Early Warning Analysis for Social Diffusion Events

There is considerable interest in developing predictive capabilities for social diffusion processes, for instance to permit early identification of emerging contentious situations, rapid detection of disease outbreaks, or accurate forecasting of the ultimate reach of potentially viral ideas or behaviors. This paper proposes a new approach to this predictive analytics problem, in which analysis of meso-scale network dynamics is leveraged to generate useful predictions for complex social phenomena. We begin by deriving a stochastic hybrid dynamical systems (S-HDS) model for diffusion processes taking place over social networks with realistic topologies; this modeling approach is inspired by recent work in biology demonstrating that S-HDS offer a useful mathematical formalism with which to represent complex, multi-scale biological network dynamics. We then perform formal stochastic reachability analysis with this S-HDS model and conclude that the outcomes of social diffusion processes may depend crucially upon the way the early dynamics of the process interacts with the underlying network's community structure and core-periphery structure. This theoretical finding provides the foundations for developing a machine learning algorithm that enables accurate early warning analysis for social diffusion events. The utility of the warning algorithm, and the power of network-based predictive metrics, are demonstrated through an empirical investigation of the propagation of political memes over social media networks. Additionally, we illustrate the potential of the approach for security informatics applications through case studies involving early warning analysis of large-scale protests events and politically-motivated cyber attacks

Modelling the Interfacial Flow of Two Immiscible Liquids in Mixing Processes

This paper presents an interface tracking method for modelling the flow of immiscible metallic liquids in mixing processes. The methodology can provide an insight into mixing processes for studying the fundamental morphology development mechanisms for immiscible interfaces. The volume-of-fluid (VOF) method is adopted in the present study, following a review of various modelling approaches for immiscible fluid systems. The VOF method employed here utilises the piecewise linear for interface construction scheme as well as the continuum surface force algorithm for surface force modelling. A model coupling numerical and experimental data is established. The main flow features in the mixing process are investigated. It is observed that the mixing of immiscible metallic liquids is strongly influenced by the viscosity of the system, shear forces and turbulence. The numerical results show good qualitative agreement with experimental results, and are useful for optimisating the design of mixing casting processes

An accurate and efficient Lagrangian sub-grid model

A computationally efficient model is introduced to account for the sub-grid scale velocities of tracer particles dispersed in statistically homogeneous and isotropic turbulent flows. The model embeds the multi-scale nature of turbulent temporal and spatial correlations, that are essential to reproduce multi-particle dispersion. It is capable to describe the Lagrangian diffusion and dispersion of temporally and spatially correlated clouds of particles. Although the model neglects intermittent corrections, we show that pair and tetrad dispersion results nicely compare with Direct Numerical Simulations of statistically isotropic and homogeneous $3D$ turbulence. This is in agreement with recent observations that deviations from self-similar pair dispersion statistics are rare events

A new numerical strategy with space-time adaptivity and error control for multi-scale streamer discharge simulations

This paper presents a new resolution strategy for multi-scale streamer discharge simulations based on a second order time adaptive integration and space adaptive multiresolution. A classical fluid model is used to describe plasma discharges, considering drift-diffusion equations and the computation of electric field. The proposed numerical method provides a time-space accuracy control of the solution, and thus, an effective accurate resolution independent of the fastest physical time scale. An important improvement of the computational efficiency is achieved whenever the required time steps go beyond standard stability constraints associated with mesh size or source time scales for the resolution of the drift-diffusion equations, whereas the stability constraint related to the dielectric relaxation time scale is respected but with a second order precision. Numerical illustrations show that the strategy can be efficiently applied to simulate the propagation of highly nonlinear ionizing waves as streamer discharges, as well as highly multi-scale nanosecond repetitively pulsed discharges, describing consistently a broad spectrum of space and time scales as well as different physical scenarios for consecutive discharge/post-discharge phases, out of reach of standard non-adaptive methods.Comment: Support of Ecole Centrale Paris is gratefully acknowledged for several month stay of Z. Bonaventura at Laboratory EM2C as visiting Professor. Authors express special thanks to Christian Tenaud (LIMSI-CNRS) for providing the basis of the multiresolution kernel of MR CHORUS, code developed for compressible Navier-Stokes equations (D\'eclaration d'Invention DI 03760-01). Accepted for publication; Journal of Computational Physics (2011) 1-2

25 Years of Self-Organized Criticality: Solar and Astrophysics

Shortly after the seminal paper {\sl "Self-Organized Criticality: An explanation of 1/f noise"} by Bak, Tang, and Wiesenfeld (1987), the idea has been applied to solar physics, in {\sl "Avalanches and the Distribution of Solar Flares"} by Lu and Hamilton (1991). In the following years, an inspiring cross-fertilization from complexity theory to solar and astrophysics took place, where the SOC concept was initially applied to solar flares, stellar flares, and magnetospheric substorms, and later extended to the radiation belt, the heliosphere, lunar craters, the asteroid belt, the Saturn ring, pulsar glitches, soft X-ray repeaters, blazars, black-hole objects, cosmic rays, and boson clouds. The application of SOC concepts has been performed by numerical cellular automaton simulations, by analytical calculations of statistical (powerlaw-like) distributions based on physical scaling laws, and by observational tests of theoretically predicted size distributions and waiting time distributions. Attempts have been undertaken to import physical models into the numerical SOC toy models, such as the discretization of magneto-hydrodynamics (MHD) processes. The novel applications stimulated also vigorous debates about the discrimination between SOC models, SOC-like, and non-SOC processes, such as phase transitions, turbulence, random-walk diffusion, percolation, branching processes, network theory, chaos theory, fractality, multi-scale, and other complexity phenomena. We review SOC studies from the last 25 years and highlight new trends, open questions, and future challenges, as discussed during two recent ISSI workshops on this theme.Comment: 139 pages, 28 figures, Review based on ISSI workshops "Self-Organized Criticality and Turbulence" (2012, 2013, Bern, Switzerland