54 research outputs found

    Nonsingular α-rigid maps

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    On the continuing relevance of Mandelbrot’s non-ergodic fractional renewal models of 1963 to 1967

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    The problem of “1∕ƒ” noise has been with us for about a century. Because it is so often framed in Fourier spectral language, the most famous solutions have tended to be the stationary long range dependent (LRD) models such as Mandelbrot’s fractional Gaussian noise. In view of the increasing importance to physics of non-ergodic fractional renewal models, and their links to the CTRW, I present preliminary results of my research into the history of Mandelbrot’s very little known work in that area from 1963 to 1967. I speculate about how the lack of awareness of this work in the physics and statistics communities may have affected the development of complexity science, and I discuss the differences between the Hurst effect, “1∕ƒ” noise and LRD, concepts which are often treated as equivalent

    Process-design intensification : direct synthesis of adipic acid in flow

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    Micro process technology and flow chemistry have given a strong push to continuous chemical manufacture. This was based on the so-called transport intensification field which considerably improves mass and heat transfer given by the miniaturization of flow dimensions. The emerging second chemical intensification field uses highly intensified, unusual and typically harsh process conditions to boost micro-processing (Hessel et al., 2012). Beyond these, a third Process-Design Intensification Field heads for integrated and simplified flow process design in a more holistic picture. Chemical and process-design intensification constitute Novel Process Windows. As first-hour demonstration example for the latter, the direct oxidation of cyclohexene with hydrogen peroxide for adipic acid synthesis provides an innovative alternative to the industrial technologies currently being used. Profound simplification of the process scheme leads to fewer unit operations enabling reduction of investment cost, although the microreactor costs are higher than those of the batch reactor. Through simplification or elimination of energy intensive separation units energy consumption is reduced significantly. This leads to lower utility requirement and lowers the operating cost
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