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A mean field description of particle coalescence and Ostwald ripening is presented.
The interface in between the two domains occupies exactly one lattice site and is chosen such that the mean field description is still accurate there.
The method preserves stochastic features such as extinction not observable in the mean field description, and is significantly faster to simulate on a computer than the pure stochastic model.
It is found that while a continuum model based on a mean field description of the surface is adequate to predict ignition, large discrepancies from the multiscale predictions are observed on the ignited branch and for the extinction temperature due to adjacency requirements at the microscopic level.
Comparisons were made for population sizes of the order hundreds, where deviations between the stochastic model and its mean field description would be fairly pronounced.
Yet, both the mean field description and the simulations show that the network is able to sustain three different states for a given range of parameters λ̅ and w+.
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The mean-field description has also deep theoretical implications in neuroscience.
9, where we cover recent results for Winfree networks that provide an exact mean-field description in terms of a complex order parameter.
Strictly speaking, the mean-field description is only valid in the thermodynamic limit N → ∞, and provided that this limit is taken before the limit t → ∞ [24].
This network analog of stochastic resonance is not captured by a mean-field description that incorporates topology only on the level of the average degree, indicating that the detailed network topology plays a significant role in signal propagation.
Moreover we prove that in general it is not possible to find a mean-field description à la Sznitman of the network, if the anatomical connections are too sparse or our three sources of variability are correlated.
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