Exponential Decay of Correlations for Strongly Coupled Toom Probabilistic Cellular Automata

We investigate the low-noise regime of a large class of probabilistic cellular automata, including the North-East-Center model of Toom. They are defined as stochastic perturbations of cellular automata belonging to the category of monotonic binary tessellations and possessing a property of erosion. We prove, for a set of initial conditions, exponential convergence of the induced processes toward an extremal invariant measure with a highly predominant spin value. We also show that this invariant measure presents exponential decay of correlations in space and in time and is therefore strongly mixing.Comment: 21 pages, 0 figure, revised version including a generalization to a larger class of models, structure of the arguments unchanged, minor changes suggested by reviewers, added reference

A product-form "loss network" with a form of queueing

Berezner, S. A. ; Krzesinski, A. E. ; Taylor, P. G

On the inverse of Erlang's function

Berezner, S. A. ; Krzesinski, A. E. ; Taylor, P. G

Deformation of Al85Y8Ni5Co2 Metallic Glasses under Cyclic Mechanical Load and Uniform Heating

Modelling of the deformation process of Al85Y8Ni5Co2 amorphous alloys was carried out under simultaneous application of cyclic mechanical load (at 0.3 or 3 Hz frequencies) and continuously increasing temperature (heating rate 5 K/min). It is shown that deformation of the amorphous specimens occurs by the hyperbolic temporal dependence. It is analytically determined and experimentally proved that for non-isothermal cyclic deformation, the wave effects take place as a result of the superposition of thermal-activated and mechanical components. The behaviour of the material under thermo-mechanical action was described qualitatively within the framework of Spaepen’s model. The dependencies for the reaction force of the samples were obtained as two-parameter functions of the frequency and temperature. A reaction force surface of a specimen, as a function of the different forcing frequencies and time, has been plotted