Fluid Dynamics of Watercolor Painting : Experiments and Modelling

In his classic study in 1908, A.M. Worthington gave a thorough account of splashes and their formation through visualization experiments. In more recent times, there has been renewed interest in this subject, and much of the underlying physics behind Worthington\u27s experiments has now been clarified. One specific set of such recent studies, which motivates this thesis, concerns the fluid dynamics behind Jackson Pollock\u27s drip paintings. The physical processes and the mathematical structures hidden in his works have received serious attention and have made the scientific pursuit of art a compelling area of exploration. Our current work explores the interaction of watercolors with watercolor paper. Specifically, we conduct experiments to analyze the settling patterns of droplets of watercolor paint on wet and frozen paper. Variations in paint viscosity, paper roughness, paper temperature, and the height of a released droplet are examined from time of impact, through its transient stages, until its final, dry state. Observable phenomena such as paint splashing, spreading, fingering, branching, rheological deposition, and fractal patterns are studied in detail and classified in terms of the control parameters. Using the one-dimensional (1-D) Saint-Venant differential equations, which are a simplification of the three-dimensional (3-D) Navier-Stokes equations from fluid dynamics, we created a computer-simulated, mathematical model of a droplet splash of watercolor paint onto a flat surface. The mathematical model is analyzed using a MATLAB code which considered changes in droplet height, radius, and velocity of dispersal over time. We also implemented a stochastic version of the Saint-Venant equations which captured the random fingering patterns of a droplet splash. Initial conditions for height, radius, and velocity of a radially spreading droplet were given at the onset of the simulation. Dynamic viscosity and fluid density were parameters incorporated into this system of differential equations, which could be easily adjusted in the MATLAB code for the paint type to be simulated. The stochastic nature of our model was designed to recreate the complex behavior of water splashes, the non-homogeneity of the watercolor paper, and the resulting patterns. We then computed the fractal dimension of each computer-generated droplet image to compare theoretical and experimental values. Analysis of the set of data consisting of over 10,000 trials was conducted to determine any significant statistical correlations among the spreading pattern, the number of fingers, viscosity, density and fractal dimension. Finally, we extended the system of differential equations based on the Saint-Venant equations to include the effects of temperature upon the paint-spreading pattern. In a similar manner, we compared the theoretical values of fractal dimensions generated by our MATLAB model to the experimental results for paint droplets on a frozen substrate

On the Dynamics of Human Proximity for Data Diffusion in Ad-Hoc Networks

We report on a data-driven investigation aimed at understanding the dynamics of message spreading in a real-world dynamical network of human proximity. We use data collected by means of a proximity-sensing network of wearable sensors that we deployed at three different social gatherings, simultaneously involving several hundred individuals. We simulate a message spreading process over the recorded proximity network, focusing on both the topological and the temporal properties. We show that by using an appropriate technique to deal with the temporal heterogeneity of proximity events, a universal statistical pattern emerges for the delivery times of messages, robust across all the data sets. Our results are useful to set constraints for generic processes of data dissemination, as well as to validate established models of human mobility and proximity that are frequently used to simulate realistic behaviors.Comment: A. Panisson et al., On the dynamics of human proximity for data diffusion in ad-hoc networks, Ad Hoc Netw. (2011

Activity clocks: spreading dynamics on temporal networks of human contact

Dynamical processes on time-varying complex networks are key to understanding and modeling a broad variety of processes in socio-technical systems. Here we focus on empirical temporal networks of human proximity and we aim at understanding the factors that, in simulation, shape the arrival time distribution of simple spreading processes. Abandoning the notion of wall-clock time in favour of node-specific clocks based on activity exposes robust statistical patterns in the arrival times across different social contexts. Using randomization strategies and generative models constrained by data, we show that these patterns can be understood in terms of heterogeneous inter-event time distributions coupled with heterogeneous numbers of events per edge. We also show, both empirically and by using a synthetic dataset, that significant deviations from the above behavior can be caused by the presence of edge classes with strong activity correlations

Predicting the extinction of Ebola spreading in Liberia due to mitigation strategies

The Ebola virus is spreading throughout West Africa and is causing thousands of deaths. In order to quantify the effectiveness of different strategies for controlling the spread, we develop a mathematical model in which the propagation of the Ebola virus through Liberia is caused by travel between counties. For the initial months in which the Ebola virus spreads, we find that the arrival times of the disease into the counties predicted by our model are compatible with World Health Organization data, but we also find that reducing mobility is insufficient to contain the epidemic because it delays the arrival of Ebola virus in each county by only a few weeks. We study the effect of a strategy in which safe burials are increased and effective hospitalisation instituted under two scenarios: (i) one implemented in mid-July 2014 and (ii) one in mid-August—which was the actual time that strong interventions began in Liberia. We find that if scenario (i) had been pursued the lifetime of the epidemic would have been three months shorter and the total number of infected individuals 80% less than in scenario (ii). Our projection under scenario (ii) is that the spreading will stop by mid-spring 2015.H.E.S. thanks the NSF (grants CMMI 1125290 and CHE-1213217) and the Keck Foundation for financial support. L.D.V. and L.A.B. wish to thank to UNMdP and FONCyT (Pict 0429/2013) for financial support. (CMMI 1125290 - NSF; CHE-1213217 - NSF; Keck Foundation; UNMdP; Pict 0429/2013 - FONCyT)Published versio

A Cellular Automata Model for Citrus Variagated Chlorosis

A cellular automata model is proposed to analyze the progress of Citrus Variegated Chlorosis epidemics in S\~ao Paulo oranges plantation. In this model epidemiological and environmental features, such as motility of sharpshooter vectors which perform L\'evy flights, hydric and nutritional level of plant stress and seasonal climatic effects, are included. The observed epidemics data were quantitatively reproduced by the proposed model varying the parameters controlling vectors motility, plant stress and initial population of diseased plants.Comment: 10 pages, 10 figures, Scheduled tentatively for the issue of: 01Nov0

Activity driven modeling of time varying networks

Network modeling plays a critical role in identifying statistical regularities and structural principles common to many systems. The large majority of recent modeling approaches are connectivity driven. The structural patterns of the network are at the basis of the mechanisms ruling the network formation. Connectivity driven models necessarily provide a time-aggregated representation that may fail to describe the instantaneous and fluctuating dynamics of many networks. We address this challenge by defining the activity potential, a time invariant function characterizing the agents' interactions and constructing an activity driven model capable of encoding the instantaneous time description of the network dynamics. The model provides an explanation of structural features such as the presence of hubs, which simply originate from the heterogeneous activity of agents. Within this framework, highly dynamical networks can be described analytically, allowing a quantitative discussion of the biases induced by the time-aggregated representations in the analysis of dynamical processes.Comment: 10 pages, 4 figure

Sampling of stochastic operators

We develop sampling methodology aimed at determining stochastic operators that satisfy a support size restriction on the autocorrelation of the operators stochastic spreading function. The data that we use to reconstruct the operator (or, in some cases only the autocorrelation of the spreading function) is based on the response of the unknown operator to a known, deterministic test signal

Linear stability analysis of an insoluble surfactant monolayer spreading on a thin liquid film

Recent experiments by several groups have uncovered a novel fingering instability in the spreading of surface active material on a thin liquid film. The mechanism responsible for this instability is yet to be determined. In an effort to understand this phenomenon and isolate a possible mechanism, we have investigated the linear stability of a coupled set of equations describing the Marangoni spreading of a surfactant monolayer on a thin liquid support. The unperturbed flows, which exhibit simple linear behavior in the film thickness and surfactant concentration, are self-similar solutions of the first kind for spreading in a rectilinear geometry. The solution of the disturbance equations determines that the rectilinear base flows are linearly stable. An energy analysis reveals why these base flows can successfully heal perturbations of all wavenumbers. The details of this analysis suggest, however, a mechanism by which the spreading can be destabilized. We propose how the inclusion of additional forces acting on the surfactant coated spreading film might give rise to regions of adverse mobility gradients known to produce fingering instabilities in other fluid flows