2023-06-05 13:50:07
Researchers from the Carlos III University of Madrid (UC3M) and the Complutense University of Madrid (UCM) have discovered a phase change between chaotic states which can appear in herds of animals and, in particular, in swarms of insects. This advance can help to better understand their behavior or be applied to the study of the movement of cells or tumors.
And phase change It occurs when the conditions of a system vary drastically, for example, when water changes from a liquid to a solid state when it freezes. In this research, recently published in the journal Physical Review Ethis group of mathematicians has found such a phenomenon in swarms.
“The insects in the swarm stay in a limited volume, even if they are in a park or in an open space. To explain this, we assume that there is a harmonic potential, a kind of restorative force that confines them (like that of a spring that tries to return to its rest position when we stretch or contract it)”, explains one of the authors of the study, Luis L. Bonilladirector of the Gregorio Millán Barbany Institute of the UC3M.
The confinement of insects responds to a constant of proportionality between force and displacement
This confinement of insects responds to a constant of proportionality between force and displacement. The researchers have verified that for low confinement values, the movement of the insects in the swarm is chaotic (their movements change a lot if the initial conditions are changed).
In this context, the phase change occurs when the swarm divides into several that, however, are closely related to each other, because there are insects that pass from one to another. At the critical line between phases of this change, the distance between two insects in the swarm that are influenced by each other is proportional to the size of the swarm, even if the number of insects in the swarm grows indefinitely. This is called “stop-free chaos” and hasn’t been discovered until now, the researchers say.
“As the number of insects grows, the critical line moves toward zero confinement. What happens is that the maximum distance between two insects that still feel each other’s influence is proportional to the size of the swarm. It doesn’t matter how many insects we put in it. And that represents an absolute novelty that we have discovered”, indicates Bonilla.
Scale-free chaotic behavior
Specifically, what these mathematicians predict through numerical simulations is that certain swarms of insects (specifically a class of small flies) have a scale-free chaotic behavior, which translates into certain power laws with exponents similar to those that have been measured in nature. They have also found a simplified mean-field theory that supports the scale-free chaos phase shift.
“It would be good to look for and find that phase change between chaotic phases that we predict, either in observations in the middle of nature or in controlled laboratory studies,” says another of the authors of the research, the UCM mathematician, Rafael Gonzalez Albaladejo.
The formation of herds is one of the manifestations of the so-called “active matter”, composed of self-propelled individuals that make up a whole.
The formation of herds is one of the manifestations of the so-called “active matter”, made up of something like self-propelled individuals that make up a whole, the researchers explain. It can be a swarm of insects, a flock of sheep, a flock of birds, a school of fish, but also bacteria on the move, melanocytes (the cells that distribute pigments in the skin) or artificial systems such as irregular grains or seeds. shaken periodically.
“The herd formation mechanisms play a role in some of these systems, so the results we have obtained can be linked with biology, with the study of cells, and beyond, with the study of tumors and other diseases”, adds González.
move accordingly
How do so many animals move in unison together? These researchers explain that each individual feels only its neighbors and moves accordingly, even though they do not have a perspective on the movement of the entire herd. And depending on whether they use sight, hearing or the vibrations of the fluid in which they are immersed, the concept of neighbor can change quite a bit. Some sheep that move together, see and feel those around them, while some birds in a flock see their nearest neighbors, even if they are quite far from each other.
“The thing about move accordingly, it can mean that they move in the same direction as their neighbors (usually) or they can adopt different strategies depending on the situation. For example, if a crowd is trying to get out of a crowded area with more than one door, there are times when not following the neighbors is advantageous,” they explain.
Each individual feels only its neighbors and moves accordingly, even if it does not have a perspective on the movement of the entire herd.
These mathematicians have taken about two years to carry out this research work. At first, they planned to explain some experiments studying the conventional phase change among a multitude of insects that fill a space with constant density and that are ordered when a critical value of the control parameter passes (for example, when noise decreases). But then they decided to add a harmonic potential to confine the swarm and explore what happens when the force of attraction between individuals decreases.
“We discovered many periodic, quasi-periodic, and finally chaotic states for a fixed number of insects that were increasing. What is surprising is the transition between chaotic states that we did not know or suppose existed and we were able to find the correct arguments and tests to support its existence”, indicates another of the authors of the study, Ana Carpiofrom the Department of Mathematical Analysis and Applied Mathematics of the UCM, who specifies that there is still a lot to be done based on this work.
“From seeking experimental confirmation of our predictions and better adapting the model to experimental observations, to carrying out theoretical and mathematical investigations that go beyond our numerical simulations,” he concludes.
Reference:
González-Albaladejo, R. Carpio, A. Bonilla, LL (2023). Scale-free chaos in the confined Vicsek flocking model. Phys. Rev. HAVE BEEN.
Gonzalez-Albaladejo, R. Bonilla, LL (2023). Mean field theory of chaotic insect swarms. Phys. Rev. HAVE BEEN
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