Ferromagnetic king systems with four different arrangements of antiferromagnetic impurities are considered. Using the high-temperature series expansion method, T, is determined and compared with respective values for a system containing the same amount of impurities but distributed randomly. It is shown that T, is much more sensitive to the concentration of antiferromagnetic bonds and their strength than to the amount of frustration present in the system.
We consider two applications of the stochastic discrete particles method. The first one is concerned with the dispersion of a passive pollutant by a turbulent stream with a scale dependent diffusion coefficient. The second application deals with the problem of an oil spill spreading on the water surface described by transport-diffusion equation with a nonlinear diffusion coefficient. For the first problem we develop a discrete particles algorithm provided the diffusion coefficient obeys Richardson's "4/3" law and show good correspondence with the numerical and analytical results. The second problem is more involved and we develop a heuristic procedure based on the standard discrete particles random walk algorithm updating the dependence of each particle step variance on the dependent function. The obtained solution coincides well with analytical and direct one-dimensional finite-difference solutions both for instantaneous and continuous oil release.
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