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Invasion Sandpile Model
M. N. Najafi, Z. Moghaddam, M. Samadpour +1
Motivated by multiphase flow in reservoirs, we propose and study a two-species sandpile model in two dimensions. A pile of particles becomes unstable and topples if, at least one o…
The symbiotic contact process: phase transitions, hysteresis cycles, and bistability
C. I. N. Sampaio Filho, T. B. dos Santos, N. A. M. Araújo +3
We performed Monte Carlo simulations of the symbiotic contact process on different spatial dimensions (). On the complete and random graphs (infinite dimension), we observe hyst…
Random Sequential Adsorption on mobile patches
Diogo E. P. Pinto, Nuno A. M. Araujo
An extension of the Random Sequential Adsorption (RSA) model has been proposed recently, motivated by the coverage of oil droplets by DNA-functionalized colloidal particles. Partic…
Schramm-Loewner Evolution and isoheight lines of correlated landscapes
N. Pose, K. J. Schrenk, N. A. M. Araujo +1
Real landscapes are usually characterized by long-range height-height correlations, which are quantified by the Hurst exponent . We analyze the statistical properties of the iso…
Kinetic interfaces of patchy particles
N. A. M. Araújo, C. S. Dias, M. M. Telo da Gama
We study the irreversible adsorption of patchy particles on substrates in the limit of advective mass transport. Recent numerical results show that the interface roughening depends…
Recent advances and open challenges in percolation
N. A. M. Araújo, P. Grassberger, B. Kahng +2
Percolation is the paradigm for random connectivity and has been one of the most applied statistical models. With simple geometrical rules a transition is obtained which is related…
Retention capacity of correlated surfaces
K. J. Schrenk, N. A. M. Araujo, R. M. Ziff +1
We extend the water retention model [C. L. Knecht et al., Phys. Rev. Lett. 108, 045703 (2012)] to correlated random surfaces. We find that the retention capacity of discrete random…
Crossover behavior of conductivity in a discontinuous percolation model
Seongmin Kim, Y. S. Cho, N. A. M. Araujo +1
When conducting bonds are occupied randomly in a two-dimensional square lattice, the conductivity of the system increases continuously as the density of those conducting bonds exce…
Percolation with long-range correlated disorder
K. J. Schrenk, N. Pose, J. J. Kranz +3
Long-range power-law correlated percolation is investigated using Monte Carlo simulations. We obtain several static and dynamic critical exponents as function of the Hurst exponent…
Stacked triangular lattice: Percolation properties
K. J. Schrenk, N. A. M. Araujo, H. J. Herrmann
The stacked triangular lattice has the shape of a triangular prism. In spite of being considered frequently in solid state physics and materials science, its percolation properties…
Effect of particle polydispersity on the irreversible adsorption of fine particles on patterned substrates
J. F. Marques, A. B. Lima, N. A. M. Araujo +1
We performed extensive Monte Carlo simulations of the irreversible adsorption of polydispersed disks inside the cells of a patterned substrate. The model captures relevant features…
Watersheds are Schramm-Loewner Evolution curves
E. Daryaei, N. A. M. Araujo, K. J. Schrenk +2
We show that in the continuum limit watersheds dividing drainage basins are Schramm-Loewner Evolution (SLE) curves, being described by one single parameter . Several numerical e…
Single to Double Hump Transition in the Equilibrium Distribution Function of Relativistic Particles
M. Mendoza, N. A. M. Araújo, S. Succi +1
We unveil a transition from single peaked to bimodal velocity distribution in a relativistic fluid under increasing temperature, in contrast with a non-relativistic gas, where only…
How to share underground reservoirs
K. J. Schrenk, N. A. M. Araújo, H. J. Herrmann
Many resources, such as oil, gas, or water, are extracted from porous soils and their exploration is often shared among different companies or nations. We show that the effective s…
Bohman-Frieze-Wormald model on the lattice, yielding a discontinuous percolation transition
K. J. Schrenk, A. Felder, S. Deflorin +3
The BFW model introduced by Bohman, Frieze, and Wormald [Random Struct. Algorithms, 25, 432 (2004)] and recently investigated in the framework of discontinuous percolation by Chen…
Towards designing robust coupled networks
Christian M. Schneider, Nuri Yazdani, Nuno A. M. Araujo +2
Natural and technological interdependent systems have been shown to be highly vulnerable due to cascading failures and an abrupt collapse of global connectivity under initial failu…
Transitions between epitaxial growth regimes: A (1+1)-dimensional kinetic Monte Carlo study
Cristovao S. Dias, Nuno A. M. Araujo, Antonio Cadilhe
To study epitaxial thin-film growth, a new model is introduced and extensive kinetic Monte Carlo simulations performed for a wide range of fluxes and temperatures. Varying the depo…
From invasion percolation to flow in rock fracture networks
Salomon J. Wettstein, Falk K. Wittel, Nuno A. M. Araujo +2
The main purpose of this work is to simulate two-phase flow in the form of immiscible displacement through anisotropic, three-dimensional (3D) discrete fracture networks (DFN). The…
Watersheds and Explosive percolation
Hans J. Herrmann, Nuno A. M. Araujo
The recent work by Achlioptas, D'Souza, and Spencer opened up the possibility of obtaining a discontinuous (explosive) percolation transition by changing the stochastic rule of bon…
Fracturing ranked surfaces
K. J. Schrenk, N. A. M. Araujo, J. S. Andrade +1
Discretized landscapes can be mapped onto ranked surfaces, where every element (site or bond) has a unique rank associated with its corresponding relative height. By sequentially a…
Fractality of eroded coastlines of correlated landscapes
Pablo A. Morais, Erneson A. Oliveira, Nuno A. M. Araujo +2
Using numerical simulations of a simple sea-coast mechanical erosion model, we investigate the effect of spatial long-range correlations in the lithology of coastal landscapes on t…
Optimal path cracks in correlated and uncorrelated lattices
E. A. Oliveira, K. J. Schrenk, N. A. M. Araújo +2
The optimal path crack model on uncorrelated surfaces, recently introduced by Andrade et al. (Phys. Rev. Lett. 103, 225503, 2009), is studied in detail and its main percolation exp…
Tricritical point in explosive percolation
Nuno A. M. Araujo, Jose S. Andrade, Robert M. Ziff +1
The suitable interpolation between classical percolation and a special variant of explosive percolation enables the explicit realization of a tricritical percolation point. With hi…
q-state Potts model on the Apollonian network
Nuno A. M. Araújo, Roberto F. S. Andrade, Hans J. Herrmann
The q-state Potts model is studied on the Apollonian network with Monte Carlo simulations and the Transfer Matrix method. The spontaneous magnetization, correlation length, entropy…