Stability of inhomogeneous states in mean-field models with an external potential

Stability of inhomogeneous states in mean-field models with an external potential

The Vlasov equation is well known to provide a good description of the dynamics of mean-field systems in the N → ∞ limit. This equation has an infinity of stationary states and the case of homogeneous states, for which the single-particle distribution function is independent of the spatial variable, is well characterized analytically. On the other hand, the inhomogeneous case often requires som...

Front stability in mean-field models of diffusion-limited growth.

We present calculations of the stability of planar fronts in two mean field models of diffusion limited growth. The steady state solution for the front can exist for a continuous family of velocities, we show that the selected velocity is given by marginal stability theory. We find that naive mean field theory has no instability to transverse perturbations, while a threshold mean field theory h...

Mean field theory of inhomogeneous fluid mixtures

Mean-field Analysis of Large Scale Markov Fluid Models with Fluid Dependent and Time-inhomogeneous Rates

We consider a subset of Markov fluid models where the discrete background process is a Population Continuous Time Markov Chain (PCTMC) – a Markov process capturing interactions between large groups of identically behaved components. We allow the transition and fluid evolution rates to depend on the fluid level. Additionally, we include time-inhomogeneous rate parameters, which can be used to in...

Mean-field analysis of hybrid Markov population models with time-inhomogeneous rates

We consider a hybrid extension of Population Continuous Time Markov Chains (PCTMC) – a class of Markov processes capturing interactions between large groups of identically behaved agents. We augment the discrete state space of a PCTMC with continuous variables that evolve as integrals over the population vector and that can simultaneously provide feedback to the rates of transitions in the PCTM...