Self-organising criticality: how SOC characterises epidemics and polymer networks
In 1987, Per Bak, along with colleagues Tang and Weisenfeld, published a landmark paper in Physics Review Letters (PRL). The paper, Self-organized criticality: An explanation of the 1/f noise, represented a giant leap in the understanding and modelling of dynamical systems. In this article, we shed light on why this paper has had such an impact across every scientific field. It comes at a time when understanding the COVID crisis has made it imperative for us to understand the self-organised system of the spread of the virus.
The paper proposes that organised states of matter, or other populations, share a degree of universality. In essence, drastically different populations and data can share the same power laws, regardless of their scale or physical location, even across different scientific disciplines. Power laws describe the behaviour of systems with interdependent variables that naturally organise to a tipping point; a state of criticality when a seismic volume of change occurs.
What is self-organising criticality?
“Why does the River Nile flow the way that it does?”
“What affects the point at which a sandpile collapses underneath itself?”
“At what point does the spread of a potentially deadly virus become uncontrollable?”
As scientists, we are in the business of making empirical observations. We record what we see and seek to establish scientific facts. Using patterns, we learn the relationship between variables, which brings us a better understanding of the relationship, which can result in devastating consequences – as we have witnessed during the COVID-19 pandemic.
Take another potentially disastrous critical situation, a volcanic eruption. We can record the explosiveness and violence of an eruption over time. Through analysis, geologists can spot patterns and guesstimate when violent eruptions are likely to occur. These patterns are better predicted by power laws, showing the point at which a volcano reaches self-organised criticality. But what Bak proposed is that other states of matter, or indeed other populations, can share these power laws, indicating a degree of universality.
Universality: the same power-law dynamics can apply anywhere
Power laws describe the relationship between two variables. Bak explains how two completely independent systems can share the same power laws. Power laws are universal, they can be shared across disciplines, at widely different scales––from the astronomical to the microscopic–– in natural and man-made systems.
There are many natural systems in the world that self-organise. In some of these, they obey power laws that naturally organise themselves to a state nearing criticality, a big, notable event. This might be an earthquake, neurons in your brain or even the stock markets – at every scale that a scientist may want to build an understanding.
One of the most significant events of 2020 can even be characterised as a self-organising system – the COVID-19 pandemic. The model can be applied and used to explain power laws in a huge variety of systems.
Virus modelling: SOC for COVID-19
Viruses are another example of a self-organizing, self-similar system that can be modelled using self-organising criticality.
There are already a number of papers examining the spread of COVID-19 using models based on the ideas of Per Bak. Virus modelling has become increasingly sophisticated since Bak’s original paper, although many modern models are fundamentally guided by the ideas presented in the concept of self-organised criticality.
Self-organising criticality can explain how viruses can exist in remote locations, then, after reaching a critical number of infections, can spread almost globally. New models take into account the instability and adaptability of viruses, particularly due to their mutation rates. However, understanding the tipping points – the critical number – is crucial in understanding the rate of infection.
At Makevale, the science we use is very much guided by the work of Per Bak. Although Bak’s work provides plenty of value with work on the raw polymer chemistry theory, manufacturers like Makevale are downstream recipients of the value this work provides.
Polymer reactions are yet another example of a self-organising system that becomes critical. But as reactions can be influenced by so many different variables, the mathematics can be incredibly complex.
In SOC systems, one singular disturbance can cause a tsunami of change. Bak’s classic example is that one single grain of sand can cause a landslide. These changes can exist at every different scale, according to Bak. This is called a scale-free distribution of effects and they are present in lots of different self-similar systems like blood vessel networks.
A coastline, for example, is a highly complex system. If you were a geologist tasked with understanding a beach, you would quickly understand that complexity exists at almost every scale, from the individual rocks to the coastline as a whole. Fractals are recursive patterns that exist at different length-scales; complexity in rock roughness is just as complex as a sandy beach.
There are various scaling laws involved in polymer science, which is why fractal concepts provide a lot of value in Makevale’s work. For example, the average end-to-end distance of a polymer chain is determined by a power law, dictated by the number of monomers present.
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