Alignment phase transition in socially driven motion

Collective human movement is a hallmark of complex systems, exhibiting emergent order across contexts from pedestrian flows to biological collectives. In high-speed, directional settings, alignment ensures efficient navigation, whereas in low-speed, undirectional, socially engaged contexts, alignment arises from interpersonal interaction rather than locomotion goals. Using high-resolution spatial and orientation data from preschool classrooms, we uncover a sharp distance-dependent transition in pairwise alignment that reflects a spontaneous symmetry breaking between behavioral phases: below a threshold of ∼ 0.65 m, side-by-side orientations dominate, while face-to-face orientations prevail at larger distances. This transition stems from a distance-dependent competition among three alignment mechanisms: parallelization, opposition, and reciprocation, whose interplay generates a bifurcation structure in the effective interaction potential. Fourier decomposition of orientation distribution..., All study procedures were reviewed and approved by the University of Miami Institutional Review Board (IRB Protocol 20160509). Written informed consent was obtained from all participating teachers, and parental/guardian consent was obtained for all participating children. The study involved preschool-aged children in a familiar classroom environment, and no interventions were introduced by the research team during data collection. All data were anonymized prior to analysis., UWB-RFID Technology:
We used Ultra-Wideband Radio Frequency Identification (UWB-RFID) technology to continuously track children’s positions within the classroom. Each child wore a vest equipped with two UWB-RFID tags sewn near the left and right hips. These tags transmitted spatial data, including time, tag ID, and three-dimensional coordinates, at a frequency of 2-4 Hz to four receivers mounted at the corners of the classroom. This dual-tag configuration enabled high-resolution tracking of both position and orientation during natural preschool activities without disrupting classroom routines.
Studied Classrooms:
The study was conducted in preschool classrooms in Florida, over a four-year period from 2016 to 2020, involving multiple cohorts of children. Children wore RFID-equipped vests and participated in typical daily activities such as play, reading, painting, eating, and handwashing. Movements outside the classroom (e.g., bathroom trips) were excluded. Wearing the vests did not noti..., # Alignment phase transition in socially driven motion

## Overview

**This Dryad deposit contains:**

1\) **Processed dyad-alignment datasets** needed to reproduce the main θ₁–θ₂ alignment heatmaps and analysis reported in the associated manuscript accepted at *Science Advances*, and

2\) **Raw per-individual time series** (2D position and absolute heading) provided for transparency and for additional/alternative analyses beyond the published workflow.

The repository is designed to be usable without reading the article. All variables, units, coordinate conventions, and geometric definitions are documented below.

**Contents at a glance**

**Folders**

1\. `Datasets_dyad_alignment___r_theta1_theta2/`

Primary reproducibility dataset. Dyad-level samples with three columns per row: `r`, `theta1`, `theta2`.

2\. `Datasets_Raw___Time_X_Y_Alpha/`

Raw per-individual trajectories and absolute orientations, organized by condition, year, and observation session.

3\. `Codes_for_Datasets_dyad_a...