Classical site percolation was used to study numerically the effect of interplane coupling in the range 10(-1)-10(-6) of the in-plane coupling on the static correlation length exponent nu and the critical dimension D. It was found that even for the smallest coupling values the exponents take their three-dimensional (3D) values for sufficiently large system sizes. The percolation threshold p(c),...

The problem of random walk is considered in one dimension in the simultaneous presence of a quenched random force field and long-range connections, the probability of which decays with the distance algebraically as p(l)≃βl(-s). The dynamics are studied mainly by a numerical strong disorder renormalization group method. According to the results, for s>2 the long-range connections are irrelevant,...

We derive the fractional master equation with space-dependent anomalous exponent. We analyze the asymptotic behavior of the corresponding lattice model both analytically and by Monte Carlo simulation. We show that the subdiffusive fractional equations with constant anomalous exponent μ in a bounded domain [0,L] are not structurally stable with respect to the nonhomogeneous variations of paramet...

We give a method for obtaining radially symmetric solutions for the critical exponent problem ?u + a(x)u = u q + u 2 ?1 in R N u > 0 and R R N jruj 2 < 1 where, outside a ball centered at the origin, the non-negative function a is bounded from below by a positive constant ao > 0. We remark that, diierently from the literature, we do not require any conditions on a at innnity.

This paper describes, in detail, techniques for measuring the Hurst parameter. Measurements are given on artificial data both in a raw form and corrupted in various ways to check the robustness of the tools in question. Measurements are also given on real data, both new data sets and well-studied data sets. All data and tools used are freely available for download along with simple “recipes” wh...

Transmission of a Gaussian source over a timevarying multiple-input multiple-output (MIMO) channel is studied under strict delay constraints. Availability of a correlated side information at the receiver is assumed, whose quality, i.e., its correlation with the source signal, also varies over time. A block-fading model is considered for the states of the time-varying channel and side informatio...

We give the first nonconstant lower bounds for the approximability of the Independent Set Problem on the Power Law Graphs. These bounds are of the form n in the case when the power law exponent satisfies β < 1. In the case when β = 1, the lower bound is of the form log(n) . The embedding technique used in the proof could also be of independent interest.

A one-dimensional tight-binding Hamiltonian describes the evolution of a single impurity interacting locally with N electrons. The impurity spectral function has a power-law singularity A(ω) ∝| ω− ω0 |−1+β with the same exponent β that characterizes the logarithmic decay of the quasiparticle weight Z with the number of electrons N , Z ∝ N−β. The exponent β is computed by (1) perturbation theory...

We study the asymptotic expansions with respect to h of

We show that seismic waiting time distributions in California and Iceland have many features in common as, for example, a power-law decay with exponent α ≈ 1.1 for intermediate and with exponent γ ≈ 0.6 for short waiting times. While the transition point between these two regimes scales proportionally with the size of the considered area, the full distribution is not universal and depends in a ...