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We derive an explicit form for the Cucker-Smale (CS) model on the special orthogonal group $\mathrm{SO}(3)$ by identifying closed form expressions for geometric quantities such as covariant derivative and parallel transport in exponential…
In this paper we propose and study a hybrid discrete in continuous mathematical model of collective motion under alignment and chemotaxis effect. Starting from the paper by Di Costanzo et al (2015a), in which the Cucker-Smale model (Cucker…
Traffic jams on roadways, echo chambers on social media, crowds of moving pedestrians, and opinion dynamics during elections are all complex social systems. These applications may seem disparate, but some of the questions that they motivate…
Self-organisation of individuals within large collectives occurs throughout biology. Mathematical models can help elucidate the individual-level mechanisms behind these dynamics, but analytical tractability often comes at the cost of…
We consider the kinetic Cucker-Smale model with local alignment as a mesoscopic description for the flocking dynamics. The local alignment was first proposed by Karper, Mellet and Trivisa \cite{K-M-T-3}, as a singular limit of a normalized…
In this paper, we discuss the flocking phenomenon for the Cucker-Smale and Motsch-Tadmor models in continuous time on a general oriented and weighted graph with a general communication function. We present a new approach for studying this…
The Motsch-Tadmor (MT) model is a variant of the Cucker-Smale model with a normalized communication weight function. The normalization poses technical challenges in analyzing the collective behavior due to the absence of conservation of…
We study the swarming behavior of hydrodynamic alignment. Alignment reflects steering towards a weighted average heading. We consider the class of so-called $p$-alignment hydrodynamics, based on $2p$-Laplacians, and weighted by a general…
We present the hydrodynamic theory of coherent collective motion ("flocking") at a solid-liquid interface, and many of its predictions for experiment. We find that such systems are stable, and have long-range orientational order, over a…
Understanding collective self-organization in active matter, such as bird flocks and fish schools, remains a grand challenge in physics. Interactions that induce alignment are essential for flocking; however, alignment alone is generally…
The collective motion of groups of animals emerges from the net effect of the interactions between individual members of the group. In many cases, such as birds, fish, or ungulates, these interactions are mediated by sensory stimuli that…
Representing social systems as networks, starting from the interactions between individuals, sheds light on the mechanisms governing their dynamics. However, networks encode only pairwise interactions, while most social interactions occur…
We consider a nonlinear coupled discrete-time model of population dynamics. This model describes the movement of populations within a heterogeneous landscape, where the growth of subpopulations are modelled by (possibly different) bounded…
The study of collective behavior in multi-agent systems has attracted the attention of many researchers due to its wide range of applications. Among them, the Cucker-Smale model was developed to study the phenomenon of flocking, and various…
In this paper the spatial-temporal dynamics of the members of interacting populations is described by nonlinear partial differential equations. We consider the migration as a diffusion process influenced by the changing values of the birth…
We study a stochastic model of collective motion in which individuals update their orientation through pairwise aligning or anti-aligning copying interactions. We analyze both annealed dynamics, where interaction types are chosen…
This paper develops the basic analytical theory related to some recently introduced crowd dynamics models. Where well posedness was known only locally in time, it is here extended to all of $\reali^+$. The results on the stability with…
In this note we reveal new classes of solutions to hydrodynamic Euler alignment systems governing collective behavior of flocks. The solutions describe unidirectional parallel motion of agents, and are globally well-posed in…
Video-based high-density crowd analysis and prediction has been a long-standing topic in computer vision. It is notoriously difficult due to, but not limited to, the lack of high-quality data and complex crowd dynamics. Consequently, it has…
In this paper we deal with pedestrian modeling, aiming at simulating crowd behavior in normal and emergency scenarios, including highly congested mass events. We are specifically concerned with a new agent-based, continuous-in-space,…