Low-coverage heteroepitaxial growth with interfacial mixing

We investigate the influence of intermixing on heteroepitaxial growth dynamics, using a two-dimensional point island model, expected to be a good approximation in the early stages of epitaxy. In this model, which we explore both analytically and numerically, every deposited B atom diffuses on the surface with diffusion constant $D_{\rm B}$, and can exchange with any A atom of the substrate at constant rate. There is no exchange back, and emerging atoms diffuse on the surface with diffusion constant $D_{\rm A}$. When any two diffusing atoms meet, they nucleate a point island. The islands neither diffuse nor break, and grow by capturing other diffusing atoms. The model leads to an island density governed by the diffusion of one of the species at low temperature, and by the diffusion of the other at high temperature. We show that these limit behaviors, as well as intermediate ones, all belong to the same universality class, described by a scaling law. We also show that the island-size distribution is self-similarly described by a dynamic scaling law in the limits where only one diffusion constant is relevant to the dynamics, and that this law is affected when both $D_{\rm A}$ and $D_{\rm B}$ play a role.Comment: 16 pages, 6 figure

A non trivial extension of the two-dimensional Ising model: the d-dimensional "molecular" model

A recently proposed molecular model is discussed as a non-trivial extension of the Ising model. For d=2 the two models are shown to be equivalent, while for d>2 the molecular model describes a peculiar second order transition from an isotropic high temperature phase to a low-dimensional anisotropic low temperature state. The general mean field analysis is compared with the results achieved by a variational Migdal-Kadanoff real space renormalization group method and by standard Monte Carlo sampling for d=3. By finite size scaling the critical exponent has been found to be 0.44\pm 0.02 thus establishing that the molecular model does not belong to the universality class of the Ising model for d>2.Comment: 25 pages, 5 figure

Converting genetic network oscillations into somite spatial pattern

In most vertebrate species, the body axis is generated by the formation of repeated transient structures called somites. This spatial periodicity in somitogenesis has been related to the temporally sustained oscillations in certain mRNAs and their associated gene products in the cells forming the presomatic mesoderm. The mechanism underlying these oscillations have been identified as due to the delays involved in the synthesis of mRNA and translation into protein molecules [J. Lewis, Current Biol. {\bf 13}, 1398 (2003)]. In addition, in the zebrafish embryo intercellular Notch signalling couples these oscillators and a longitudinal positional information signal in the form of an Fgf8 gradient exists that could be used to transform these coupled temporal oscillations into the observed spatial periodicity of somites. Here we consider a simple model based on this known biology and study its consequences for somitogenesis. Comparison is made with the known properties of somite formation in the zebrafish embryo . We also study the effects of localized Fgf8 perturbations on somite patterning.Comment: 7 pages, 7 figure

The Naming Game in Social Networks: Community Formation and Consensus Engineering

We study the dynamics of the Naming Game [Baronchelli et al., (2006) J. Stat. Mech.: Theory Exp. P06014] in empirical social networks. This stylized agent-based model captures essential features of agreement dynamics in a network of autonomous agents, corresponding to the development of shared classification schemes in a network of artificial agents or opinion spreading and social dynamics in social networks. Our study focuses on the impact that communities in the underlying social graphs have on the outcome of the agreement process. We find that networks with strong community structure hinder the system from reaching global agreement; the evolution of the Naming Game in these networks maintains clusters of coexisting opinions indefinitely. Further, we investigate agent-based network strategies to facilitate convergence to global consensus.Comment: The original publication is available at http://www.springerlink.com/content/70370l311m1u0ng3

Opinion dynamics: models, extensions and external effects

Recently, social phenomena have received a lot of attention not only from social scientists, but also from physicists, mathematicians and computer scientists, in the emerging interdisciplinary field of complex system science. Opinion dynamics is one of the processes studied, since opinions are the drivers of human behaviour, and play a crucial role in many global challenges that our complex world and societies are facing: global financial crises, global pandemics, growth of cities, urbanisation and migration patterns, and last but not least important, climate change and environmental sustainability and protection. Opinion formation is a complex process affected by the interplay of different elements, including the individual predisposition, the influence of positive and negative peer interaction (social networks playing a crucial role in this respect), the information each individual is exposed to, and many others. Several models inspired from those in use in physics have been developed to encompass many of these elements, and to allow for the identification of the mechanisms involved in the opinion formation process and the understanding of their role, with the practical aim of simulating opinion formation and spreading under various conditions. These modelling schemes range from binary simple models such as the voter model, to multi-dimensional continuous approaches. Here, we provide a review of recent methods, focusing on models employing both peer interaction and external information, and emphasising the role that less studied mechanisms, such as disagreement, has in driving the opinion dynamics. [...]Comment: 42 pages, 6 figure

Enhanced light emission in Si-nanoclusters arrays

An array of silicon nanoclusters aimed at producing light emission upon injection of electrons and holes from external sources is studied by Monte Carlo simulations. The conditions for obtaining a significant charge accumulation in the emitting nanoclusters are investigated as a function of array geometry and applied electric fields. It is found that if a stationary state, reached for an applied field F 0, is suddenly perturbed by a field F 1≫F 0, a significant increase in electron-hole pairs population can be obtained with respect to the case of a single field of constant intensity F 1, leading to enhanced light emission when the conductivity of the array is above 6×10 -10  [ Ω cm] -1 . The excess population thus created gets fully recombined on the time scale of milliseconds, suggesting a device that can produce enhanced light emission in the range of kilohertz. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 200685.60.Jb Light-emitting devices, 05.10.Ln Monte Carlo methods, 73.63.-b Electronic transport in nanoscale materials and structures,

Effects of Coulomb interaction on charge transport in a silicon-based nanocluster array

The effects of Coulomb interaction on charge transport in a model of light emission from an array of silicon nanoclusters are studied by Monte Carlo simulations. The array is sandwiched between a p-type and an n-type doped silicon crystals and electrons and holes are driven into the array by an applied electric field. Radiative recombinations of electrons and holes take place near the center of the array producing the emission of red light, and the total emission power is approximately proportional to the current injected into the system. It is found that the carrier-carrier interaction plays a crucial role in charge transport. Specifically, the self-interaction of charges inside each nanocluster is found to be the dominant interaction term for the semiclassical Hamiltonian considered. In addition, it drastically limits the current in the device giving rise to a strong non-linear relation between current and density of free carriers in the doped silicon crystals. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2005