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Extensive Monte Carlo data analysis gives clear evidence that collapsed linear polymers in two dimensions fall in the universality class of athermal, dense self-avoiding walks, as conjectured by B.Duplantier [Phys.Rev.Lett. 71, 4274…
We determine the dimensional dependence of the percolative exponents of the jamming transition via numerical simulations in four and five spatial dimensions. These novel results complement literature ones, and establish jamming as a mixed…
The exact solution of directed self-avoiding walks confined to a slit of finite width and interacting with the walls of the slit via an attractive potential has been calculated recently. The walks can be considered to model the…
We consider the discrete directed polymer model with i.i.d. environment and we study the fluctuations of the tail $n^{(d-2)/4}(W_\infty - W_n)$ of the normalized partition function. It was proven by Comets and Liu, that for sufficiently…
Consider a realization of a Poisson process in R^2 with intensity 1 and take a maximal up/right path from the origin to (N,N) consisting of line segments between the points, where maximal means that it contains as many points as possible.…
We numerically investigate the influence of self-attraction on the critical behaviour of a polymer in two dimensions, by means of an analysis of finite-size results of transfer-matrix calculations. The transfer matrix is constructed on the…
The diffusive transport in two-dimensional incompressible turbulent fields is investigated with the aid of high-quality direct numerical simulations. Three classes of turbulence spectra that are able to capture both short and long-range…
A problem of the crossover from percolation to diffusion transport is considered. A general scaling theory is proposed. It introduces phenomenologically four critical exponents which are connected by two equations. One exponent is…
We have simulated an automaton version of the quenched Kardar-Parisi-Zhang (qKPZ) equation in one and two dimensions in order to study the scaling properties of the interface at the depinning transition. Specifically, the $\alpha$, $\beta$,…
We study continuum percolation of overlapping circular discs of two sizes. We propose a phenomenological scaling equation for the increase in the effective size of the larger discs due to the presence of the smaller discs. The critical…
We review recent results of the field theoretical renormalization group analysis on the scaling properties of star polymers. We give a brief account of how the numerical values of the exponents governing the scaling of star polymers were…
We describe some recent results concerning the statistical properties of a self-interacting polymer stretched by an external force. We concentrate mainly on the cases of purely attractive or purely repulsive self-interactions, but our…
We propose a novel finite size scaling analysis for percolation transition observed in complex networks. While it is known that cooperative systems in growing networks often undergo an infinite order transition with inverted…
Using grand canonical Monte Carlo simulations, we investigate the percolation behavior of a square well fluid with an ultra-short range of attraction in three dimension (3D) and in confined geometry. The latter is defined through two…
We provide a new proof of the near-critical scaling relation $\beta=\xi_1\nu$ for Bernoulli percolation on the square lattice already proved by Kesten in 1987. We rely on a novel approach that does not invoke Russo's formula, but rather…
We present structural properties of two-dimensional polymers as far as they can be described by percolation theory. The percolation threshold, critical exponents and fractal dimensions of clusters are determined by computer simulation and…
The effect of an electric field on conduction in a disordered system is an old but largely unsolved problem. Experiments cover an wide variety of systems - amorphous/doped semiconductors, conducting polymers, organic crystals, manganites,…
The one dimensional direct polymer in random media model is investigated using a variational approach in the replica space. We demonstrate numerically that the stable point is a maximum and the corresponding statistical properties for the…
For the quantum Ising model with ferromagnetic random couplings $J_{i,j}>0$ and random transverse fields $h_i>0$ at zero temperature in finite dimensions $d>1$, we consider the lowest-order contributions in perturbation theory in…
The estimates on the fluctuations of first-passsage percolation due to Talagrand (a tail bound) and Benjamini--Kalai--Schramm (a sublinear variance bound) are transcribed into the positive-temperature setting of random Schroedinger…