Related papers: Self-organization on Riemannian manifolds
Consider a holomorphic automorphism acting hyperbolically on an invariant compact set. It has been conjectured that the arising stable manifolds are all biholomorphic to Euclidean space. Such a stable manifold is always equivalent to the…
We consider an individual based model of phenotypic evolution in hermaphroditic populations which includes random and assortative mating of individuals. By increasing the number of individuals to infinity we obtain a nonlinear transport…
Recordings of increasingly large neural populations have revealed that the firing of individual neurons is highly coordinated. When viewed in the space of all possible patterns, the collective activity forms non-linear structures called…
We study a class of self-repelling diffusions on compact Riemannian manifolds whose drift is the gradient of a potential accumulated along their trajectory. When the interaction potential admits a suitable spectral decomposition, the…
Extending our previous work on 2D growth for the Laplace equation we study here {\it multidimensional} growth for {\it arbitrary elliptic} equations, describing inhomogeneous and anisotropic pattern formations processes. We find that these…
We characterize isometric actions whose principal orbits are hypersurfaces through the existence of a linear connection satisfying a set of covariant equations in the same spirit as the Ambrose-Singer Theorem for homogeneous space. These…
For robots to be a part of our daily life, they need to be able to navigate among crowds not only safely but also in a socially compliant fashion. This is a challenging problem because humans tend to navigate by implicitly cooperating with…
Despite the long history of modelling human mobility, we continue to lack a highly accurate approach with low data requirements for predicting mobility patterns in cities. Here, we present a population-weighted opportunities model without…
Random organizing hyperuniform fluid induced by reciprocal activation is a non-equilibrium fluid with vanishing density fluctuations at large length scales like crystals. Here we extend this new state of matter to a closed manifold, namely…
Macroscopic models of crowd flow incorporating individual pedestrian choices present many analytic and computational challenges. Anisotropic interactions are particularly subtle, both in terms of describing the correct "optimal" direction…
We study analytically the emergence of spontaneous collective motion within large bidimensional groups of self-propelled particles with noisy local interactions, a schematic model for assemblies of biological organisms. As a central result,…
Human mobility is investigated using a continuum approach that allows to calculate the probability to observe a trip to anyarbitrary region, and the fluxes between any two regions. The considered description offers a general and unified…
In this paper we derive and analyse mean-field models for the dynamics of groups of individuals undergoing a random walk. The random motion of individuals is only influenced by the perceived densities of the different groups present as well…
A recently introduced particle-based model for fluid dynamics with effective excluded volume interactions is analyzed in detail. The interactions are modeled by means of stochastic multiparticle collisions which are biased and depend on…
This paper reviews (and expands) some recent results on the modeling of aggregation-diffusion phenomena at various scales, focusing on the emergence of collective dynamics as a result of the competition between attractive and repulsive…
This paper presents an overview and discussion of magnetocapillary self-assemblies. New results are presented, in particular concerning the possible development of future applications. These self-organizing structures possess the notable…
This paper studies the problem of distributed Riemannian optimization over a network of agents whose cost functions are geodesically smooth but possibly geodesically non-convex. Extending a well-known distributed optimization strategy…
A new approach for the description of phenomena of social aggregation is suggested. On the basis of psychological concepts (as for instance social norms and cultural coordinates), we deduce a general mechanism for the social aggregation in…
The bulk macroscopic response of a system of particles or inclusions with field-induced forces is studied. The susceptibilities and transport coefficients in such a system are expressed as averages of a multiple scattering expansion. A…
Competition for a limited resource is the hallmark of many complex systems, and often, that resource turns out to be the physical space itself. In this work, we study a novel model designed to elucidate the dynamics and emergence in complex…