Biomedical subjects

A M Povolotsky

Publications and source records attributed to A M Povolotsky.

5 recordsLinked to original sources

PubMed2005

Organization of complex networks without multiple connections.

We find a new structural feature of equilibrium complex random networks without multiple and self-connections. We show that if the number of connections is sufficiently high, these networks contain a core of highly interconnected vertices. The number of vertices in this core varies in the range between const x N1/2 and const x N2/3, where is the number of vertices in a network. At the birth point of the core, we obtain the size-dependent cutoff of the distribution of the number of connections and find that its position differs from earlier estimates.

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PubMed2004

Bethe ansatz solution of zero-range process with nonuniform stationary state.

The eigenfunctions and eigenvalues of the master equation for zero-range process with totally asymmetric dynamics on a ring are found exactly using the Bethe ansatz weighted with the stationary weights of particle configurations. The Bethe ansatz applicability requires the rates of hopping of particles out of a site to be the q numbers [n](q). This is a generalization of the rates of hopping of noninteracting particles equal to the occupation number n of a site of departure. The noninteracting case can be restored in the limit q-->1. The limiting cases of the model for q=0, infinity correspond to the totally asymmetric exclusion process, and the drop-push model, respectively. We analyze the partition function of the model and apply the Bethe ansatz to evaluate the generating function of the total distance traveled by particles at large time in the scaling limit. In case of nonzero interaction, q not equal 1, the generating function has the universal scaling form specific for the Kardar-Parizi-Zhang universality class.

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PubMed2003

Transition from Kardar-Parisi-Zhang to tilted interface critical behavior in a solvable asymmetric avalanche model.

We use a discrete-time formulation of the asymmetric avalanche process (ASAP) [Phys. Rev. Lett. 87, 084301 (2001)]] of p particles on a finite ring of N sites to obtain an exact expression for the average avalanche size as a function of toppling probabilities and particle density rho=p/N. By mapping the model onto driven interface problems, we find that the ASAP incorporates the annealed Kardar-Parizi-Zhang and quenched tilted interface dynamics for rho rho(c), respectively, with rho(c) being the critical density for given toppling probabilities and N--> infinity. We analyze the crossover between two regimes and show which parameters are relevant near the transition point.

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PubMed2001

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.

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PubMed1999

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.

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