Condensate dynamics with non-local interactions

Opinion Dynamics with Local Interactions

We study convergence properties of opinion dynamics with local interactions and limited information exchange. We adopt a general model where the agents update their opinions in rounds to a weighted average of the opinions in their neighborhoods. For fixed neighborhoods, we present a simple randomized protocol that converges in expectation to the stable state of the Friedkin-Johnsen model. For o...

Local molecular dynamics with coulombic interactions.

We propose a local, O(N) molecular dynamics algorithm for the simulation of charged systems. The long ranged Coulomb potential is generated by a propagating electric field that obeys modified Maxwell equations. On coupling the electrodynamic equations to an external thermostat we show that the algorithm produces an effective Coulomb potential between particles. On annealing the electrodynamic d...

Competition of local and non-local interactions: Mass media effect in social dynamics

Fluctuations impact on a pattern-forming model of population dynamics with non-local interactions

A model of interacting random walkers is presented and shown to give rise to patterns consisting in periodic arrangements of fluctuating particle clusters. The model represents biological individuals that die or reproduce at rates depending on the number of neighbors within a given distance. We evaluate the importance of the discrete and fluctuating character of this particle model on the patte...

Local amplitude equation from non-local dynamics

– We derive a closed equation for the shape of the free surface of a magnetic fluid subject to an external magnetic field. The equation is strongly non-local due to the long range character of the magnetic interaction. We develop a systematic multiple scale perturbation expansion in which the non-locality is reduced to the occurrence of the Hilbert transform of the surface profile. The resultin...