Understanding pattern formation in crossing pedestrian flows is essential for
analyzing and managing high-density crowd dynamics in urban environments. This
study presents two complementary methodological approaches to detect and
characterize stripe formations, an emergent structure observed when two
pedestrian groups cross at various angles. First, we propose a matrix-based
method that utilizes time-resolved trajectory data to determine the relative
crossing order of pedestrians from opposing groups. By identifying points of
minimal spatial separation between individuals and analyzing associated time
differences, we construct a crossing matrix that captures the sequence and
composition of stripes. Second, we introduce a geometric model based on
elliptical approximations of pedestrian groups, enabling analytical prediction
of two key macroscopic quantities: the number of stripes and the interaction
time between groups. The model captures how these quantities vary with the
crossing angle and shows strong agreement with experimental data. Further
analysis reveals that group elongation during crossing correlates with the
vertical cross-section of the elliptical shape. These methods provide effective
tools for analyzing large-scale movement datasets, informing the design of
public spaces, and calibrating mechanistic models. The study also presents
hypotheses about pattern transitions in continuous pedestrian streams,
suggesting promising directions for future research on collective motion under
varying flow geometries and densities.

Questo articolo esplora i giri e le loro implicazioni.

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