A proactive measure to increase the robustness of heterogeneously loaded networks against cascades of overload failures is proposed. It is based on load-dependent weights. Compared to simple hop weights, respective shortest flow paths turn a previously heterogeneous load distribution into a more homogeneous one for the nodes and links of the network. The use of these flow paths increases the networks robustness and at the same time reduces the investment costs into the networks capacity layout. These findings are of relevance for critical infrastructures like communication and transportation networks.

Fluctuating fluxes on a complex network lead to load fluctuations at the vertices, which may cause them to become overloaded and to induce a cascading failure. A characterization of the one-point load fluctuations is presented, revealing their dependence on the nature of the flux fluctuations and on the underlying network structure. Based on these findings, an alternate robustness layout of the network is proposed. Taking load correlations between the vertices into account, an analytical prediction of the probability for the network to remain fully efficient is confirmed by simulations. Compared to previously proposed mean-flux layouts, the alternate layout comes with significantly less investment costs in the high-confidence limit.

Measures to reduce carbon dioxide emissions are often considered separately, in terms of electricity, heating, transport, and industry. This can lead to the measures being prioritised in the wrong sectors, and neglects interactions between the sectors. In addition, studies often focus on specific greenhouse gas reduction targets, despite the uncertainty regarding what targets are desirable and when. In this paper, these issues are examined for the period after 2030 in an existing openly-available, hourly-resolved, per-country, and highly-renewable model of the European energy system, PyPSA-Eur-Sec-30, that includes electricity, land transport, and space and water heating. A parameter sweep of different reduction targets for direct carbon dioxide emissions is performed, ranging from no target down to zero direct emissions. The composition of system investments, the interactions between the energy sectors, shadow prices, and the market values of the system components are analysed as the carbon dioxide limit changes. Electricity and land transport are defossilised first, while the reduction of emissions in space and water heating is delayed by the expense of new components and the difficulty of supplying heat during cold spells with low wind and solar power generation. For deep carbon dioxide reduction, power-to-gas changes the system dynamics by reducing curtailment and increasing the market values of wind and solar power. Using this model setup, cost projections for 2030, and optimal cross-border transmission, the costs of a zero-direct-emission system in these sectors are marginally cheaper than today’s system, even before the health and environmental benefits are taken into account.

Motivated by possible observations of the black hole candidate in the centre of our Galaxy and the galaxy M87, ray-tracing methods are applied to both standard General Relativity (GR) and a recently proposed extension, the pseudo-complex GR (pc-GR). The correction terms due to the investigated pc-GR model lead to slower orbital motions close to massive objects. Also the concept of an innermost stable circular orbit is modified for the pc-GR model, allowing particles to get closer to the central object for most values of the spin parameter a than in GR. Thus, the accretion disc, surrounding a massive object, is brighter in pc-GR than in GR. Iron Kα emission-line profiles are also calculated as those are good observables for regions of strong gravity. Differences between the two theories are pointed out.