Related papers: Swarm equilibria in domains with boundaries

We show that the nonequilibrium dynamics of systems with many interacting elements located on a small-world network can be much slower than on regular networks. As an example, we study the phase ordering dynamics of the Ising model on a…

The nonequilibrium stationary state of an exclusive genetic switch is considered. The model comprises two competing species and a single binding site which, when bound to by a protein of one species, causes the other species to be…

We investigate the ground states of a free energy functional on sphere. The energy consists of an entropy and a nonlocal interaction term that are in competition with each other, as they favour spreading and aggregation, respectively.…

We study networks of interacting queues governed by utility-maximising service-rate allocations in both discrete and continuous time. For {\em finite} networks we establish stability and some steady-state moment bounds under natural…

We study the linear stability of flock and mill ring solutions of two individual based models for biological swarming. The individuals interact via a nonlocal interaction potential that is repulsive in the short range and attractive in the…

This work deals with the Landau equation in a bounded domain with the Maxwell reflection condition on the boundary for any (possibly smoothly position dependent) accommodation coefficient and for the full range of interaction potentials,…

Despite many attempts, ordered equilibrium microphases have yet to be obtained in experimental colloidal suspensions. The recent computation of the equilibrium phase diagram of a microscopic, particle-based microphase former [Zhuang et al.,…

It is known from both theory and experiments that introducing time delays into the communication network of mobile-agent swarms produces coherent rotational patterns. Often such spatio-temporal rotations can be bistable with other swarming…

This paper is concerned with equilibrium configurations of one-dimensional particle system with non-convex nearest-neighbour and next-to-nearest-neighbour interactions and its passage to the continuum. The goal is to derive compactness…

Existence of solution and stability results on a class of Non Linear Schroedinger type equations with a bounded nonlinearity are obtained, for a bounded domain and with Dirichlet boundary conditions. The kind of stability under discussion…

Marginally stable systems exhibit rich critical mechanical behavior. Such isostatic assemblies can be driven out of equilibrium by internal activity, but it remains unclear how the isostatic and critical nature of such systems affects their…

Domain walls between spatially periodic patterns with different wave numbers, can arise in pattern-forming systems with a neutral curve that has a double minimum. Within the framework of the phase equation, the interaction of such walls is…

Ecological models traditionally explain stability and coexistence through pairwise interactions among species. These interactions can also involve groups of three or more species, higher-order interactions, which recent theory suggests can…

Under certain assumptions in terms of information and models, equilibria correspond to possible stable outcomes in conflicting or cooperative scenarios where rational entities interact. For wireless engineers, it is of paramount importance…

A classic measure of ecological stability describes the tendency of a community to return to equilibrium after small perturbation. While many advances show how the network structure of these communities severely constrains such tendencies,…

This paper is concerned with the long-time dynamics of semilinear wave equation subject to dissipative boundary condition. To do so, we first analyze the set of equilibria, and show it could contain infinitely many elements. Second, we show…

We show that certain free energy functionals that are not convex with respect to the usual convex structure on their domain of definition, are strictly convex in the sense of displacement convexity under a natural change of variables. We…

In this article we give an in depth overview of the recent advances in the field of equilibrium networks. After outlining this topic, we provide a novel way of defining equilibrium graph (network) ensembles. We illustrate this concept on…

In this paper, we investigate the robustness to external disturbances of switched discrete and continuous systems with multiple equilibria. It is shown that if each subsystem of the switched system is Input-to-State Stable (ISS), then under…

We consider an economy made of competing firms which are heterogeneous in their capital and use several inputs for producing goods. Their consumption policy is fixed rationally by maximizing a utility and their capital cannot fall below a…