1. Making sense of a complex world Chris Budd

2. Much of natural (and human!) behavior appears complex and hard to understand Rocks underground

3. Atmosphere and climate El Nino

4. Flocking Turbulence Geology

5. Aircraft undercarriage Complex designs Photonic crystals

6. Human behavior Crowds Stock markets

7. What do we mean by a complex system? Many components with individual behavior Nonlinear Coupling between components Many different scales in space and time The weather.. Air, oceans, sun, CO2 The earth.. Disease spread.. People, viruses, pollutants

8. Human body Stomach Small intestine: 7m x 1.25cm Intestinal wall: Villi and Microvilli

9. Can scientists, mathematicians and engineers make any sense of complexity? And can we use this knowledge to our advantage?

10. Traditional view Things are complicated because there are lots of independent things all going on at once

11. Example: The tides a complicated system which isn’t complex h(t) t Bombay tides 1872

12. Kelvin decomposed h(t) into 37 independent periodic functions Kelvin calculated the coefficients using past data and added them up using an analogue computer

13. US Tidal predictorKelvin’s Tidal predictor

14. But many examples of complexity in nature are not like this! In the tides we see complicated behavior due to a large number of independent uncoupled systems combining their effects The tides are a resultant property of this combination

15. The Double Pendulum.. An example of complex behavior in a simple coupled system Motion can be Periodic in phase : predictable Periodic out of phase : predictable Chaotic : unpredictable

16. Newton’s laws apply to the double pendulum! Angle of top part Angle of bottom part

17. Each part of the system is relatively simple, with easy to understand behavior It is the coupling which leads to new complex emergent behavior In this case chaotic motion

18. Aircraft undercarriage can be very similar

19. Motion of the asteroids is chaotic: will the human race survive?

20. Emergence.. A property of a complex system which is more than the sum of its parts Emergence arises from the way that the components interact with each other and not just from their individual properties

21. Emergent properties of complex systems can allow us to make predictions and even to new designs Emergent Properties Include Coherent Patterns.. Exotic macroscopic behavior Scaling laws Understandable behavior ‘in the large’

22. Coherent Patterns

23. Emergent Patterns often arise because of the way that things interact and communicate with each other Slime mould BZ reaction Can often describe using differential equations Flocking

24. Singularity Patterns in rocks

25. Crowds

26. Scaling laws

27. Microstructure of a real technical ceramic. Al 2 O 3 -TiO 2 R TiO 2 C Al 2 O 3

28. Frequency Conductivity

29. PERCOLATION DETERMINED DC CONDUCTIVITY POWER LAW EMERGENT PROPERTY The ac conductivity of 255 2D squae networks randomly filled with 512 components 60% 1 k  resistors & 40% 1 nF capacitors Emergent scaling law Frequency Random percolation Conductivity

30. An emergent scaling law a is something we can measure b is something that changes They are related by an equation of the form If

31. A very complex example.. The H Bomb r: Radius of fireball E: Energy of the bomb t: Time after the explosion G I Taylor Scaling law

32. We see examples of scaling laws in many other complex systems: The Internet Networks of friends Disease Mechanical systems Protein and gene interactions Porous media Homogeneous system

33. This is VERY useful for environmental predictions Scaling law allows us to make calculations at a finer scale than any computational mesh These computations are important in understanding the transport of pollutants underground over long times

34. Bringing this all together … forecasting the weather The atmosphere/ocean is a very complex system with many length and time scales

35. Need to make predictions but … System has far more degrees of freedom than data Small scale behavior is very can be chaotic Small and large scales interact Lots of random events Turbulence Computations are hard!

36. Make use of all of the previous ideas to improve predictability Scaling laws indicate how energy is transferred from small to large scales and from small heights to large heights which allows us to greatly speed up computations Can fit expected patterns of weather such as depressions and fronts to the sparse data to start and monitor computer weather forecasts allowing for uncertainty Data assimilation Homogenisation Stochastic

37. Complexity.. May apply to many many other problems Where many things interact with each other Spread of disease Customer behavior Transport networks Chemical reactions Much still to be discovered!!!

38. The BICS team: Darryl Almond, Chris Bowen, Nick Britton, Chris Budd, Guler Ergun, Ivan Graham, Giles Hunt, Merilee Hurn, Ilia Kamotski,Vladimir Kamotski, Jan van Lent, Ann Linfield, Nick McCullen, Cathryn Mitchell, Ruth Salway, Rob Scheichl, Hartmut Schwetlick, Valery Smyshlyaev, Chris Williams, Johannes Zimmer