Pith. sign in

REVIEW 4 major objections 6 minor 44 references

Alignment Phase Transition in Socially Driven Motion

T0 review · 4 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read Preschool children's body orientation switches phases at 0.65 m, a spontaneous symmetry-breaking transition in low-speed social motion.

desk verdict A valuable empirical observation about distance-dependent orientation, with the phase-transition interpretation outrunning the statistics. read the letter →

arxiv 2506.01550 v1 pith:7L3KYXA2 submitted 2025-06-02 physics.soc-ph cond-mat.stat-mechnlin.AO

Debasish Sarker , Yi Zhang , Lynn K. Perry , Daniel S. Messinger , Chaoming Song This is my paper
classification physics.soc-phcond-mat.stat-mechnlin.AO
keywords socialalignmentphasetransitionorientationdynamicsactivematterpreschoolchildrenFourierdecompositionpseudo-potentialcollectivemotion
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper claims that socially engaged, low-speed human motion contains a genuine symmetry-breaking phase transition in pairwise body orientation. Using high-resolution tracking of 89 preschool children in two classrooms, it finds that children predominantly stand side-by-side when their interpersonal distance is below roughly 0.65 m, and face-to-face beyond that distance, with no coordination beyond about 3 m. The authors derive a minimal pseudo-potential $V(r,\theta_1,\theta_2)$ from a Fourier expansion of the empirical orientation distributions, identifying three distance-dependent competing mechanisms: parallelization, opposition, and reciprocation. The model's stability analysis shows the preferred configuration is controlled by the sign of $\Delta J = J_o - J_p$, and the empirically measured $\Delta J$ crosses zero at $r_c \approx 0.65$ m, matching the transition point. Monte Carlo simulations with the inferred terms reproduce the orientation heatmaps, supporting the claim that low-speed social alignment is a non-equilibrium phase transition governable by a small number of interaction rules.

What carries the argument

The load-bearing object is the pseudo-potential $V(r,\theta_1,\theta_2)$ in Eq. (3), a minimal Fourier-truncated representation of the empirical log-probability: $V=J_p\cos(\theta_1-\theta_2)-2J_o(\cos\theta_1+\cos\theta_2)-J_r\cos(\theta_1+\theta_2)+V_0(r)$. Each angular harmonic encodes a distinct social mechanism: $J_p$ favors parallel headings, $J_o$ favors facing the partner's position (opposition), and $J_r$ favors mirror-symmetric reciprocal orientation. The machinery works because the stationary points of this potential, computed from Eqs. (4), have stability controlled by the Hessian eigenvalues, so the side-by-side solution $\cos\theta_1=J_o/J_p$ is stable exactly when $J_o<J_p$, face-to-face when $J_o>J_p$, and both degenerate at $J_o=J_p$. Fourier decomposition of the binned empirical distributions supplies the distance-dependent coefficients, and the zero crossing of $\Delta J=J_o-J_p$ at $r_c\approx0.65$ m is the observable signature of the transition.

What would settle it

Bootstrap the Fourier coefficients across dyads or time blocks to assign error bars to $\Delta J(r)$; if the zero crossing near 0.65 m is not statistically distinguishable from zero, or if including the next Fourier harmonic (for example $\cos(2\theta_1-2\theta_2)$) moves the crossover by more than its uncertainty, the claimed transition lacks support. A complementary test is to measure the orientation order-parameter distribution in a narrow band around $r_c$: a true symmetry-breaking transition should show emerging bimodality or strongly enhanced fluctuations, while a smooth crossover would not.

Watch

Extended reading notes

Core claim

On the paper's own terms, the discovery is that body-orientation alignment in preschool free play is not a smooth statistical function of distance but a distance-tuned symmetry-breaking transition between two ordered phases. In the joint distribution $P(\theta_1,\theta_2)$ of the two individuals' orientations relative to the inter-person axis, short-range data show peaks at $(\pm\pi/2,\mp\pi/2)$ (side-by-side), intermediate data show a central peak at $(0,0)$ (face-to-face), and large distances give a flat distribution. Fourier analysis of $-\ln P$ yields dominant cosine terms corresponding to parallelization $\cos(\theta_1-\theta_2)$, opposition $\cos\theta_1+\cos\theta_2$, and reciprocation $\cos(\theta_1+\theta_2)$; combining them into Eq. (3) gives a pseudo-potential whose Hessian eigenvalues are $2(J_r+J_o)$ and $2(J_o-J_p)$. The equilibrium is face-to-face when $J_o>J_p$, side-by-side when $J_o<J_p$, and degenerate at $J_o=J_p$, and the empirically reconstructed difference $\Delta J(r)$ crosses zero at $r_c\approx0.65$ m in each dataset. Monte Carlo simulations using the same potential reproduce the empirical heatmaps, which the paper takes as evidence that the crossover is an emergent phase transition rather than a modeling artifact.

Load-bearing premise

The interpretation rests on the assumption that the binned empirical orientation distributions are stationary states of the pseudo-potential in Eq. (3), with $J_p,J_o,J_r$ estimated from Fourier modes of those same distributions; if the apparent $\Delta J=0$ crossing at 0.65 m is within sampling noise, or if higher harmonics or mixed activities shift it, the transition is a fitting artifact rather than an emergent phase.

Editorial extensions

If this is right

  • Side-by-side and face-to-face are distinct ordered phases of low-speed social motion, selected by the sign of $J_o - J_p$, so any model of socially driven movement must include both opposition and reciprocation in addition to parallelization.
  • The empirical crossover at $r_c\approx0.65$ m is reproduced with the same inferred potential in two different classrooms, so the phase structure is a property of interpersonal interaction rather than a peculiarity of one layout or activity.
  • Vicsek-style parallelization alone cannot produce the face-to-face peak; the proposed pseudo-potential is the minimal model that does, making the three-term Fourier truncation a candidate microscopic rule for interaction-driven swarms.
  • At the critical distance the two alignment configurations are degenerate, so pairwise orientations there should be maximally labile; this is the predicted location for largest fluctuations and slowest relaxation.
  • The framework extends to any low-speed interacting-agent system, including robotic swarms and pedestrian social groups, because the transition depends only on the competition of the three angular couplings.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Inference beyond the paper: the degeneracy at $r_c$ implies measurable critical phenomena, such as enhanced orientation variance or bimodal switching between side-by-side and face-to-face states in time series near 0.65 m; a time-resolved reanalysis of the dyad tracks could test this directly.
  • Inference beyond the paper: if the transition is truly structural, the critical distance should scale with body size or typical interpersonal-distance norms across ages and species, so repeating the Fourier decomposition with adult dyads or non-human pairs would either confirm or falsify the universality of the 0.65 m value.
  • Inference beyond the paper: the same pseudo-potential could be turned into a control rule for human-robot or swarm-robot interaction by programming the $J_p,J_o,J_r$ couplings directly; the predicted bifurcation then gives a design target for eliciting side-by-side versus face-to-face coordination.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 6 minor

Summary. The manuscript analyzes high-resolution UWB-RFID tracking of 89 preschoolers in two classrooms (236 h of 2–4 Hz dyadic traces) to study how the joint orientation distribution P(θ1, θ2) depends on interpersonal distance r. It reports a crossover from side-by-side peaks at short range to a face-to-face peak beyond r ≈ 0.65 m. The authors decompose −ln P into Fourier modes and identify three dominant terms: parallelization cos(θ1−θ2), opposition cos(θ1)+cos(θ2), and reciprocation cos(θ1+θ2). These are assembled into the pseudo-potential V in Eq. (3); Monte Carlo sampling of exp(−V) reproduces the empirical heatmaps. A Hessian analysis of the stationary points predicts a transition when ΔJ = Jo − Jp changes sign, and Fig. 4 shows ΔJ crossing zero at r_c ≈ 0.65 m in both datasets. The authors interpret this as a spontaneous symmetry-breaking, non-equilibrium phase transition between side-by-side and face-to-face alignment phases.

Significance. The paper addresses an underexplored regime of collective motion—low-speed, socially engaged orientation dynamics—and brings a physics-style pseudo-potential approach to a rich naturalistic dataset. If the transition is statistically robust, the work would be a valuable contribution to the active-matter and social-physics literature. The manuscript has clear strengths: the analytic Hessian calculation in Methods B is internally consistent with Eq. (4) and yields the stated stability condition; the Monte Carlo implementation is transparent; and the qualitative agreement between the two classrooms is encouraging. However, the central empirical claim currently rests on in-sample fits without uncertainty quantification, and the symmetry-breaking interpretation is not supported by dynamical or per-dyad evidence. The contribution is potentially significant but requires substantial additional analysis before the phase-transition language is warranted.

major comments (4)
  1. [Fig. 4 and Methods A] The zero crossing of ΔJ(r) at r_c ≈ 0.65 m is presented without any uncertainty estimate. The raw sample of 236 h at 2–4 Hz is heavily autocorrelated at the dyad level, so the effective number of independent observations is far smaller than the number of frames. A dyad- or session-level block bootstrap is needed to place error bars on Jp(r), Jo(r), and ΔJ(r); if the bootstrap interval for ΔJ overlaps zero over several radial bins, the claimed sharp transition is not established. In addition, the binning [0, 0.6), [0.6, 1.2), ... means that the value 0.65 m is interpolated from a bin boundary, not directly resolved by the data.
  2. [Eqs. (2)–(3) and Fig. 2m–t] The model is fitted and tested on the same binned distributions. The coefficients Jp, Jo, Jr are extracted by Fourier-projecting the empirical −ln P(θ1, θ2) of each radial bin, and the Monte Carlo sampling of exp(−V) with those coefficients reproduces the input histograms by construction (up to truncation). This verifies only that the three retained harmonics capture most of the structure; it does not validate the three mechanisms or the transition. I recommend an out-of-sample test, for example fitting the potential on a randomly chosen half of dyads or sessions and predicting the held-out distributions, and comparing against a null model with additional harmonics or against a non-interacting baseline.
  3. [Methods B and Fig. 5] The label 'spontaneous symmetry breaking' is not justified by the analyses shown. The joint distribution is symmetric under (θ1, θ2) → (−θ1, −θ2), and the empirical short-range heatmaps display both side-by-side peaks simultaneously; this is a static bimodality, not a broken-symmetry state. Demonstrating symmetry breaking requires a dynamical or per-realization order parameter: for example, per-dyad time series showing that a dyad occupies one of the two mirror-image orientations for a sustained period and switches between them, with the ensemble distribution as the symmetric average. Without such evidence, the paper establishes a distance-dependent crossover in a static distribution, not spontaneous symmetry breaking.
  4. [Results, Fig. 2a–h] Activity or context mixing is a plausible alternative explanation for the observed distance dependence. If short-range side-by-side orientations occur mostly during seated table activities and face-to-face orientations during free play, the apparent 'interaction potential' could be a composition of activity-specific distributions rather than a distance-dependent pairwise force. The manuscript does not report any analysis stratified by activity type, session, or dyad. I request either a per-activity or per-dyad-session analysis, or an explicit argument for why these confounds cannot generate the observed crossover.
minor comments (6)
  1. [Fig. 1 caption] The caption contains 'Orientations (®)', which appears to be a typographical artifact; it should read '(θ)'.
  2. [Eq. (2)] The Fourier expansion is written with complex exponentials, but only real cosine coefficients are discussed; the normalization, truncation order, and treatment of the (0,0) mode should be stated explicitly.
  3. [Fig. 3] The legend lists several higher-order harmonics, but the text does not explain why they are negligible; a short paragraph or SI section quantifying their residual contribution would strengthen the truncation argument.
  4. [Introduction, Eq. (1)] The statement that 'V_VM lacks symmetry due to active matter effects' is unclear, since the displayed V_VM is symmetric under (θ1, θ2) → (−θ1, −θ2); please clarify the intended meaning.
  5. [Methods B] The side-by-side solution should state the admissibility condition |Jo/Jp| ≤ 1 and identify which of the two mirror minima is selected in a given realization.
  6. [Abstract and Fig. 4] The abstract calls the transition 'sharp' while the text says 'approximately 0.65 m'; please align the wording with the actual resolution and uncertainty of the data.

Circularity Check

2 steps flagged · score 6.0 of 10

The 0.65 m transition is an in-sample Fourier fit: the pseudo-potential is built from the same empirical angle distributions, and the phase boundary is the zero crossing of the fitted coefficient difference, so the Monte Carlo 'reproduction' and the phase diagram do not provide independent confirmation.

  1. fitted input called prediction [Section II, Eqs. (2)-(3) and Fig. 2m–t]
    "To explain these transitions, we perform a Fourier expansion: −lnP(θ1,θ2)= Σ_{n,m} a_{n,m} e^{i(nθ1+mθ2)}, (2) extracting spectral components a_{n,m} that dominate alignment behavior. ... We integrate these mechanisms into a minimal pseudo-potential model: V(r,θ1,θ2)=Jp(r)cos(θ1−θ2)−2Jo(r)(cos(θ1)+cos(θ2))−Jr(r)cos(θ1+θ2)+V0(r). (3) ... Monte Carlo simulations using Eq. (3) yield heatmaps that closely reproduce the empirical alignment patterns across LC1 and LC2 (Fig. 2m–t), demonstrating the predictive sufficiency of the model."

    The coefficients Jp, Jo, Jr are the leading Fourier coefficients of -ln P estimated from the very same binned empirical distributions P(θ1,θ2) that the model is then compared against. Writing V as the truncated Fourier expansion of -ln P means that Monte Carlo sampling of exp(-V) reproduces the input histogram by construction, up to truncation error. The statement that the simulations 'closely reproduce the empirical patterns' therefore verifies the Fourier truncation, not the existence of the three mechanisms or the predicted transition. This is an in-sample fit presented as predictive sufficiency, not an independent test.

  2. fitted input called prediction [Section II, Fig. 4 and surrounding text]
    "The critical configuration depends on the sign of ΔJ=Jo−Jp. When ΔJ<0, parallelization dominates, yielding a side-by-side phase ... Figure 4 shows ΔJ(r) from empirical data. A crossover at r_c≈0.65 m confirms the predicted transition, robust across classrooms with different layouts and movement patterns."

    The 'predicted transition' is the condition ΔJ=0 derived from the Hessian of the pseudo-potential V, but V was itself constructed from the empirical Fourier coefficients. Thus ΔJ(r) is not an independent theoretical prediction; it is a fitted function whose zero crossing is identified as the critical distance. Calling this crossover a confirmation of the predicted transition makes the empirical data serve simultaneously as the input that fixes the model parameters and as the evidence that validates the model. The threshold r_c≈0.65 m is therefore a fitted zero-crossing, not an emergent prediction tested against independent data.

full rationale

The central circularity is that the model's potential V is the truncated Fourier expansion of the empirical log-distribution, so the Monte Carlo reproduction of Fig. 2m–t is a consistency check of the fit, not independent confirmation. Likewise, the phase diagram in Fig. 4 is the zero crossing of the fitted difference ΔJ=Jo−Jp, so the 'critical point' is a property of the fitting procedure rather than a derived prediction. The analytic bifurcation analysis (Eqs. 4–5) is mathematically valid, but it only analyzes the landscape of a potential whose coefficients were taken from the same data it is said to explain. No load-bearing self-citation chain is present: the authors' prior work [12] is cited for an analogy to phase coexistence, but the derivation here does not reduce to that citation. The paper does contain an independent empirical description of distance-dependent orientation distributions, but the specific claim of a spontaneous symmetry-breaking phase transition predicted by a pseudo-potential reduces by construction to the fitted Fourier coefficients. Hence score 6: partial circularity, with the empirical patterns retaining independent descriptive content.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The model is assembled from Fourier coefficients estimated on the same data it is tested against; the three J(r) profiles are free functions of distance. This makes the main prediction an in-sample reproduction. No new physical entities are postulated; the pseudo-potential is a fitted mathematical summary of observed orientation statistics.

free parameters (4)
  • Jp(r)
    Parallelization strength as a function of distance, fitted from the cos(θ1-θ2) Fourier coefficient in Eq. (3) and Fig. 3.
  • Jo(r)
    Opposition strength as a function of distance, fitted from the cos(θ1)+cos(θ2) Fourier coefficient in Eq. (3) and Fig. 3.
  • Jr(r)
    Reciprocation strength as a function of distance, fitted from the cos(θ1+θ2) Fourier coefficient in Eq. (3) and Fig. 3.
  • V0(r)
    Distance-dependent normalization term in Eq. (3) that adjusts marginals; chosen to make the pseudo-potential match empirical single-variable distributions.
assumptions (5)
  • ad hoc to paper The joint orientation distribution can be represented as a Boltzmann-like exponential of a pairwise pseudo-potential: ln P ≈ -V.
    Invoked in Eq. (1) and Eq. (3); there is no derivation from a dynamical process, and it is applied to the empirically binned distributions.
  • domain assumption Pairwise orientation statistics depend only on relative angles θ1, θ2 and distance r, with no higher-order group or activity context.
    The model in Eq. (3) and the distance-binned heatmaps in Fig. 2 assume dyadic factorization; activity type, group size, and classroom layout are not included.
  • ad hoc to paper Only three Fourier harmonics, cos(θ1-θ2), cos(θ1)+cos(θ2), and cos(θ1+θ2), suffice to capture the transition.
    The Fourier expansion in Eq. (2) is truncated to these terms in Eq. (3); higher-order terms are deferred to the Discussion.
  • domain assumption The UWB dual-tag shoulder sensors accurately reconstruct each child's position and facing direction.
    The entire orientation measurement rests on this hardware assumption; calibration and preprocessing are only referenced to the SI.
  • domain assumption The Monte Carlo simulations reach equilibrium of the pseudo-potential, so the simulated distributions represent the potential's stationary states.
    Used in Fig. 2m-t and Methods IV B; no convergence diagnostics or detailed balance arguments are given.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Alignment Phase Transition in Socially Driven Motion." pith.science (2026). https://pith.science/paper/7L3KYXA2

@misc{pith2026250601550,
  author       = {Pith},
  title        = {Pith review of: Alignment Phase Transition in Socially Driven Motion},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7L3KYXA2}},
  note         = {Machine review of arXiv:2506.01550}
}
read the original abstract

Collective human movement is a hallmark of complex systems, exhibiting emergent order across diverse settings, from pedestrian flows to biological collectives. In high-speed scenarios, alignment interactions ensure efficient flow and navigation. In contrast, alignment in low-speed, socially engaged contexts emerges not from locomotion goals but from interpersonal interaction. Using high-resolution spatial and orientation data from preschool classrooms, we uncover a sharp, distance-dependent transition in pairwise alignment patterns that reflects a spontaneous symmetry breaking between distinct behavioral phases. Below a critical threshold of approximately 0.65\,m, individuals predominantly align side-by-side; beyond this range, face-to-face orientations prevail. We show that this transition arises from a distance-dependent competition among three alignment mechanisms: parallelization, opposition, and reciprocation, whose interplay generates a bifurcation structure in the effective interaction potential. A Fourier-based decomposition of empirical orientation distributions reveals these mechanisms, enabling the construction of a minimal pseudo-potential model that captures the alignment transition as a non-equilibrium phase transition. Monte Carlo simulations using the inferred interaction terms closely reproduce the empirical patterns. These findings establish a quantitative framework for social alignment in low-speed human motion, extending active matter theory to a previously unexplored regime of socially mediated orientation dynamics, with implications for modeling coordination and control in biological collectives and artificial swarms.

Figures

Figures reproduced from arXiv: 2506.01550 by the authors.

Figure 1
Figure 1. FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p011_5.png]

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

44 extracted references · 38 canonical work pages

  1. [1]

    Touchette, The large deviation approach to statistical mechanics, Physics Reports478, 1 (2009)

    H. Touchette, The large deviation approach to statistical mechanics, Physics Reports478, 1 (2009)

    2009

  2. [2]

    V. L. Ginzburg and L. D. Landau, On the theory of superconductivity, inOn Superconductivity and Superfluidity: A Scientific Autobiography(Springer Berlin Heidelberg, Berlin, Heidelberg,

    work page

  3. [3]

    M. C. Marchetti, J. F. Joanny, S. Ramaswamy, T. B. Liverpool, J. Prost, M. Rao, and R. A. Simha, Hydrodynamics of soft active matter, Rev. Mod. Phys.85, 1143 (2013)

    2013

  4. [4]

    Rodrigue,The Geography of Transport Systems, 6th ed

    J.-P. Rodrigue,The Geography of Transport Systems, 6th ed. (Routledge, London, 2024) p. 402

    work page 2024

  5. [5]

    Castles, H

    S. Castles, H. de Haas, and M. Miller,The Age of Migration, Fifth Edition: International Population Movements in the Modern World(Guilford Publications, 2013)

    work page 2013

  6. [6]

    Helbing and P

    D. Helbing and P. Moln´ ar, Social force model for pedestrian dynamics, Phys. Rev. E51, 4282 (1995)

    work page 1995

  7. [7]

    D. R. Montello, Navigation, inThe Cambridge Handbook of Visuospatial Thinking, Cambridge Handbooks in Psychology, edited by P. Shah and A. Miyake (Cambridge University Press,

    work page

  8. [8]

    Moussa ¨ ıd, N

    M. Moussa ¨ ıd, N. Perozo, S. Garnier, D. Helbing, and G. Theraulaz, The walking behaviour of pedestrian social groups and its impact on crowd dynamics, PLOS ONE5, 1 (2010)

    work page 2010

Show all 44 references
  1. [9]

    Feliciani and K

    C. Feliciani and K. Nishinari, Empirical analysis of the lane formation process in bidirectional pedestrian flow, Phys. Rev. E94, 032304 (2016)

    2016

  2. [10]

    Veiga and C

    G. Veiga and C. Rieffe, Monitoring children’s behaviors in their natural settings: Applying rfid sensors to study child development, inSAGE Research Methods Cases Part 2(SAGE Publications Ltd, London, 2018) online publication date: 3 January 2018

    2018

  3. [11]

    J. L. Silverberg, M. Bierbaum, J. P. Sethna, and I. Cohen, Collective motion of humans in mosh and circle pits at heavy metal concerts, Phys. Rev. Lett.110, 228701 (2013). 12

    2013

  4. [12]

    Zhang, D

    Y. Zhang, D. Sarker, S. Mitsven, L. Perry, D. Messinger, U. Rudolph, M. Siller, and C. Song, Emergence of social phases in human movement, Phys. Rev. E110, 044303 (2024)

    2024

  5. [13]

    Willems, A

    J. Willems, A. Corbetta, V. Menkovski, and F. Toschi, Pedestrian orientation dynamics from high-fidelity measurements, Scientific Reports10, 11653 (2020)

    2020

  6. [14]

    Bain and D

    N. Bain and D. Bartolo, Dynamic response and hydrodynamics of polarized crowds, Science 363, 46 (2019)

    2019

  7. [15]

    Tordeux, M

    A. Tordeux, M. Chraibi, A. Seyfried, and A. Schadschneider, Prediction of pedestrian dynam- ics in complex architectures with artificial neural networks, Journal of Intelligent Transporta- tion Systems24, 556 (2020)

    2020

  8. [16]

    C. A. Pouw, A. Corbetta, A. Gabbana, C. van der Laan, and F. Toschi, High-statistics pedes- trian dynamics on stairways and their probabilistic fundamental diagrams, Transportation Research Part C: Emerging Technologies159, 104468 (2024)

    2024

  9. [17]

    Moussa ¨ ıd, D

    M. Moussa ¨ ıd, D. Helbing, and G. Theraulaz, How simple rules determine pedestrian behavior and crowd disasters, Proceedings of the National Academy of Sciences108, 6884 (2011)

    2011

  10. [18]

    Vicsek, A

    T. Vicsek, A. Czir´ ok, E. Ben-Jacob, I. Cohen, and O. Shochet, Novel type of phase transition in a system of self-driven particles, Phys. Rev. Lett.75, 1226 (1995)

    1995

  11. [19]

    Helbing, L

    D. Helbing, L. Buzna, A. Johansson, and T. Werner, Self-organized pedestrian crowd dynam- ics: Experiments, simulations, and design solutions, Transportation Science39, 1 (2005)

    2005

  12. [20]

    I. D. Couzin, J. Krause, N. R. Franks, and S. A. Levin, Effective leadership and decision- making in animal groups on the move, Nature433, 513 (2005)

    2005

  13. [21]

    Helbing, Traffic and related self-driven many-particle systems, Rev

    D. Helbing, Traffic and related self-driven many-particle systems, Rev. Mod. Phys.73, 1067 (2001)

    2001

  14. [22]

    Zanlungo, T

    F. Zanlungo, T. Ikeda, and T. Kanda, Potential for the dynamics of pedestrians in a socially interacting group, Phys. Rev. E89, 012811 (2014)

    2014

  15. [23]

    E. T. Hall,The Hidden Dimension(Anchor Books, New York, 1966)

    1966

  16. [24]

    Argyle and J

    M. Argyle and J. Dean, Eye-contact, distance and affiliation, Sociometry28, 289 (1965)

    1965

  17. [25]

    K. W. Rio, G. C. Dachner, and W. H. Warren, Local interactions underlying collective motion in human crowds, Proceedings of the Royal Society B: Biological Sciences285, 20180611 (2018)

    2018

  18. [26]

    Schmitz and A

    L. Schmitz and A. T. Reader, Smaller preferred interpersonal distance for joint versus parallel action, PLOS ONE18, 1 (2023). 13

    2023

  19. [27]

    Gifford, Projected interpersonal distance and orientation choices: Personality, sex, and social situation, Social Psychology Quarterly45, 145 (1982)

    R. Gifford, Projected interpersonal distance and orientation choices: Personality, sex, and social situation, Social Psychology Quarterly45, 145 (1982)

    1982

  20. [28]

    Hornischer, P

    H. Hornischer, P. J. Pritz, J. Pritz, M. G. Mazza, and M. Boos, Modeling of human group coordination, Phys. Rev. Res.4, 023037 (2022)

    2022

  21. [29]

    Kendon,Conducting interaction: Patterns of behavior in focused encounters, Studies in Interactional Sociolinguistics, Vol

    A. Kendon,Conducting interaction: Patterns of behavior in focused encounters, Studies in Interactional Sociolinguistics, Vol. 7 (Cambridge University Press, New York, NY, US, 1990) pp. xi, 292

    1990

  22. [30]

    D. S. Messinger, E. B. Prince, M. Zheng, K. Martin, S. G. Mitsven, S. Huang, T. St¨ olzel, N. Johnson, U. Rudolph, L. K. Perry, B. Laursen, and C. Song, Continuous measurement of dynamic classroom social interactions, International Journal of Behavioral Development43, 263 (2019)

    2019

  23. [31]

    I. D. Couzin, J. Krause, R. James, G. D. Ruxton, and N. R. Franks, Collective memory and spatial sorting in animal groups, Journal of Theoretical Biology218, 1 (2002)

    2002

  24. [32]

    M. E. J. Newman and G. T. Barkema,Monte Carlo Methods in Statistical Physics(Oxford University Press, 1999)

    1999

  25. [33]

    Ransom, B

    A. Ransom, B. LaGrant, A. Spiteri, T. Kushnir, A. K. Anderson, and E. D. Rosa, Face-to-face learning enhances the social transmission of information, PLOS ONE17, e0264250 (2022)

    2022

  26. [34]

    X. Wang, K. Lu, Y. He, Z. Gao, and N. Hao, Close spatial distance and direct gaze bring better communication outcomes and more intertwined neural networks, NeuroImage261, 1 (2022)

    2022

  27. [35]

    Gregorj, Z

    A. Gregorj, Z. Y¨ ucel, F. Zanlungo, C. Feliciani, and T. Kanda, Social aspects of collision avoidance: a detailed analysis of two-person groups and individual pedestrians, Scientific Reports13, 5756 (2023)

    2023

  28. [36]

    M. C. Cross and P. C. Hohenberg, Pattern formation outside of equilibrium, Rev. Mod. Phys. 65, 851 (1993)

    1993

  29. [37]

    P. M. Chaikin and T. C. Lubensky,Principles of Condensed Matter Physics(Cambridge University Press, 1995)

    1995

  30. [38]

    Kardar, Collective behavior, from particles to fields, inStatistical Physics of Fields(Cam- bridge University Press, 2007) p

    M. Kardar, Collective behavior, from particles to fields, inStatistical Physics of Fields(Cam- bridge University Press, 2007) p. 1–18

    2007

  31. [39]

    Ising, Beitrag zur theorie des ferromagnetismus, Zeitschrift f¨ ur Physik31, 253 (1925)

    E. Ising, Beitrag zur theorie des ferromagnetismus, Zeitschrift f¨ ur Physik31, 253 (1925). 14

    1925

  32. [40]

    H. E. Stanley,Phase transitions and critical phenomena, Vol. 7 (Clarendon Press, Oxford, 1971)

    1971

  33. [41]

    Zhang, Y

    Y. Zhang, Y. Tao, M.-L. Shyu, L. K. Perry, P. R. Warde, D. S. Messinger, and C. Song, Simulating covid19 transmission from observed movement, Scientific Reports12, 3044 (2022)

    2022

  34. [42]

    Repiso, A

    E. Repiso, A. Garrell, and A. Sanfeliu, Adaptive side-by-side social robot navigation to ap- proach and interact with people, International Journal of Social Robotics12, 909 (2020)

    2020

  35. [43]

    Messinger, L

    D. Messinger, L. Perry, S. Mitsven, Y. Tao, J. Moffitt, R. Fasano, S. Custode, and C. Jerry, Chapter seven - computational approaches to understanding interaction and development, in New Methods and Approaches for Studying Child Development, Advances in Child Develop- ment and...

    2022

  36. [44]

    Cattuto, W

    C. Cattuto, W. Van den Broeck, A. Barrat, V. Colizza, J.-F. Pinton, and A. Vespignani, Dynamics of person-to-person interactions from distributed rfid sensor networks, PLOS ONE 5, 1 (2010). 15

    2010

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.