Exact multileg correlation functions for the dense phase of branching polymers in two dimensions.

We consider branching polymers on the planar square lattice with open boundary conditions and exactly calculate correlation functions of k polymer chains that connect two lattice sites with a large distance r apart for odd number of polymer chains k. We find that besides the standard power-law factor the leading term also has a logarithmic multiplier.

Exact phase diagram for an asymmetric avalanche process.

The Bethe ansatz method and an iterative procedure based on detailed balance are used to obtain exact results for an asymmetric avalanche process on a ring. The average velocity of particle flow, v, is derived as a function of the toppling probabilities and the density of particles, rho. As rho increases, the system shows a transition from intermittent to continuous flow, and v diverges at a critical point rho(c) with exponent alpha. The exact phase diagram of the transition is obtained and alpha is found to depend on the toppling rules.

Inversion symmetry and exact critical exponents of dissipating waves in the sandpile model.

By an inversion symmetry, we show that in the Abelian sandpile model the probability distribution of dissipating waves of topplings that touch the boundary of the system shows a power-law relationship with critical exponent 5/8 and the probability distribution of those dissipating waves that are also last in an avalanche has an exponent of 1. Our extensive numerical simulations not only support these predictions, but also show that inversion symmetry is useful for the analysis of the two-wave probability distributions.

Dynamical real space renormalization group applied to sandpile models.

A general framework for the renormalization group analysis of self-organized critical sandpile models is formulated. The usual real space renormalization scheme for lattice models when applied to nonequilibrium dynamical models must be supplemented by feedback relations coming from the stationarity conditions. On the basis of these ideas the dynamically driven renormalization group is applied to describe the boundary and bulk critical behavior of sandpile models. A detailed description of the branching nature of sandpile avalanches is given in terms of the generating functions of the underlying branching process.

[Temperature denaturation of erythrocyte spectrin: rheology, deformability and resistance to detergents]. / Temperaturnaia denaturatsiia spektrina eritrotsitov: reologiia, deformiruemost' i detergentoustoichivost'.

Detergent resistance of erythrocytes and viscosity of whole blood altered sharply already on the first stages of spectrin denaturation process (46-48 degrees C). Alternatively, deformability changes arise above 50 degrees C. Further insignificant increase in viscosity proceeded above 50 degrees C. Yield stress decreased to zero at t < 50 degrees C and at higher temperatures suspension demonstrated Newton's behavior. So, the following order of events can be seen: 1) the initial stages of denaturation process (46-48 degrees C) lead to shape modifications of erythrocytes (spicula formation on the cell rim-echinocytosis), with the detergent resistance of erythrocytes decreasing significantly and capability of echinocytes to aggregate with fibrinogen participation being lost. 2) Above 50 degrees C vesiculation and spherulation of erythrocytes lead to a sharp alteration of deformability with an insignificant increase of viscosity. Thus, deformability of erythrocytes, which is a very important factor in the capillary circulation, may be of lesser rheological role in large vessels.