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The Kuramoto model: A simple paradigm for synchronization phenomena
Synchronization phenomena in large populations of interacting elements are the subject of intense research efforts in physical, biological, chemical, and social systems. A successful approach to the
Nonlinear stability of incoherence and collective synchronization in a population of coupled oscillators
A mean-field model of nonlinearly coupled oscillators with randomly distributed frequencies and subject to independent external white noises is analyzed in the thermodynamic limit. When the frequency
Oscillatory wave fronts in chains of coupled nonlinear oscillators.
Wave front pinning and propagation in damped chains of coupled oscillators are studied and an approximate analytical description of smooth nonlinearities is found by means of the active point theory.
Non-linear dynamics of semiconductor superlattices
In the last decade, non-linear dynamical transport in semiconductor superlattices (SLs) has witnessed significant progress in theoretical descriptions as well as in experimentally observed non-linear
Asymptotic Behavior of an Initial-Boundary Value Problem for the Vlasov-Poisson-Fokker-Planck System
It is proven that the distribution of particles tends for large time to a Maxwellian determined by the solution of the Poisson--Boltzmann equation with Dirichlet boundary condition.
Hybrid modeling of tumor-induced angiogenesis.
This work sets up a conceptual stochastic model including branching, elongation, and anastomosis of vessels and derives a mean field approximation for their densities, which leads to a deterministic integropartial differential system that describes the formation of the Stochastic vessel network.
Self-synchronization of populations of nonlinear oscillators in the thermodynamic limit
A population of identical nonlinear oscillators, subject to random forces and coupled via a mean-field interaction, is studied in the thermodynamic limit. The model presents a nonequilibrium phase
Active Ornstein-Uhlenbeck particles.
  • L. Bonilla
  • Mathematics
    Physical review. E
  • 13 May 2019
A theorem on the time reversed form of the AOUP Langevin-Ito equations is proved that they have an equilibrium probability density invariant under time reversal if and only if their smooth interaction potential has zero third derivatives.
High-field limit of the Vlasov-Poisson-Fokker-Planck system: A comparison of different perturbation methods
A reduced drift-diffusion (Smoluchowski–Poisson) equation is found for the electric charge in the high-field limit of the Vlasov–Poisson–Fokker–Planck system, both in one and three dimensions. The
Ripples in a graphene membrane coupled to Glauber spins
We propose a theory of ripples in suspended graphene sheets based on two-dimensional elasticity equations that are made discrete on the honeycomb lattice and then periodized. At each point carbon