̽��ֱ�� of Cambridge - Adriana Pesci

Swarming cicadas, stock traders, and the wisdom of the crowd

sc604 — Thu, 01 Feb 2024 14:36:51 +0000

Pick almost any location in the eastern United States – say, Columbus Ohio. Every 13 or 17 years, as the soil warms in springtime, vast swarms of cicadas emerge from their underground burrows singing their deafening song, take flight and mate, producing offspring for the next cycle.

This noisy phenomenon repeats all over the eastern and southeastern US as 17 distinct broods emerge in staggered years. In spring 2024, billions of cicadas are expected as two different broods – one that appears every 13 years and another that appears every 17 years – emerge simultaneously.

Previous research has suggested that cicadas emerge once the soil temperature reaches 18°C, but even within a small geographical area, differences in sun exposure, foliage cover or humidity can lead to variations in temperature.

Now, in a paper published in the journal Physical Review E, researchers from the ̽��ֱ�� of Cambridge have discovered how such synchronous cicada swarms can emerge despite these temperature differences.

̽��ֱ��researchers developed a mathematical model for decision-making in an environment with variations in temperature and found that communication between cicada nymphs allows the group to come to a consensus about the local average temperature that then leads to large-scale swarms. ̽��ֱ��model is closely related to one that has been used to describe ‘avalanches’ in decision-making like those among stock market traders, leading to crashes.

Mathematicians have been captivated by the appearance of 17- and 13-year cycles in various species of cicadas, and have previously developed mathematical models that showed how the appearance of such large prime numbers is a consequence of evolutionary pressures to avoid predation. However, the mechanism by which swarms emerge coherently in a given year has not been understood.

In developing their model, the Cambridge team was inspired by previous research on decision-making that represents each member of a group by a ‘spin’ like that in a magnet, but instead of pointing up or down, the two states represent the decision to ‘remain’ or ‘emerge’.

̽��ֱ��local temperature experienced by the cicadas is then like a magnetic field that tends to align the spins and varies slowly from place to place on the scale of hundreds of metres, from sunny hilltops to shaded valleys in a forest. Communication between nearby nymphs is represented by an interaction between the spins that leads to local agreement of neighbours.

̽��ֱ��researchers showed that in the presence of such interactions the swarms are large and space-filling, involving every member of the population in a range of local temperature environments, unlike the case without communication in which every nymph is on its own, responding to every subtle variation in microclimate.

̽��ֱ��research was carried out Professor Raymond E Goldstein, the Alan Turing Professor of Complex Physical Systems in the Department of Applied Mathematics and Theoretical Physics (DAMTP), Professor Robert L Jack of DAMTP and the Yusuf Hamied Department of Chemistry, and Dr Adriana I Pesci, a Senior Research Associate in DAMTP.

“As an applied mathematician, there is nothing more interesting than finding a model capable of explaining the behaviour of living beings, even in the simplest of cases,” said Pesci.

̽��ֱ��researchers say that while their model does not require any particular means of communication between underground nymphs, acoustical signalling is a likely candidate, given the ear-splitting sounds that the swarms make once they emerge from underground.

̽��ֱ��researchers hope that their conjecture regarding the role of communication will stimulate field research to test the hypothesis.

“If our conjecture that communication between nymphs plays a role in swarm emergence is confirmed, it would provide a striking example of how Darwinian evolution can act for the benefit of the group, not just the individual,” said Goldstein.

This work was supported in part by the Complex Physical Systems Fund.

Reference:
R E Goldstein, R L Jack, and A I Pesci. ‘How Cicadas Emerge Together: Thermophysical Aspects of their Collective Decision-Making.’ Physical Review E (2024). DOI: 10.1103/PhysRevE.109.L022401

̽��ֱ��springtime emergence of vast swarms of cicadas can be explained by a mathematical model of collective decision-making with similarities to models describing stock market crashes.

Ed Reschke via Getty Images

Adult Periodical Cicada

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A new twist on soap films

sc604 — Fri, 23 May 2014 15:13:03 +0000

̽��ֱ��way in which soap films collapse and re-form when twisted or stretched could hold the key to predicting the formation and location of mathematical singularities, which can be seen in the motion of solar flares and other natural phenomena.

Research on the processes by which soap films undergo transitions from one stable state to another has led to conjectures on the nature and location of the singular events that occur during the change of form, connecting two previously separate areas in mathematics.

In mathematics, singularities occur when an equation or surface breaks down and ‘explodes’. In surfaces such as soap films, singularities occur when the surface collides with itself, changing shape in the blink of an eye.

Researchers from the ̽��ֱ�� of Cambridge have shown that identifying a special type of curve on the surface can help predict where these singularities are likely to occur in soap films, which could in turn aid in the understanding of singularities in the natural world. ̽��ֱ��results are published in the journal Proceedings of the National Academy of Sciences (PNAS).

We are all familiar with the simplest soap films, which are formed by dipping a wire loop into a soap solution: the flat surface that spans the wire and the bubbles which are formed when we blow on the film. With suitably shaped wires however, much more complex structures can be formed, such as Möbius strips.

All static soap films are ‘minimal surfaces’, for they have the least area of all possible surfaces that span a given wire frame.

What is less understood are the dynamic processes which occur when a minimal surface like a soap film is made unstable by deforming the supporting wire. ̽��ֱ��film typically moves in a fraction of a second to a new configuration through a singular point, at which the surface collides with itself and changes its connectivity.

These kinds of violent events also occur in the natural world – in fluid turbulence and in the motion of solar flares emanating from the sun – and one of the great challenges has been to predict where they will occur.

In research supported by the EPSRC, a team from the Department of Applied Mathematics and Theoretical Physics attempted to understand how to predict where the singularity will occur when soap films are twisted or stretched to a point of instability. For example, it is well-known that the surface spanning two separate wire loops will collapse to a singularity in between the loops.

In previous work, the group had shown that Möbius strip singularity occurs not between the loops but at the wire frame, where there is a complex rearrangement of the surface. “What was unclear was whether there was an underlying mathematical principle by which this striking difference could be explained,” said Professor Raymond Goldstein, who collaborated with Dr Adriana Pesci, Professor Keith Moffatt, and James McTavish, a maths undergraduate, on the research.

̽��ֱ��team recognised that a geometric concept known as a systole might be the key to understanding where singularities will occur. A systole is the length of the shortest closed curve on surface that cannot be shrunk to a point while remaining on the surface. An example of this is found on a bagel, where the shortest such curve encircles the bagel like a handle. Mathematicians have studied the geometric properties of these curves in recent decades, establishing constraints on the relationship between the length of a systole and the area of the surface on which they lie.

Using new laboratory experiments and computations, the researchers found evidence that the ultimate location of the singularities that occur when soap films collapse can be deduced from the properties of the systole. If the systolic curve loops around the wire frame, then the singularity occurs at the boundary, while if there is no such linking the singularity occurs in the bulk.

“This is an example of experimental mathematics, in the sense that we are using laboratory studies to inform conjectures on mathematical connections,” said Professor Goldstein. “While they are certainly not rigorous, we hope they will stimulate further research into this new, developing area.”

Soap films with complex shapes shed light on the formation of mathematical singularities, which occur in a broad range of fields.

This is an example of experimental mathematics, in the sense that we are using laboratory studies to inform conjectures on mathematical connections

Raymond Goldstein

Singularity in a soap film

Raymond Goldstein

Soap film singularity

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