Newswise — Scientists at Universidad Carlos III de Madrid (UC3M) and Universidad Complutense de Madrid (UCM) have unearthed a phase alteration amidst disorderly conditions that can manifest within animal packs and specifically in insect swarms. This breakthrough could enhance comprehension of their conduct or be employed for examining cellular or tumor mobility.
A phase transition arises when the circumstances of a system undergo a significant shift, such as the transformation of water from a liquid to a solid state during freezing. In this recently published research featured in the journal Physical Review E, this team of mathematicians has observed a similar occurrence within swarms. "The insects within the swarm exhibit confinement to a restricted volume, even in open spaces or parks. To account for this, we posit the presence of a harmonic potential, a form of restorative force that constrains them (much like a spring's tendency to return to its original position when stretched or compressed)," elucidates Luis L. Bonilla, one of the authors of the study and the director of UC3M's Gregorio Millán Barbany Institute.
The confinement of these insects exhibits a response governed by a constant relating force and displacement. The research team has determined that when the confinement values are low, the movement of the swarm becomes chaotic, with significant variations occurring when initial conditions are altered. Within this context, a phase shift occurs when the swarm fragments into multiple closely interconnected sub-swarms, facilitated by the movement of insects between them. Along the critical threshold of this shift, the distance between two mutually influenced insects within the swarm becomes proportional to the swarm's size, even if the number of insects within the swarm becomes infinitely large. This phenomenon, referred to as "scale-free chaos," has remained undisclosed until now, as noted by the researchers. "As the number of insects increases, the critical threshold moves towards zero confinement. What transpires is that the maximum distance between two insects that still perceive each other's influence corresponds to the size of the swarm. The number of insects we introduce becomes inconsequential. This discovery represents an absolute novelty," elucidates Luis L. Bonilla, one of the study's authors and the director of UC3M's Gregorio Millán Barbany Institute.
Based on their numerical simulations, these mathematicians make a noteworthy prediction regarding certain swarms of insects, specifically a particular group of small flies. They propose that these swarms exhibit scale-free chaotic behavior, characterized by power laws with exponents similar to those observed in natural systems. Moreover, they have developed a simplified mean-field theory that supports the notion of a phase shift towards scale-free chaos. "It would be beneficial to actively search for and identify the predicted phase shift between chaotic phases, whether through natural observations or controlled laboratory experiments," emphasizes Rafael González Albaladejo, another author of the research who is affiliated with UCM as a mathematician and has a connection with UC3M's Gregorio Millán Barbany Institute.
The researchers clarify that the emergence of herds is a characteristic feature of "active matter," which consists of self-propelled individuals that come together as a cohesive unit. This phenomenon can be observed in various systems such as swarms of insects, flocks of sheep, bird formations, schools of fish, as well as in the motion of bacteria, melanocytes (cells responsible for distributing pigments in the skin), or even artificial systems like irregular grains or periodically shaken seeds. "The mechanisms underlying herd formation are relevant to several of these systems, so the outcomes of our study can be connected to the field of biology, encompassing the study of cells, and extend further to investigations of tumors and other diseases," adds Rafael González Albaladejo.
The researchers explain that the coordinated movement of numerous animals occurs through a mechanism where each individual only perceives and responds to its immediate neighbors. Despite lacking an overall perspective of the entire herd's movement, individuals adjust their motion based on the actions of nearby companions. The concept of "neighbor" can vary depending on the sensory modality employed, such as sight, hearing, or vibrations in the surrounding fluid. For instance, sheep moving in unison rely on visual and sensory cues from their surroundings, while birds within a flock mainly observe their closest neighbors, even if they are physically distant. "Moving accordingly" implies aligning their movement with that of their neighbors, which is often the norm. However, animals may also adopt different strategies depending on the situation. For instance, when attempting to exit a crowded enclosure with multiple gates, there may be instances where deviating from the movement of neighbors can be advantageous, as the researchers explain.
The research project conducted by the mathematicians spanned approximately two years. Initially, their aim was to explain experimental observations by investigating the conventional phase shift that occurs in a crowd of insects as they transition from a state of disorder to order when a critical value of the control parameter is reached (such as reducing noise). However, they decided to introduce a harmonic potential to confine the swarm and explore the consequences of decreasing the attractive force between individuals. As they increased the number of insects, they discovered numerous periodic, quasi-periodic, and ultimately chaotic states. The most surprising finding was the transition between chaotic states, which was previously unknown and unexpected. The researchers were able to provide convincing arguments and conduct tests to support the existence of these transitions. Ana Carpio, one of the study's authors from UCM's Department of Mathematical Analysis and Applied Mathematics, highlights that there is still much work to be done based on these findings. This includes seeking experimental confirmation of their predictions, refining the model to align with empirical observations, and pursuing further theoretical and mathematical investigations beyond their numerical simulations.
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