Search results for "Large number limit"
showing 2 items of 2 documents
Modelling of Systems with a Dispersed Phase: “Measuring” Small Sets in the Presence of Elliptic Operators
2016
When modelling systems with a dispersed phase involving elliptic operators, as is the case of the Stokes or Navier-Stokes problem or the heat equation in a bounded domain, the geometrical structure of the space occupied by the dispersed phase enters in the homogenization process through its capacity, a quantity which can be used to define the equivalence classes in \(H^1\). We shall review the relationship between capacity and homogenization terms in the limit when the number of inclusions becomes large, focusing in particular on the situation where the distribution of inclusions is not necessarily too regular (i.e. it is not periodic).
Large Number Asymptotics for Two-Component Systems with Self-Consistent Coupling
2014
We shall consider the large number asymptotics of particle models for partial differential equations describing two component mixtures with simplest kind of self-consistent couplings. We shall recall in particular two examples related to different classes of models, the first one having both particle-like components and the second one having only one particle-like component (the other being described as a fluid); for these examples, different techniques on the probabilistic and analytic point of view are to be used to rigorously prove the convergence to a limit of the self-consistent terms in a “mean-field”-like asymptotics. The two models were analysed resp. in Bernardin and Ricci (Kinet R…