Coupling and Bernoullicity in random-cluster and Potts models

An explicit coupling construction of random-cluster measures is presented. As one of the applications of the construction, the Potts model on amenable Cayley graphs is shown to exhibit at every temperature the mixing property known as Bernoullicity

Explicit coupling argument for nonuniformly hyperbolic transformations

The transfer operator corresponding to a uniformly expanding map enjoys good spectral properties. We verify that coupling yields explicit estimates that depend continuously on the expansion and distortion constants of the map. For non-uniformly expanding maps with a uniformly expanding induced map, we obtain explicit estimates for mixing rates (exponential, stretched exponential, polynomial) that again depend continuously on the constants for the induced map together with data associated with the inducing time. Finally, for non-uniformly hyperbolic transformations, we obtain the corresponding estimates for rates of decay of correlations

Collection of Mutually Synchronized Chaotic Systems

A general explicit coupling for mutual synchronization of two arbitrary identical continuous systems is proposed. The synchronization is proved analytically. The coupling is given for all 19 systems from Sprott's collection. For one of the systems the numerical results are shown in detail. The method could be adopted for the teaching of the topic.Comment: Published in Physics Letters A 352 (2006) 222-22

A non-geodesic motion in the R^-1 theory of gravity tuned with observations

In the general picture of high order theories of gravity, recently, the R^-1 theory has been analyzed in two different frameworks. In this letter a third context is added, considering an explicit coupling between the R^-1 function of the Ricci scalar and the matter Lagrangian. The result is a non-geodesic motion of test particles which, in principle, could be connected with Dark Matter and Pioneer anomaly problems.Comment: Accepted for Modern Physics Letters

An unfitted Nitsche method for incompressible fluid-structure interaction using overlapping meshes

We consider the extension of the Nitsche method to the case of fluid–structure interaction problems on unfitted meshes. We give a stability analysis for the space semi-discretized problem and show how this estimate may be used to derive optimal error estimates for smooth solutions,irrespectively of the mesh/interface intersection. We also discuss different strategies for the time discretization, using either fully implicit or explicit coupling (loosely coupled) schemes. Some numerical examples illustrate the theoretical discussion