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We investigate transport properties of percolating clusters generated by irreversible cooperative sequential adsorption (CSA) on square lattices with Arrhenius rates given by k_i ≡ q^n_i, where n_i is the number of occupied neighbors of the site i, and q a controlling parameter. Our results show a dependence of the prefactors non q and a strong finite size effect for small values of this parameter, both impacting the size of the backbone and the global conductance of the system. These results might be pertinent to practical applications in processes involving adsorption of particles.

Studies in spin dynamics of disordered media and multiple ultra-small angle neutron scattering are considered. The experiments were carried out on unique installations designed in ITEP laboratory of neutron physics: beta-NMR spectrometer and universal neutron diffractometer. The main attention is paid to random walks in disordered systems and ultra-small angle neutron scattering (USANS) on objects with space correlations in positions of scatterers. Synthesis of concentration expansion, semi-phenomenological theory and numerical simulations produced satisfactory description of the nuclear polarization transfer within disordered ⁸Li–⁶Li spin subsystem in LiF single crystal. The theory of USANS starts from eikonal approximation for the scattering amplitude, which (a) reproduces the phenomenological Moliere–Bethe theory for the observable neutron angular distributions for uncorrelated random positions of scatterers, and (b) gives a possibility to take into account their spatial correlations.

We study the correction to scaling of the rms displacements of random walks in disordered media consisted of connected networks of the lattice percolation in two, three, and four dimensions. The two types of ensemble averages, i.e. an infinite-network average of random walks starting from an infinite network and an all-cluster average starting from any occupied site, are investigated using both the myoptic ants and the blind ants models. We find that the rms displacements exhibit strong nonanalytic corrections in all dimensions. The correction exponent δ defined by the rms displacement of t-step random walks via R_t=At^1/d_w (1+Bt^-δ+Ct^-1+⋯) was found as δ≃0.39, 0.27, and 0.27 for, respectively, two, three, and four dimensions for an infinite-network average, and δ≃0.37, 0.28, and 0.24 for an all-cluster average.