When people interact what happens?
City living means constantly coping with crowds. Whether you walk or take the tube, you’ll be trying to find the best route, and avoiding walking into anyone!
When viewed from above, patterns emerge in the crowd.But how we move through a tube station is very different to moving around an office, or through a public exhibition. These different situations mean we use different strategies, so the patterns that emerge are different too.
What’s your strategy for getting across a crowded room? What about when you are walking through a park?
Mathematics helps us understand the patterns that emerge in crowds. Agent-based models (ABMs) are computer simulations of interactions between ‘agents’ (for example people or cars). Each agent has rules to say how it interacts with its neighbours. Computer simulations and mathematical analysis show what types of overall behaviour or patterns emerge as time passes.
ABMs are being used to help understand how to manage traffic to avoid ‘phantom’ traffic jams, how to design buildings, and how to deal with outbreaks of new diseases.
Networks are mathematical descriptions of connections between ‘things’. These ‘things’ can be computers (e.g., the internet), people (social networks in person or online), towns (connected by road or rail), power stations, mobile phone masts or satellites in orbit.
We can learn a lot about a network from the way its connections are put together (its ‘topology’). For example, in the internet many computers connect to one or a few others, while only a relatively small number of nodes (‘hubs’) connect to many other nodes. This overall level of organisation makes the internet more resilient against failure.
The National Grid is a complex network supplying electricity to our homes. Careful balancing across the network is needed for a reliable electricity supply. In the USA and Canada, catastrophic power failure occurred on 14 August 2003 when small problems in Northeastern Ohio cascaded through the network and caused a blackout affecting 55 million people!
Energy harvesters lie at the opposite end of the scale, extracting small amounts of energy from unpredictable and challenging environments. For example, Stirling Engines turn heat into power and dynamos extract energy from motion. Though they are small, they are enough to power modern micro-devices such as environ-mental sensors. Batteries can be thrown in the bin!
A battery-free temperature sensor (top) and a heat-powered stirling engine (left).