It is shown that, for d-dimensional random walks with fixed end points, the rth moments at the ith step are rth order polynomials of i. The results are applicable to (1 + 1)-dimensional SOS models of interfaces.

We have found the conditions under which some spin S Ising models on the honeycomb lattice have the same partition functions as the exactly solvable S = 12 Ising model. The exact critical temperatures for the S = 32 and S = 2 models have been found as solutions of nonlinear equations.

We present a spin-32 Ising model which is equivalent to a “two-layer” Ising model. We find a solvable spin-32 Ising model and show that a system may have several critical exponents η corresponding to correlation functions of different Ising-type variables. We find two phase-transition...

We present a short description of the properties of granular gas. In particular, we analyse clusterization, compartmentalization, non-Gaussian velocity distributions, and breaking of equipartition of energy.

Each year perhaps millions of young people face the following dilemma: should I continue my education or rather start working with already acquired skills. Right decision must take into account somebody's own abilities, accessibility to education institutions, competition, and potential...

Using Monte Carlo simulations we show that for 2D and 3D Ising models at zero temperature the average life-time τ of a square/cubic-like domain of the linear size L is proportional to L2. However, for certain initial configurations τ increases much faster: it scales as L3 for the 2D model and...

We show that a partial ordering appears in the limit S → ∞ at the ground state of the 1D spin-S antiferromagnetic Ising model with next-nearest-neighbour interaction. This is an analogue of the ordering which appears at finite S = Sc ≈ 3 in the nearest-neighbour Ising antiferromagnet on...

We show that the mixed-spin Ising model with four-spin interaction on the union jack (centered square) lattice is equivalent to the eight-vertex model. In certain subspaces of parameters the model is solvable and we can locate exactly the coexistence surface between two ordered phases of the...

We study a lattice model of a prey–predator system. Mean-field approximation predicts that the active phase, i.e., one with a finite fraction of preys and predators, is a generic phase of this model. Moreover, within this approximation the model exhibits quasi-oscillations resembling...

Roulette-wheel selection is a frequently used method in genetic and evolutionary algorithms or in modeling of complex networks. Existing routines select one of N individuals using search algorithms of O(N) or O(logN) complexity. We present a simple roulette-wheel selection algorithm, which...