11 Interfakultäre Einrichtungen

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    Stochastic model for energy propagation in disordered granular chains
    (2021) Taghizadeh, Kianoosh; Shrivastava, Rohit; Luding, Stefan
    Energy transfer is one of the essentials of mechanical wave propagation (along with momentum transport). Here, it is studied in disordered one-dimensional model systems mimicking force-chains in real systems. The pre-stressed random masses (other types of disorder lead to qualitatively similar behavior) interact through (linearized) Hertzian repulsive forces, which allows solving the deterministic problem analytically. The main goal, a simpler, faster stochastic model for energy propagation, is presented in the second part, after the basic equations are re-visited and the phenomenology of pulse propagation in disordered granular chains is reviewed. First, the propagation of energy in space is studied. With increasing disorder (quantified by the standard deviation of the random mass distribution), the attenuation of pulsed signals increases, transiting from ballistic propagation (in ordered systems) towards diffusive-like characteristics, due to energy localization at the source. Second, the evolution of energy in time by transfer across wavenumbers is examined, using the standing wave initial conditions of all wavenumbers. Again, the decay of energy (both the rate and amount) increases with disorder, as well as with the wavenumber. The dispersive ballistic transport in ordered systems transits to low-pass filtering, due to disorder, where localization of energy occurs at the lowest masses in the chain. Instead of dealing with the too many degrees of freedom or only with the lowest of all the many eigenmodes of the system, we propose a stochastic master equation approach with reduced complexity, where all frequencies/energies are grouped into bands. The mean field stochastic model, the matrix of energy-transfer probabilities between bands, is calibrated from the deterministic analytical solutions by ensemble averaging various band-to-band transfer situations for short times, as well as considering the basis energy levels (decaying with the wavenumber increasing) that are not transferred. Finally, the propagation of energy in the wavenumber space at transient times validates the stochastic model, suggesting applications in wave analysis for non-destructive testing, underground resource exploration, etc.
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    Teaching power-sector models social and political awareness
    (2022) Garcia-Teruel, Anna; Scholz, Yvonne; Weimer-Jehle, Wolfgang; Prehofer, Sigrid; Cao, Karl-Kiên; Borggrefe, Frieder
    Energy-system scenarios are widely used to relate the developments of the energy supply and the resulting carbon-emission pathways to political measures. To enable scenario analyses that adequately capture the variability of renewable-energy resources, a specialised type of power-sector model (PSM) has been developed since the beginning of this century, which uses input data with hourly resolution at the national or subnational levels. These models focus on techno-economic-system optimisation, which needs to be complemented with expert socioeconomic knowledge in order to prevent solutions that may be socially inacceptable or that oppose political goals. A way to integrate such knowledge into energy-system analysis is to use information from framework scenarios with a suitable geographical and technological focus. We propose a novel methodology to link framework scenarios to a PSM by applying complexity-management methods that enable a flexible choice of base scenarios that are tailored to suit different research questions. We explain the methodology, and we illustrate it in a case study that analyses the influence of the socioeconomic development on the European power-system transition until 2050 by linking the power-sector model, REMix (renewable-energy mix), to regional framework scenarios. The suggested approach proves suitable for this purpose, and it enables a clearer link between the impact of political measures and the power-system development.