Generalized Farey trees, transfer Operators and phase transitions

We consider a family of Markov maps on the unit interval, interpolating between the tent map and the Farey map. The latter map is not uniformly expanding. Each map being composed of two fractional linear transformations, the family generalizes many particular properties which for the case of the Farey map have been successfully exploited in number theory. We analyze the dynamics through the spectral analysis of generalized transfer operators. Application of the thermodynamic formalism to the family reveals first and second order phase transitions and unusual properties like positivity of the interaction function.Comment: 39 pages, 10 figure

Effect of shock-induced mesoscopic processes on dynamic strength of solids

Dynamic deformation and fracture behavior of a series of metals under uniaxial strain conditions are studied by using light gas gun facility and velocity interferometer. In the majority of tests the thickness of target and impactor were adjusted to provide spallation. Spall-strength is found to be sensitively depended on the plastic instability of a material under compression. It is considered to be important strength-characteristic of material. Specifically, for all the tested material the value of instability threshold determined in uniaxial strain tests coincides with the strength-component of resistance to high-velocity penetration in Alekseevskii-Tate model

Kinetics of mesostructure and reloading behavior of dynamically compressed solids

Experimental study of shock reloading processes during the uniaxial strain loading of aluminum alloy targets reveals a dependence of reloading response of material on the particle velocity dispersion behavior. This response is found to be elastic-plastic in case the velocity dispersion at the plateau of compressive pulse equals zero. In the presence of the velocity dispersion the reloading response is pure plastic. This phenomenon is considered from the position of nonlocal hydrodynamic theory developed for description of high-non-equilibrium processes in heterogeneous media