics [2][3][4][5][6][7][8][9][10][11][12]. For chaotic systems, synchronization typically emerges only within a specific range of coupling strengths and is impossible otherwise [1,[13][14][15].In this letter, we propose and analyze a way of inducing synchronization between coupled chaotic oscillators by transient uncoupling: If the system is in a certain predefined subset of its state space, coupling is active; otherwise it is inactive. We systematically study the dependence of successful synchronization on the fraction of state space where coupling is active. Synchronization may emerge even for systems that coupled continuously in time (i.e., standard coupling) do not synchronize. Furthermore, the system may synchronize for an infinite range of coupling strengths, although this is often not possible for ordinarily coupled chaotic systems.A systematic numerical analysis reveals how transverse stability properties vary across the attractor with the location of active coupling, not only between more or less stable synchrony but all the way from stability to instability for the same system. This demonstrates that transient uncoupling modifies the collective dynamics in a non-trivial way. These results may find applications in inducing synchrony in systems whose local coupling parameters cannot be continuously varied with ease but only switched on or off. * malte@nld.ds.mpg.de †

Crackling noise is a common feature in many systems that are pushed slowly, the most familiar instance of which is the sound made by a sheet of paper when crumpled. In percolation and regular aggregation, clusters of any size merge until a giant component dominates the entire system. Here we establish 'fractional percolation', in which the coalescence of clusters that substantially differ in size is systematically suppressed. We identify and study percolation models that exhibit multiple jumps in the order parameter where the position and magnitude of the jumps are randomly distributed-characteristic of crackling noise. This enables us to express crackling noise as a result of the simple concept of fractional percolation. In particular, the framework allows us to link percolation with phenomena exhibiting non-self-averaging and power law fluctuations such as Barkhausen noise in ferromagnets.

The individualization and customization of products is one the most important trends for industrial companies. New technologies like additive manufacturing (e. g. 3D-printing) are enablers for the further development of this trend. Companies offering production systems for those technologies are more and more required to embed Industrial Product Service Systems (IPSS) to assert theirselves on the market. The aim of this research is to develop a business model which evaluates process costs of additive manufacturing technologies. The relevant technologies are Stereolithography, Selective Laser Melting, Fused Deposition Modeling, Selective Laser Melting, Electron Beam Melting and Laser Cladding. Product costs can be calculated easily and the outcome of the evaluation will serve as a valuable decision base for industrial decision makers on how to invest in a special technology. By embedding this service in the production system/ machines software, a big step for a new industrial service is provided. The paper is structured in four steps. Firstly, based on a detailed description of the state of the art research, an analysis of the most important process steps in additive manufacturing is presented. A new business model for additive manufacturing technologies is introduced afterwards including the implementation of this business model in a software tool. Furthermore case studies for different product types and product quantities are explained and detailed values for process costs are provided. In the last step, a sensitivity analysis is done to find the most important parameters (cost drivers) for those case studies. The business model and the evaluation of cost structures for additive manufacturing technologies is unique in the field of IPSS. Using a cost and investment calculation, the companies can significantly increase the effort and quality of price calculations for their products. Furthermore cost drivers are evaluated and recommendations for technology related investments are given.

No abstract

We analyze the properties of order parameters measuring synchronization and phase locking in complex oscillator networks. First, we review network order parameters previously introduced and reveal several shortcomings: none of the introduced order parameters capture all transitions from incoherence over phase locking to full synchrony for arbitrary, finite networks. We then introduce an alternative, universal order parameter that accurately tracks the degree of partial phase locking and synchronization, adapting the traditional definition to account for the network topology and its influence on the phase coherence of the oscillators. We rigorously proof that this order parameter is strictly monotonously increasing with the coupling strength in the phase locked state, directly reflecting the dynamic stability of the network. Furthermore, it indicates the onset of full phase locking by a diverging slope at the critical coupling strength. The order parameter may find applications across systems where different types of synchrony are possible, including biological networks and power grids.Many dynamical system in physics, biology or engineering can be described as coupled phase oscillators, often in a network with a complex interaction topology. The prototypical model considered in this context are networks of Kuramoto oscillators. To study the synchronization in such systems several order parameters have been introduced, adapting the original Kuramoto order parameter, defined for all-to-all coupled oscillators, to complex interaction networks. However, none of the order parameters manages to fully track the transition from oscillators moving at their individual frequencies to full synchronization of the network. Here we propose a universal order parameter to study synchronization in finite networks of phase oscillators, tracking all stages of synchronization. This order parameter may be used to study systems where different stages of synchrony are relevant. Additionally, we rigorously proof several helpful qualities relating the order parameter not only to the synchrony but also to the dynamical stability of the network.

Synchronization constitutes one of the most fundamental collective dynamics across networked systems and often underlies their function. Whether a system may synchronize depends on the internal unit dynamics as well as the topology and strength of their interactions. For chaotic units with certain interaction topologies synchronization might be impossible across all interaction strengths, meaning that these networks are non-synchronizable. Here we propose the concept of interaction control, generalizing transient uncoupling, to induce desired collective dynamics in complex networks and apply it to synchronize even such non-synchronizable systems. After highlighting that non-synchronizability prevails for a wide range of networks of arbitrary size, we explain how a simple binary control may localize interactions in state space and thereby synchronize networks. Intriguingly, localizing interactions by a fixed control scheme enables stable synchronization across all connected networks regardless of topological constraints. Interaction control may thus ease the design of desired collective dynamics even without knowledge of the networks’ exact interaction topology and consequently have implications for biological and self-organizing technical systems.