Simple deterministic dynamical systems with fractal diffusion coefficients

We analyze a simple model of deterministic diffusion. The model consists of a one-dimensional periodic array of scatterers in which point particles move from cell to cell as defined by a piecewise linear map. The microscopic chaotic scattering process of the map can be changed by a control parameter. This induces a parameter dependence for the macroscopic diffusion coefficient. We calculate the diffusion coefficent and the largest eigenmodes of the system by using Markov partitions and by solving the eigenvalue problems of respective topological transition matrices. For different boundary conditions we find that the largest eigenmodes of the map match to the ones of the simple phenomenological diffusion equation. Our main result is that the difffusion coefficient exhibits a fractal structure by varying the system parameter. To understand the origin of this fractal structure, we give qualitative and quantitative arguments. These arguments relate the sequence of oscillations in the strength of the parameter-dependent diffusion coefficient to the microscopic coupling of the single scatterers which changes by varying the control parameter.Comment: 28 pages (revtex), 12 figures (postscript), submitted to Phys. Rev.

Are Solar Active Regions with Major Flares More Fractal, Multifractal, or Turbulent than Others?

Multiple recent investigations of solar magnetic field measurements have raised claims that the scale-free (fractal) or multiscale (multifractal) parameters inferred from the studied magnetograms may help assess the eruptive potential of solar active regions, or may even help predict major flaring activity stemming from these regions. We investigate these claims here, by testing three widely used scale-free and multiscale parameters, namely, the fractal dimension, the multifractal structure function and its inertial-range exponent, and the turbulent power spectrum and its power-law index, on a comprehensive data set of 370 timeseries of active-region magnetograms (17,733 magnetograms in total) observed by SOHO's Michelson Doppler Imager (MDI) over the entire Solar Cycle 23. We find that both flaring and non-flaring active regions exhibit significant fractality, multifractality, and non-Kolmogorov turbulence but none of the three tested parameters manages to distinguish active regions with major flares from flare-quiet ones. We also find that the multiscale parameters, but not the scale-free fractal dimension, depend sensitively on the spatial resolution and perhaps the observational characteristics of the studied magnetograms. Extending previous works, we attribute the flare-forecasting inability of fractal and multifractal parameters to i) a widespread multiscale complexity caused by a possible underlying self-organization in turbulent solar magnetic structures, flaring and non-flaring alike, and ii) a lack of correlation between the fractal properties of the photosphere and overlying layers, where solar eruptions occur. However useful for understanding solar magnetism, therefore, scale-free and multiscale measures may not be optimal tools for active-region characterization in terms of eruptive ability or, ultimately,for major solar-flare prediction.Comment: 25 pages, 7 figures, 2 tables, Solar Phys., in pres

The Irish Transport and General Workers' Union and the labour press in Ireland, 1909-1920

Officially launched by iconic labour leader James Larkin in January 1909, the Irish Transport and General Workers’ Union (ITGWU) quickly became the largest trade union in Ireland and a key institution in the country’s modern history. By 1920 membership stood at over 100,000, a peak figure until the union’s recovery in the late 1940s after several decades of decline. A notable feature of the ITGWU’s spectacular level of growth during the union’s formative years was its issuing of a series of weekly newspapers, each of which were forcefully suppressed during the First World War (1914-18) and Irish War of Independence (1919-21). What was the reason behind this succession of suppression? How did Larkin, James Connolly and Cathal O’Shannon perform as ITGWU editors throughout the period? Who were the key ITGWU press contributors? In addition to putting the union’s newspapers into context by discussing other contemporary Irish labour titles, as well as examining the first uncovered issues of Larkin’s 1917 American edition of his landmark Irish Worker newspaper, this thesis addresses these questions. Mostly utilising a close reading of the relevant ITGWU organs in conjunction with material taken from a range of declassified British intelligence files, this thesis examines the history of the union’s press up until 1920. The ITGWU’s papers are central to the story, not used as source material to chronicle the union’s turbulent early years. This thesis proves that British authorities were concerned about the potential for inciting violence in the ITGWU’s press from as early as August 1911, but it was not until the outbreak of the First World War three years later and resultant passing of the Defence of the Realm Act that the union began encountering what would prove to be six years of suppression due to its advocating in print of advanced Irish nationalism.2021-10-0