Gauge theory of self-similar system

On the basis of a dilatation invariant Lagrangian, governed equations are determined for probability density and gauge potential of the non-stationary self-similar stochastic system. It is shown that an automodel regime is observed at small time interval determined by the Tsallis' parameter $q>1$. An exponential falling down happens at large time where the dilatation parameter and the partial scale tend to constant values.Comment: 8 pages, LaTe

Supersymmetry approach to the random heteropolymer theory

The effective equation of motion that describes the different monomer alternation along the heteropolymer chain is proposed. On this basis the supersymmetry field scheme is built up to analyze memory and ergodicity breaking effects.Comment: 10 pages, 1 figur

Two Simple Approaches to Sol-Gel Transition

We represent a theory of polymer gelation as an analogue of liquid-glass transition in which elastic fields of stress and strain shear components appear spontaneously as a consequence of the cross-linking of macromolecules. This circumstance is explained on the basis of obvious combinatoric arguments as well as a synergetic Lorenz system, where the strain acts as an order parameter, a conjugate field is reduced to the elastic stress, and the number of cross-links is a control parameter. Both the combinatoric and synergetic approaches show that an anomalous slow dependence of the shear modulus on the number of cross-links is obtained.Comment: 10 pages, LaTe