We study the magnetic properties in the vicinity of a single carbon defect in a monolayer of graphene. We include the unbound σ orbital and the vacancy induced bound π state in an effective two-orbital single impurity model. The local magnetic moments are stabilized by the Coulomb interaction as well as a significant ferromagnetic Hund's rule coupling between the orbitals predicted by a density functional theory calculation. A hybridization between the orbitals and the Dirac fermions is generated by the curvature of the graphene sheet in the vicinity of the vacancy. We present results for the local spectral function calculated using Wilson's numerical renormalization group approach for a realistic graphene band structure and find three different regimes depending on the filling, the controlling chemical potential, and the hybridization strength. These different regions are characterized by different magnetic properties. The calculated spectral functions qualitatively agree with recent scanning tunneling spectra on graphene vacancies.

To protect cables from damage by too high temperatures, classically fuses are used. Those often lead to over-dimensioned cables due to their melting behaviour or simple tripping strategies. Therefore, smart fuses can be advantageous. Here, a more powerful control circuit can estimate the cable temperature and operate as switch, when the temperature exceeds a given limit. The control circuit needs to run a thermal simulation of the cable to be protected. Critical temperatures can be detected this way. Thermal cable models can be very complex and computationally intensive, especially when numeric methods are used. In this contribution, a new analytic approach for the transient axial temperature distribution along a single cable is presented. Using this solution, a significant reduction of the time needed for calculation is achieved.

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