English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We study the convergence of a sequence of evolution equations for measuressupported on the nodes of a graph. The evolution equations themselves can beinterpreted as the forward Kolmogorov equations of Markov jump processes, orequivalently as the equations for the concentrations in a network of linearreactions. The jump rates or reaction rates are divided in two classes; `slow'rates are constant, and `fast' rates are scaled as~$1/\epsilon$, and we provethe convergence in the fast-reaction limit $\epsilon\to0$.  We establish a $\Gamma$-convergence result for the rate functional in termsof both the concentration at each node and the flux over each edge (thelevel-2.5 rate function). The limiting system is again described by afunctional, and characterizes both fast and slow fluxes in the system.  This method of proof has three advantages. First, no condition of detailedbalance is required. Secondly, the formulation in terms of concentration andflux leads to a short and simple proof of the $\Gamma$-convergence; the priceto pay is a more involved compactness proof. Finally, the method of proof dealswith approximate solutions, for which the functional is not zero but small,without any changes.

Fast reaction limits via $\Gamma$-convergence of the Flux Rate Functional