Related papers: On the Mathematics of Swarming: Emergent Behavior …
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 study the long-time hydrodynamic behavior of systems of multi-species which arise from agent-based description of alignment dynamics. The interaction between species is governed by an array of symmetric communication kernels. We prove…
We study the large-time behavior of hydrodynamic model which describes the collective behavior of continuum of agents, driven by pairwise alignment interactions with additional external potential forcing. The external force tends to compete…
We introduce a new class of models for emergent dynamics. It is based on a new communication protocol which incorporates two main features: short-range kernels which restrict the communication to local geometric balls, and anisotropic…
We study the large-time behavior of continuum alignment dynamics based on Cucker-Smale (CS)-type interactions which involve short-range kernels, that is, communication kernels with support much smaller than the diameter of the crowd. We…
In this note we continue our study of unidirectional solutions to hydrodynamic Euler alignment systems with strongly singular communication kernels $\phi(x):=|x|^{-(n+\alpha)}$ for $\alpha\in(0,2)$. The solutions describe unidirectional…
We study the spatial pattern formation and emerging long range correlations in a model of three species coevolving in space and time according to stochastic contact rules. Analytical results for the pair correlation functions, based on a…
The collective swimming of soft robots in an infinite viscous fluid is an emergent phenomenon due to the non-reciprocal hydrodynamic interactions between individual swimmers. These physical interactions give rise to unique spatiotemporal…
Swarming phenomena are ubiquitous in various physical, biological, and social systems, where simple local interactions between individual units lead to complex global patterns. A common feature of diverse swarming phenomena is that the…
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…
Aggregation-diffusion equations are foundational tools for modelling biological aggregations. Their principal use is to link the collective movement mechanisms of organisms to their emergent space use patterns in a concrete mathematical…
Understanding how species persist under interacting stressors is a central challenge in ecology. We develop a spatially explicit reaction-diffusion framework to investigate competing species in landscapes shaped by climate variability,…
The fundamental derivation of macroscopic model equations to describe swarms based on microscopic movement laws and mathematical analyses into their self-organisation capabilities remains a challenge from the perspective of both modelling…
When an ensemble of particles interact hydrodynamically, they generically display large-scale transient structures such as swirls in sedimenting particles [1], or colloidal strings in sheared suspensions [2]. Understanding these…
We consider the problem of understanding the coordinated movements of biological or artificial swarms. In this regard, we propose a learning scheme to estimate the coordination laws of the interacting agents from observations of the swarm's…
We propose a simple adaptive-network model describing recent swarming experiments. Exploiting an analogy with human decision making, we capture the dynamics of the model by a low-dimensional system of equations permitting analytical…
We classify and predict the asymptotic dynamics of a class of swarming models. The model consists of a conservation equation in one dimension describing the movement of a population density field. The velocity is found by convolving the…
Computational models of collective behavior in birds has allowed us to infer interaction rules directly from experimental data. Using a generic form of these rules we explore the collective behavior and emergent dynamics of a simulated…
Many classical examples of models of self-organized dynamics, including the Cucker-Smale, Motsch-Tadmor, multi-species, and several others, include an alignment force that is based upon density-weighted averaging protocol. Those protocols…
We analyze networked heterogeneous nonlinear systems, with diffusive coupling and interconnected over a generic static directed graph. Due to the network's hetereogeneity, complete synchronization is impossible, in general, but an emergent…