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Making sense of a complex world Chris Budd

Explore the intricacies of complex systems such as the National Electricity Grid, Atmosphere, Clouds, El Nino, and more. Learn how scientists and mathematicians make sense of complexity and its emergent properties, from turbulence to human behavior, using mathematical models. Discover the concept of emergence and scaling laws in predicting behavior in systems like aircraft undercarriage and crowds. Delve into forecasting weather by understanding the interactions and dynamics of complex systems, utilizing computations and data assimilation. Unravel the mysteries of complexity in various fields and the ongoing quest for knowledge in deciphering intricate systems.

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Making sense of a complex world Chris Budd

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  1. Making sense of a complex world Chris Budd

  2. Many natural (and human!) systems appear complex and hard to understand National Electricity Grid

  3. Atmosphere and climate Clouds El Nino

  4. Turbulence Flocking Geology

  5. Complex designs Aircraft undercarriage

  6. Human behaviour Crowds

  7. What makes a system complex ? Many components with individual behavior Coupling between components Many different scales in space and time

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

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

  10. A complicated example: The tides Bombay tides 1872 h(t) t

  11. Kelvin decomposed h(t) into 37 independent components He found these out using past data andadded them up using an analogue computer

  12. Kelvin’s Tidal predictor US Tidal predictor

  13. In the tides we seecomplicatedbehaviour due to alarge numberof independentuncoupledsystems combining their effects The tides are a resultant property of this combination But many examples ofcomplexityin nature are not like this!

  14. The Double Pendulum .. An example ofcomplex behaviourin a simple coupled system Motion can be • Periodicin phase :predictable • Periodicout of phase : predictable • Chaotic :unpredictable

  15. Each part of the system is relatively simple, with easy to understand behavior It is the coupling which leads to new complex emergent behavior which we understand by using maths

  16. Aircraft undercarriage can be very similar

  17. 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

  18. Emergent properties of complex systems can allow us to make predictions and even to new designs. They include … • Coherent Patterns .. • Much of science and maths involves the search for, and study of, these patterns • Scaling laws

  19. Coherent Patterns

  20. Emergent Patterns often arise because of the way that things interact and communicate with each other Flocking Slime mould All described using mathematical equations

  21. Patterns in rocks

  22. Crowds at a scramble crossing

  23. Scaling laws

  24. Microstructure of a ceramic. Al2O3-TiO2 R TiO2 C Al2O3

  25. Frequency Conductivity

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

  27. Homogeneous system We see examples of scaling laws in many other complex systems: • The Internet • Epidemics • Mechanical systems • Rocks and water

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

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

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

  31. Make use of all of the previous ideas to improve predictability Scaling laws show howenergy is transferred from small to large scalesand fromsmall heights to large heightsand greatly speed up computations Fit coherentpatterns of weather eg. depressions to the sparse data to start and monitor computer weather forecasts (data assimilation) 1987!!

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

  33. Eg. The digestive system Stomach Intestine Intestinal wall: Villi and Microvilli

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