Density-functional fluctuation theory of crowds

Abstract

A primary goal of collective population behavior studies is to determine the rules governing crowd distributions in order to predict future behaviors in new environments. Current top-down modeling approaches describe, instead of predict, specific emergent behaviors, whereas bottom-up approaches must postulate, instead of directly determine, rules for individual behaviors. Here, we employ classical density functional theory (DFT) to quantify, directly from observations of local crowd density, the rules that predict mass behaviors under new circumstances. To demonstrate our theory-based, data-driven approach, we use a model crowd consisting of walking fruit flies and extract two functions that separately describe spatial and social preferences. The resulting theory accurately predicts experimental fly distributions in new environments and provides quantification of the crowd “mood”. Should this approach generalize beyond milling crowds, it may find powerful applications in fields ranging from spatial ecology and active matter to demography and economics.

Effects of social distancing and isolation on epidemic spreading modeled via dynamical density functional theory

“…This is done by replacing the diffusion term D ∇ 2 ϕ ( r , t ) in the standard reaction–diffusion model with the right-hand side of the DDFT equation ( 4 ) 39 – 42 . Thus, given that both static density functional theory (DFT) 43 and dynamical models for interacting agents 44 – 51 have previously been used to describe social systems, DDFT is a very promising approach for the development of extended models for epidemic spreading. In particular, the successes of DDFT in other biological contexts such as cancer growth 52 , protein adsorption 53 , ecology 54 , or active matter 55 – 61 suggest that it can be an extremely valuable tool also in the present context.…”

Synchronization of complex human networks

“…Human ensembles and crowd synchrony 19 have been investigated in recent years. Synchronized brokers in the stock market were found to earn more money 10 , the synchronization of crowd attention was shown to be a basic survival mechanism 32 , 33 , pedestrians walking on the London Millennium bridge synchronized their footsteps through the bridge vibrations to form macroscopic oscillations of the bridge above a critical number 12 , the collective movement of concert audiences showed vortexes and gas-like states 34 , 35 , the synchronized movements of dancers differ from those of nondancers 36 , 37 , music players are following each other according to their musical instrument 38 – 40 , and an audience clapping hands shows both synchronization and period doubling 41 , 42 . Synchronization in the broader sense of coordinating decision-making between humans on complex networks has also been studied 43 , 44 .…”

Local interactions and their group-level consequences in flocking jackdaws

“…Highly coordinated collective motion is a cornerstone of many biological systems at all scales, from cell colonies [1,2] to insect swarms [3][4][5][6], fish schools [7,8], bird flocks [9][10][11], ungulate herds [12][13][14], and even human crowds [15,16]. Moving together in large groups and using social information can provide numerous benefits, including enhanced predator avoidance [17][18][19], more efficient resource exploitation [20,21], energy savings [22][23][24] and efficient learning of migration routes [25,26].…”