Is it possible to sound all the church bells across the country at precisely the same time, without one central agent setting the rhythm? Indeed, it is. Future technologies, such as decentralized control mechanisms for motor vehicle traffic or robot swarms, will increasingly come to rely on the ability to function in a similarly synchronous manner. Researchers from Göttingen and Klagenfurt have now developed a new method of self-organising synchronisation and have delivered mathematical proof of the systems' guaranteed ability to achieve synchrony under their own power.
Orchestras, just like mobile telephone networks, rely on central agents that are responsible for the coordination effort. Both might experience errors: If the conductor or the mobile phone base stations are out of action for any reason, musicians and mobile phones come to a standstill. Self-organising systems offer a solution to this problem. Rather than transmitting mobile phone signals using base stations, the application allows individual mobile phones to forward signals to other mobile phones in their vicinity.
However, this collaboration of devices can only work, if their signals are synchronised. Matching models and computer simulations have been existing for many years. But only now has it been mathematically proven beyond any doubt, that such a system always synchronizes. The essential parts of the algorithm will be published in the New Journal of Physics at the end of July. Additionally, the authors, Johannes Klinglmayr and Christian Bettstetter of the Alpen-Adria-Universität, as well as Christoph Kirst and Marc Timme from the Max Planck Institute for Dynamics and Self-Organization in Göttingen, have filed a corresponding patent applications.
Using the example of church bells, Johannes Klinglmayr illustrates the method: "Imagine, that none of the sacristans has a watch, and there is no central location, that dictates the time. The set of rules that we have developed would nevertheless allow all the bells to chime simultaneously." Thanks to the newly developed method, an incremental adjustment of the time setting takes place at each location in reaction to the signals received. Consequently, after a number of chimes, all church bells sound in synchrony. The essential innovative aspect of this invention is that the method guarantees synchronicity, regardless of the time at the initial church watches. Synchrony is achieved even though some signals are not received or not heard. According to Marc Timme, the idea can be applied in a wide variety of technologies: „Groups of robots could work together to solve problems at distributed locations, making use of this ability to synchronize each other and thus coordinate."
The findings resulted from a collaboration between the Alpen-Adria-Universität Klagenfurt (Institute of Networked and Embedded Systems, Lakeside Labs) and the Max Planck Institute for Dynamics and Self-Organization Göttingen (Network Dynamics Group).
- Johannes Klinglmayr, Christoph Kirst, Christian Bettstetter, Marc Timme. Guaranteeing global synchronization in networks with stochastic interactions. New Journal of Physics, 2012; 14 (7): 073031 DOI: 10.1088/1367-2630/14/7/073031
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