🔬 condensed matter

Non-reciprocal visual perception and polar alignment drive collective states in chiral active particles

This paper investigates the collective dynamics of chiral intelligent active Brownian particles with polar alignment and vision-based sensing, revealing how the interplay between chirality, non-reciprocal perception, and alignment parameters drives the emergence of diverse collective states such as vortices, ripples, and swarms that are inaccessible to non-chiral systems.

Original authors: Diganta Bhaskar, Abhishek Chaudhuri, Anil Kumar Dasanna

Published 2026-08-20

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Diganta Bhaskar, Abhishek Chaudhuri, Anil Kumar Dasanna

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the bustling world of the very small, from the microscopic swimmers that make up bacterial colonies to the synthetic robots designed to mimic them, movement is rarely a straight line. These self-propelled particles, often called active matter, are driven by their own internal energy. Unlike a passive grain of sand drifting in a current, they push themselves forward. However, their paths are rarely simple. Interactions with their environment, their own odd shapes, or internal forces often cause them to curve, wobble, or spin. When billions of these tiny movers gather, they do not just crowd together; they organize. They form flocks, swarms, and clusters that move with a purpose, a phenomenon seen in nature from schools of fish to murmurations of starlings. Scientists have long studied how these groups form, particularly focusing on how individuals align their direction with their neighbors, much like birds in a flock keeping their heads pointed the same way. But a new layer of complexity has emerged: what happens when these particles also have a built-in tendency to turn, and when they can "see" each other?

A team of researchers at the Indian Institute of Science Education and Research Mohali has explored this exact question. They created a computer simulation of thousands of tiny, self-propelled particles that possess three distinct traits: they move forward on their own, they have a natural tendency to spin in circles due to an internal torque, and they can sense other particles within a specific field of view in front of them. By adjusting how strongly these particles try to align with their neighbors versus how much they rely on their visual perception to steer, and by tweaking how fast they spin, the researchers mapped out a rich landscape of collective behaviors. They discovered that the interplay between this built-in spinning and the ability to see and react to neighbors creates a variety of complex, living-like structures that would not exist if the particles were simple or lacked this sense of sight.

The researchers found that the outcome depends heavily on the balance between the particles' internal spinning and their ability to coordinate. When the internal spinning is very strong, the particles remain scattered and disorganized, unable to form any cohesive group. However, as the spinning slows down to a moderate level, the particles begin to organize into distinct shapes. One of the most striking formations they observed was a "spinner," a tight, compact cluster where the particles rotate together as a solid block, yet without any specific order in which direction they are facing. These clusters spin in place, driven by the visual cues they give each other, but they do not travel across the screen.

As the researchers adjusted the strength of the alignment relative to the visual steering, the groups transformed into other fascinating patterns. They saw the emergence of "vortices," which are swirling clusters where the particles align their directions and spin together, but unlike the spinners, these vortices can also drift across the space as a whole. Perhaps the most unique discovery was a state they called a "ripple." These are expanding rings of particles that grow outward in a loop. The particles in a ripple have a specific internal structure: those on the inside tilt outward, those on the outside tilt inward, and those in the middle move along the curve. This creates a wave-like motion that expands the ring until it eventually breaks apart or stabilizes into a smaller, tight circle. The researchers noted that these ripple loops only form when there are enough particles and when the visual steering is strong enough to push the group outward against its natural tendency to clump.

When the particles' ability to align with their neighbors became the dominant force, the groups shifted into "worm-like" swarms. In these formations, the particles line up to form long, trailing chains that move together, with a leader guiding the way and others following. Interestingly, the identity of the leader constantly changes as the swarm moves. At other times, the particles formed "rotary clusters," which are different from the stationary spinners. These clusters are highly organized and move in a coordinated orbit, circling a central point while traveling together, rather than just spinning in place.

The study also revealed that the size of the group and the angle of their vision play critical roles. For instance, the expanding ripple loops require a large number of particles to sustain their growth; if the group is too small, the particles simply form a breathing, pulsing vortex instead. The researchers also found that the way these groups move can be measured by how far they travel over time and how their directions change. The worm-like swarms and ripples move in a straight, ballistic fashion for a while, covering distance efficiently, while the spinning and rotating groups tend to stay in a more confined area, moving in circles or oscillating back and forth.

What makes these findings significant is that they show how non-reciprocal interactions—where particle A sees and reacts to particle B, but B might not see or react to A in the same way—combined with a built-in spin, can generate complex behaviors that simple alignment rules cannot. In systems without this chirality, or built-in spin, such diverse states as the expanding ripples or the specific rotary clusters do not appear. The researchers demonstrated that by tuning just a few parameters—the speed of the spin, the angle of the vision, and the strength of the alignment—they could guide the system from a chaotic, scattered state into highly ordered, dynamic structures. This work provides a unified framework for understanding how perception and internal mechanics shape the collective lives of active matter, offering insights that could apply to everything from the movement of bacteria to the design of future swarms of microscopic robots.

Technical Summary: Non-reciprocal visual perception and polar alignment drive collective states in chiral active particles

Problem and Motivation
Self-propelled particles, modeled as Active Brownian Particles (ABPs), typically exhibit straight-line motion unless perturbed by environmental interactions, shape asymmetry, or intrinsic torques. While isotropic ABPs with polar alignment (e.g., Vicsek model) and those with excluded volume interactions have been extensively studied, the interplay between chirality (intrinsic angular velocity), polar alignment, and non-reciprocal visual perception remains less explored. In biological and synthetic microswimmers (e.g., bacteria, sperm, synthetic swimmers), motion is often chiral, and interactions are frequently non-reciprocal, such as vision-based steering where a particle reacts to neighbors within a specific field of view. This work investigates how combining these elements—chirality, alignment, and vision-based sensing—alters collective dynamics, specifically asking whether these factors generate emergent states inaccessible to non-chiral or purely alignment-driven systems.

Methodology
The authors employ a computational model of $N$ chiral intelligent active Brownian particles (iABPs) in two dimensions. The system is governed by overdamped Langevin equations incorporating:

Self-propulsion: Constant speed $v_0$ along a unit orientation vector $\hat{e}_i$ .
Steric Interactions: Modeled via the Weeks–Chandler–Andersen (WCA) potential to prevent overlap.
Chirality: An intrinsic angular velocity $\omega$ inducing circular motion.
Polar Alignment: A torque aligning particles with the average orientation of neighbors within a radius $R_a$ .
Vision-Based Steering: A non-reciprocal torque where particles orient toward neighbors falling within a forward-facing vision cone (VC) of angle $\theta$ and range $R_V$ . This interaction includes an exponential distance decay and breaks action-reaction symmetry.

Simulations were performed using LAMMPS with a packing fraction $\Phi = 0.00785$ and Péclet numbers $Pe = 10$ (primary) and $Pe = 70$ (supplementary). The study systematically varies the ratio of alignment to visual maneuverability ( $\Omega_a/\Omega_v$ ), the vision angle ( $\theta$ ), and the reduced chirality ( $\omega/D_r$ ).

Key Contributions and Results
By mapping the parameter space, the authors construct a phase diagram revealing a rich spectrum of collective states:

Phase Diagram and State Identification:
- Dilute States: At high chirality ( $\omega/D_r$ ), particles remain dispersed. High chirality frustrates competing interactions, preventing phase locking and collective dynamics.
- Spinners: Occur at low alignment strength and moderate-to-large vision angles. These are compact, randomly oriented clusters that rotate as solid bodies without internal orientational order.
- Vortices and Ripples: Emerge when alignment and vision strengths are comparable. Vortices are compact, locally aligned clusters. Ripples are a distinct state characterized by expanding ring-like loops driven by outward torques on central particles. Ripples require a large number of particles and strong visual maneuverability to sustain expansion; they are transient and can fragment.
- Rotary Clusters: Found at high alignment strength ( $\Omega_a > \Omega_v$ ). Unlike spinners, these are globally polarized and undergo coherent orbital motion rather than spinning about a fixed axis. They exhibit re-entrant behavior at both low and high vision angles.
- Worm-like Swarms: Formed at moderate alignment and narrow vision angles, characterized by a leader-follower dynamic where the group moves collectively in an elongated shape.
Structural and Dynamical Characterization:
- Chirality's Role: Chirality acts as a competing timescale. High chirality suppresses cohesion, while moderate-to-low chirality enables cohesive, dynamic patterns.
- Dynamics: Mean-square displacement (MSD) analysis shows that worm and ripple states exhibit ballistic behavior ( $\sim t^2$ ) over intermediate timescales, whereas vortex and rotary clusters show oscillatory behavior at long times due to coherent rotation.
- Order Parameters: Global polarization ( $P$ ) distinguishes highly ordered states (worms, rotary clusters) from disordered ones (spinners, ripples). Solid-body spin (SBS) differentiates fast-spinning vortices from spinners and rotary clusters. Radial distribution functions (RDF) confirm the ring-like structure of ripples and the elongated nature of worms.
- Ripple Stability: Ripple loops are shown to be transient; they expand until rotational diffusion weakens circumferential coherence, leading to breakup. They require both a high particle count and strong visual maneuverability to form.
High Activity Regime ($Pe=70$):
At higher Péclet numbers, the system exhibits similar states but with increased rotational motion in spinners and distorted, non-circular ripples. Complex morphological transitions are observed, including the coexistence of multiple states and the transformation of vortices into milling rings or rotary worms.

Significance and Claims
The paper claims that the interplay of chirality, non-reciprocal perception, and polar alignment generates collective states that are inaccessible to non-chiral systems. Specifically:

The combination of chirality and vision-based steering creates unique morphologies like ripple loops and rotary clusters that do not appear in standard alignment-only models.
Chirality governs the morphology of the collective states: high chirality leads to dilute phases, while moderate chirality allows for cohesive, dynamic patterns.
The study establishes a unified framework connecting synthetic models with natural collective behaviors, demonstrating how intrinsic rotation and anisotropic perception can qualitatively transform active matter organization.
The authors emphasize that these findings extend the understanding of active matter beyond isotropic or purely alignment-driven systems, highlighting the critical role of non-reciprocal interactions in shaping emergent order.

The work concludes by noting that while several states share similar long-time dynamics, they can be systematically distinguished using a small set of structural and dynamical indicators (polarization, SBS, orientation correlation). The authors suggest future extensions to density-dependent transitions, confinement effects, and three-dimensional analogs but do not propose specific experimental implementations or applications beyond the theoretical framework presented.

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