Pablo Jensen

Analysis of community structure in networks of correlated data

We present a reformulation of modularity that allows the analysis of the community structure in networks of correlated data. The modularity preserves the probabilistic semantics of the original definition even when the network is directed, weighted, signed, and has self-loops. This is the most general condition one can find in the study of any network, in particular those defined from correlated data. We apply our results to a real network of correlated data between stores in the city of Lyon (France).

Effect of monomer evaporation on a simple model of submonolayer growth

We present a model for thin-film growth by particle deposition that takes into account the possible evaporation of the particles deposited on the surface. Our model focuses on the formation of two-dimensional structures. We find that the presence of evaporation can dramatically affect the growth kinetics of the film, and can give rise to regimes characterized by different ``growth exponents and island size distributions. Our results are obtained by extensive computer simulations as well as through a simple scaling approach, and the analysis of rate equations describing the system. We carefully discuss the relationship of our model with previous studies of the same physical situation, and we show that our analysis is more general.

Growth and percolation of thin films: A model incorporating deposition, diffusion and aggregation

Abstract We propose a model for describing diffusion-controlled aggregation of particles that are continually deposited on a surface. The model, which incorporates deposition, diffusion and aggregation, is motivated by recent thin film deposition experiments. We find, that the diffusion and aggregation of randomly deposited particles “builds” a wide variety of fractal structures, all characterized by a common length scale L1. This length L1 scales as the ratio of the diffusion constant over the particle flux to the power 1/4. We compare our results with several recent experiments on two-dimensional nanostructures formed by diffusion-controlled aggregation on surfaces.

A FRACTAL MODEL FOR THE FIRST STAGES OF THIN FILM GROWTH

In this paper, we briefly review a model that describes the diffusion-controlled aggregation exhibited by particles as they are deposited on a surface. This model allows us to understand many experiments of thin film deposition. In the Sec. 1, we describe the model, which incorporates deposition, particle and cluster diffusion, and aggregation. In Sec. 2, we study the dynamical evolution of the model. Finally, we analyze the effects of small cluster mobility and show that the introduction of cluster diffusion dramatically affects the dynamics of film growth. Some of these effects can be tested experimentally.

Connectivity of diffusing particles continually deposited on a surface: relation to LECBD experiments

We generalize the conventional model of two-dimensional site percolation by including both (1) continuous deposition of particles on a two-dimensional substrate, and (2) diffusion of these particles in two-dimensions. This new model is motivated by recent thin film deposition experiments using the low-energy cluster beam deposition (LECBD) technique. Depending on various parameters such as deposition flux, diffusion constant, and system size, we find a rich range of fractal morphologies including diffusion limited aggregation (DLA), cluster-cluster aggregation (CCA), and percolation.

EXPERIMENTS IN A PERFECT WORLD : COMPUTER SIMULATIONS OF GROWTH

We present two examples of computer simulations which can give unique information on the growth mechanisms of nanostructures and thin films. First, the morphologies and the island size distributions in the usual epitaxial growth models are studied. This information cannot be obtained from simple analytical approaches such as mean-field calculations or scaling analysis. Second, we analyze a new model which includes monomer evaporation and we show that computer simulations can help deciding between different mean-field analysis and lead to the correct growth exponents.