Related papers: Inhomogeneity and universality: off-critical behav…
Percolation processes on random networks have been the subject of intense research activity over the last decades: the overall phenomenology of standard percolation on uncorrelated and unclustered topologies is well known. Still some…
Scaling limits of critical percolation models show major differences between low and high dimensional models. The article discusses the formulation of the continuum limit for the former case. A mathematical framework is proposed for the…
The talk presented at ICMP 97 focused on the scaling limits of critical percolation models, and some other systems whose salient features can be described by collections of random lines. In the scaling limit we keep track of features seen…
We consider the critical behavior at an interface which separates two semi-infinite subsystems belonging to different universality classes, thus having different set of critical exponents, but having a common transition temperature. We…
The phase transitions and critical properties of two types of inhomogeneous systems are reviewed. In one case, the local critical behaviour results from the particular shape of the system. Here scale-invariant forms like wedges or cones are…
We study the possible scaling limits of percolation interfaces in two dimensions on the triangular lattice. When one lets the percolation parameter p(N) vary with the size N of the box that one is considering, three possibilities arise in…
We study the crossover scaling behavior of the height-height correlation function in interface depinning in random media. We analyze experimental data from a fracture experiment and simulate an elastic line model with non-linear couplings…
The effective transport properties of heterogeneous nanoscale materials and structures are affected by several geometrical and physical factors. Among them the presence of imperfect interfaces plays a central role being often at the origin…
We consider a diffusion process with coefficients that are periodic outside of an "interface region" of finite thickness. The question investigated in this article is the limiting long time/large scale behavior of such a process under…
Percolation problems appear in a large variety of different contexts ranging from the design of composite materials to vaccination strategies on community networks. The key observable for many applications is the percolation threshold.…
Imbibition phenomena have been widely used experimentally and theoretically to study the kinetic roughening of interfaces. We critically discuss the existing experiments and some associated theoretical approaches on the scaling properties…
We consider a diffusion process with coefficients that are periodic outside of an 'interface region' of finite thickness. The question investigated in the articles [1,2] is the limiting long time / large scale behaviour of such a process…
Global physical properties of random media change qualitatively at a percolation threshold, where isolated clusters merge to form one infinite connected component. The precise knowledge of percolation thresholds is thus of paramount…
Random graphs have played an instrumental role in modelling real-world networks arising from the internet topology, social networks, or even protein-interaction networks within cells. Percolation, on the other hand, has been the fundamental…
The properties of the absorbing states of non-equilibrium models belonging to the conserved directed percolation universality class are studied. We find that at the critical point the absorbing states are hyperuniform, exhibiting…
We consider the behaviour of a critical system in the presence of a gradient perturbation of the couplings. In the direction of the gradient an interface region separates the ordered phase from the disordered one. We develop a scaling…
This note was motivated by natural questions related to oriented percolation on a layered environment that introduces long range dependence. As a convenient tool, we are led to deal with questions on the strict decrease of the percolation…
We provide a theoretical framework to analyze the properties of frontal collisions of two growing interfaces considering different short range interactions between them. Due to their roughness, the collision events spread in time and form…
The boundary conditions at the deformable interface between two contacting fluids are derived for the general case of the large-amplitude perturbations. The interface is modeled as perturbed free boundary that evolves in time, and the…
To reach a deeper understanding of fluid interfaces it is necessary to identify a meaningful coarse-graining length that separates intrinsic fluctuations from capillary ones, given the lack of a proper statistical mechanical definition of…