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The response threshold model explains the emergence of division of labor (i.e., task specialization) in an unstructured population by assuming that the individuals have different propensities to work on different tasks. The incentive to…
Uncovering human mobility patterns is of fundamental importance to the understanding of epidemic spreading, urban transportation and other socioeconomic dynamics embodying spatiality and human travel. According to the direct travel diaries…
This paper presents a new approach to behavioral-social dynamics of human crowds. First order models are derived based on mass conservation at the macroscopic scale, while methods of the kinetic theory are used to model the decisional…
This paper studies spatial patterns formed by proximate population migration driven by real wage gradients and other idiosyncratic factors. The model consists of a tractable core-periphery model incorporating a quasi-linear log utility…
We develop an agent-based model of the motion and pattern formation of vesicles. These intracellular particles can be found in four different modes of (undirected and directed) motion and can fuse with other vesicles. While the size of…
We present a theory for the steady-state dynamics of a two-dimensional system of spherically symmetric active Brownian particles. The derivation of the theory consists of two steps. First, we integrate out the self-propulsions and obtain a…
Understanding how spatial configurations of economic activity emerge is important when formulating spatial planning and economic policy. A simple model was proposed by Simon, who assumed that firms grow at a rate proportional to their size,…
Human dynamics and sociophysics suggest statistical models that may explain and provide us with better insight into social phenomena. Here we tackle the problem of determining the distribution of the population density of a social space…
An extremely broad and important class of phenomena in nature involves the settling and aggregation of matter under gravitation in fluid systems. Some examples include: sedimenting marine snow particles in lakes and oceans (central to…
We study a simple aggregation model that mimics the clustering of traffic on a one-lane roadway. In this model, each ``car'' moves ballistically at its initial velocity until it overtakes the preceding car or cluster. After this encounter,…
A new angle of view is proposed to find the simple rules dominating complex systems and regular patterns behind random phenomena such as cities. Hierarchy of cities reflects the ubiquitous structure frequently observed in the natural world…
Analysis of the urban population fraction data for sixteen populous countries over the last fifty years reveals a universal increase in urbanization, exhibiting four qualitatively distinct temporal patterns: (i) continuously accelerating…
Mathematical models of spatial population dynamics typically focus on the interplay between dispersal events and birth/death processes. However, for many animal communities, significant arrangement in space can occur on shorter timescales,…
Traffic and pedestrian systems consist of human collectives where agents are intelligent and capable of processing available information, to perform tactical manoeuvres that can potentially increase their movement efficiency. In this study,…
The transport of self-propelled particles such as bacteria and phoretic swimmers through crowded heterogeneous environments is relevant to many natural and engineering processes, from biofilm formation and contamination processes to…
After summarizing basic features of self-organization such as entropy export, feedbacks and nonlinear dynamics, we discuss several examples in biology. The main part of the paper is devoted to a model of active Brownian motion that allows a…
We present Langevin dynamics simulations that study the collective behavior of driven particles embedded in a densely packed background consisting of passive particles. Depending on the driving force, the densities of driven and passive…
Numerous problems in development, regeneration, and disease involve simultaneous evolution of both spatial organization and the internal state of the constituents in addition to local interactions and crowding. This motivates us to study a…
We investigate the phenomenon of diffusion in a countably infinite society of individuals interacting with their neighbors in a network. At a given time, each individual is either active or inactive. The diffusion is driven by two…
Entropy relates the fast, microscopic behaviour of the elements in a system to its slow, macroscopic state. We propose to use it to explain how, as complexity theory suggests, small scale decisions of individuals form cities. For this, we…