Related papers: Synchronization in abstract mean field models
We introduce the notion of stable solution in mean field game theory: they are locally isolated solutions of the mean field game system. We prove that such solutions exist in potential mean field games and are local attractors for learning…
We introduce a novel reformulation of the mean-field system for pulse-coupled oscillators. It is based on writing a closed equation for the inverse distribution function associated to the probability density of oscillators with a given…
We show that an atomic system in a periodically modulated optical trap displays an ideal mean-field symmetry-breaking transition. The symmetry is broken with respect to time translation by the modulation period. The transition is due to the…
The phenomenon of synchronization, where entities exhibit stable oscillations with aligned frequencies and phases, has been detected in diverse areas of natural science. It plays a crucial role in achieving frequency locking in multiple…
We study synchronization properties of coupled oscillators on networks that allow description in terms of global mean field coupling. These models generalize the standard Kuramoto-Sakaguchi model, allowing for different contributions of…
Synchronization, a ubiquitous phenomenon in classical systems, has recently been extended to the quantum domain. Here, we show quantum synchronization of a bosonic mode exhibiting a Fock state-like limit cycle, manifesting as a steady state…
We propose a mean field theory for the localization of damage in a quasistatic fuse model on a cylinder. Depending on the quenched disorder distribution of the fuse thresholds, we show analytically that the system can either stay in a…
The phase field method is an effective tool for modeling microstructure evolution in materials. Many efficient implicit numerical solvers have been proposed for phase field simulations under uniform and time-invariant model parameters. We…
We show the existence of "mild solutions" for a first-order mean field game of controls under the state constraint that trajectories be confined in a closed and bounded set in euclidean space. This extends the results of Cannarsa and…
This paper develops a linear programming approach for mean field games with reflected jump-diffusion dynamics. We first prove the equivalence between the mean field equilibria in the linear programming formulation and those in the weak…
A recent dynamic mean-field theory for sequence processing in fully connected neural networks of Hopfield-type (During, Coolen and Sherrington, 1998) is extended and analized here for a symmetrically diluted network with finite connectivity…
Algorithms for the synchronisation of clocks across networks are both common and important within distributed systems. We here address not only the formal modelling of these algorithms, but also the formal verification of their behaviour.…
Exactly solvable many-body systems are few and far between, and the utility of approximate methods cannot be overestimated. Entanglement mean field theory is an approximate method to handle such systems. While mean field theories reduce the…
We analyse the properties of the synchronisation transition in a many-body system consisting of quantum van der Pol oscillators with all-to-all coupling using a self-consistent mean-field method. We find that the synchronised state, which…
In this article, we investigate mean field effects for a bosonic gas harmonically trapped above the transition temperature in the collisionless regime. We point out that those effects can play also a role in low dimensional system. Our…
We propose a formalization of generic algorithms that includes analog algorithms. This is achieved by reformulating and extending the framework of abstract state machines to include continuous-time models of computation. We prove that every…
We study the geometrical structure of the states in the low temperature phase of a mean field model for generalized spin glasses, the p-spin spherical model. This structure cannot be revealed by the standard methods, mainly due to the…
Approximate analytical solutions of the modified Langevin equation are obtained. These solutions are relatively simple and enough accurate. They are illustrated by considering a mean-field model of a system with interacting…
We study a recently introduced and exactly solvable mean-field model for the density of vibrational states $\mathcal{D}(\omega)$ of a structurally disordered system. The model is formulated as a collection of disordered anharmonic…
We summarize exact solutions of closed superstrings in a constant magnetic field, from a view point of the regularization criterion. Some models will be excluded according to this criterion. The spectrum-generating algebra is also…