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Article of the Month IAPS 2022-2023 jIAPS

February 2023 – Another way to see the synchronization

Author: Andrea Arlette ESPAÑA-TINAJERO

Universidad Autónoma de San Luis Potosí, México

Aix-Marseille Université, France

When talking about the synchronization phenomenon, the most common thing is to think of biological events where it is possible to observe it with our own eyes, for example, when dozens of birds fly in the sky and form various patterns with choreographies that seem very well rehearsed. Also, some types of fish exhibit this type of behavior when swimming; it seems that they do it harmoniously and without colliding with each other [1]. 

In our case, we will think of the synchronization phenomenon in the following way: it will be a process in which a set of agents interacts, and by allowing a long enough period to pass, then all of them will have the same state, which we will call synchronized state. In the bird example, the synchronized state might be that they are all flying north, and in the fish example, that they are all swimming south.

With this concept of synchronization that has just been defined, we can now think of another type of phenomenon, in particular, the following: consider an empty, impermeable box, without a lid (to be able to observe what happens inside), in which we will pour a liquid (none in particular, we can think of water or oil), with a volume large enough to cover the entire surface of the box. Intuition tells us that when we finish pouring the liquid, each unit of surface area of the box will be the basis of the same volume of liquid. This would be the synchronized state, and this process is more commonly called diffusion.

Imagen que contiene Dibujo de ingeniería

Descripción generada automáticamente
Figure One: Impermeable box, with markings on each area unit. Drops of different sizes and the place where the liquid is poured are shown, as well as the circular neighbourhood formed by pouring the liquid into the box.

The way in which the liquid fills the box is not a very surprising mechanism; that is, if the liquid begins to pour at a point, then a circular neighborhood around that point is expected to fill uniformly at the same time, until the entire area of the box is covered, and then, we will see how its volume increases, until the liquid runs out.

On the other hand, what happens if the box is not initially empty? Suppose that on the surface of the box there are drops of different volumes, and the liquid begins to pour at a point where there is no drop. Diffusion occurs as in the case of the empty box, but when the liquid interacts with a drop, then the circular neighborhood changes its shape to become a kind of deformed number 8, and so on with the drops that it finds in its path. What happens is a kind of agglutination phenomenon, that is, how one drop sticks to another, just before the area of the box fills up and begins to increase in volume until the liquid runs out.

So, for the case where there are drops, how could we describe the way the box is filled? First, we can identify that this phenomenon depends on some factors, the first, how many drops there are in the box at the beginning and what volume each of them has. You can even think of the effect if the box is not square or has holes inside it (without considering liquid losses, each of the holes would have a barrier that would prevent liquid loss).

Despite these new obstacles, the ways in which the synchronized state is reached are accurately described using mathematics, thanks to a new combinatorial approach. In this approach, the configurations of the droplets are encoded together with their volume and the total volume of the liquid. In this way, its route towards synchronization is fully determined [2].

The kind of mathematical objects that are used to describe and code the paths to synchronization are very simple to understand. They are called discrete increasing functions that go above the diagonal and below the constant. They take a list of length N, considering that in each place a number greater than or equal to the one on the left and less than the one on the right is placed. For example, when N=5, the diagonal is (1,2,3,4,5), the constant is (5,5,5,5,5) and two functions between them would be (2,2,3,4,5) and (2,2,4,4,5). These mathematical objects have been extensively studied; multiple characteristics and properties of them are known.

In physics, knowing how to use the tools provided by mathematics, which usually focus on calculus, differential equations, probability, and statistics, have allowed us to solve many problems in an elegant, useful, and educational way. In this case, using combinatorial and number theory tools allowed us to make an exact description of what happens before reaching synchronization, which in turn is a widely observed and studied phenomenon. No tool is left over, one day it could help us to graduate with a doctorate.

References:

  1. A. Pikovsky, M. Rosenblum, J. Kurths, Synchronization – a universal concept in nonlinear sciences, in: Cambridge Nonlinear Science Series, 2001.
  2. A. España, X. Leoncini, E. Ugalde, Combinatorics of the paths towards synchronization, 2022. doi:10.48550/ARXIV.2205.05948. URL: https://arxiv.org/abs/2205.05948

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Article of the Month IAPS 2022-2023 jIAPS

January 2023 – Social Physics

Author: Aikaterini Nikou, University of Edinburgh, UK

Happy New Year! This is the first article in an exciting new series. Every month we hope to showcase a scientific article written by an undergraduate or postgraduate physics student. Is there a topic you would like to write about? Just email your article to jiaps@iaps.info

(Word limit – 1000 words. For guidance on how to write an article, see http://iaps.ovh/wp-content/uploads/2019/01/How-to-write-an-article.pdf and http://iaps.ovh/wp-content/uploads/2022/04/jIAPS-Submission-Guidelines.pdf )

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Social Sciences; Let’s get… physical!

In the orbits of stars, in particle collisions, in chemical reactions, in vehicles’ machines… physics is everywhere. Notoriously, physics is also in human behaviours, human interactions, and social dynamics. Have you ever considered how elegantly physics could describe social phenomena?

Figure 1: Human behaviour forms patterns that can be described by mathematical models just like the laws of physics (from pixabay)

There is a particularly graceful beauty in the notion that social phenomena could be modelled, explained, analysed and predicted using mathematics in a way similar to physical phenomena. This could have a great spectrum of applications including economy (econophysics), pedagogy, tackling pandemics or even… dating. Social physics experiments conducted in the MIT media laboratory have investigated dating and found that it is possible to predict the outcome merely by analysing non-linguistic social signals such as the tone of voice [1]. A similar view could be used to analyse and predict other societal aspects including negotiating.

Social physics is a revolutionising topic in science; however, studying social phenomena through a scientific scope has existed for centuries. The English philosopher Thomas Hobbes mentioned this concept before the term Social Physics or Sociophysics was coined for the first time. He expressed the notion that social phenomena could be represented in terms of the laws of motion of physics and therefore explained through the lens of physics. In his book “De Corpore” (“On the Body”), he described the idea that the behaviour of “material bodies” can be expressed mathematically through the laws of motion invented by Galileo [2]. It seems almost natural to stop for a second and admire the beautiful diachronism of physics, as well as its interdisciplinarity in examining society from a scientific point of view.

Figure 2: Venn diagram showing the interdisciplinary of Social Physics, and its relationship with Physics, Mathematics, Social Science and Computer Science

Social Physics in Today’s Society

We live in a society where data collection is easier than ever, while there is a great number of datasets that are incredibly large and complex to analyse. Such datasets could be phone call records, web activity and credit card transactions. These datasets hold in their arms mathematical patterns that could reveal behavioural changes and patterns. Social physics can… deal with all – the so called “big-data”. It is a powerful tool that could be used for the blooming of our society. Evidently, data science is at the heart of social physics. Wonderfully, it can also help tackle world issues like the Covid-19 pandemic. A study showed that the multi-wave dynamics of Covid-19 outbreaks was dependent on the differences in responses to social stress [3].

A great benefit of social physics is that big data and exact mathematical tools can be applied in order to, in great accuracy, reflect on human behaviour as well as changes in it. It allows us to notice behavioural patterns and to therefore predict future social trends. These trends could include purchase preferences, shopping behaviour, communication behaviour, mobility or even Covid-19 cases spikes. These can then help us come up with more efficient plans to tackle climate change or urban development and traffic. It is worth noting that we could also observe and mathematically model connections between innovation and patterns of habits and communication which could greatly benefit the evolution of society. In other words, social physics can provide us with a way to more profoundly and accurately understand the mechanism of change of society. This could signal the birth of a new and innovative theory for society.

Social Physics and Machine Learning?

A question worth addressing is whether this analysis could be achieved using machine learning. Machine learning is a great tool for analysing mechanical and physical-driven data. For example, it can be invaluable in monitoring oil drill pumps control data and helping engineers prevent a possible malfunction. What about analysing financial transactions and therefore predicting customers’ preferences? Which type of customer would opt for a specific service for example? Social physics can help here as an appropriate tool for analysing human behaviour data. 

Social Physics and human development 

Moreover, social physics can also help in furthering our understanding of human development processes. Social physics has revealed a connection between the communication of a child and its brain development. The level of engagement (communication with people close to them such as parents or caretakers, inside of the red circle as seen in Fig.3) greatly affects the brain development of a child. Children that have a higher level of engagement and exploration (communication with people not in their close circle) have more developed brains and these children become more successful [4].

Figure 3: Patterns of Success. The inner of the red circle includes the “engagement”, anything outside comprises the “exploration” (from [4])

Conclusion

Recently, more and more social and societal phenomena are being studied through the lens of physics and mathematics. This interdisciplinary of social physics is particularly powerful. A great number of social physics studies have been conducted bringing to the surface revolutionising ideas, and so many more have yet to be conducted by the next generation of social physicists that could contribute to the blooming of our society. 

References

  1. Madan A, Caneel R.  Pentland A”S”. Voices of Attraction. MIT Media Laboratory Technical Note 2004 Sep; No. 584. Available from: https://dam-prod.media.mit.edu/x/files/tech-reports/TR-584.pdf
  2. Social Phyics/ Wikipedia [Internet]. Available from https://en.wikipedia.org/wiki/Social_physics 
  3. Kastalskiy AI, Pankratova VE, Mirkes ME, Kazantsev BV, Gorban NA. Social stress drives the multi-wave dynamics of COVID-19 outbreaks. Sci Rep. 2021 Nov18;11(1):22497. 
  4. MIT TEDxTalk [Intenet] Success through Social Physics Alex “Sandy”; 2014 Dec 13. Available from https://www.youtube.com/watch?v=C-wHdSJM_GI