Up and down cascades: three-dimensional magnetic field model.

In our previous works we already have proposed a two-dimensional model of geodynamo. Now we use the same approach to build a three-dimensional self-excited geodynamo model that generates a large scale magnetic field from whatever small initial field, using the up and down cascade effects of a multiscale turbulent system of cyclones. The multiscale system of turbulent cyclones evolves in six domains of an equatorial cylindrical layer of the core.

Scale invariance and invariant scaling in a mixed hierarchical system.

We consider a mixed hierarchical model with heterogeneous and monotone conditions of destruction. We investigate how scaling properties of defects in the model are related with heterogeneity of rules of destruction, determined by concentration of the mixture. The system demonstrates different kinds of criticality as a general form of system behavior.

Up and down cascade in a dynamo model: spontaneous symmetry breaking.

A multiscale turbulent model of dynamo is proposed. A secondary magnetic field is generated from a primary field by a flow made of turbulent helical vortices (cyclones) of different ranges, and amplified by an up and down cascade mechanism. The model displays symmetry breakings of different ranges although the system construction is completely symmetric.

Criticality in a dynamic mixed system.

We suggest a dynamic generalization of the simplest static hierarchical mixed model introduced by Shnirman and Blanter [Phys. Rev. Lett.