We identify the influence of nitrogen-doping on charge- and magnetotransport of single layer graphene by comparing doped and undoped samples. Both sample types are grown by chemical vapor deposition (CVD) and transferred in an identical process onto Si/SiO2 wafers. We characterize the samples by Raman spectroscopy as well as by variable temperature magnetotransport measurements. Over the entire temperature range, the charge transport properties of all undoped samples are in line with literature values. The nitrogen doping instead leads to a 6-fold increase in the charge carrier concentration up to 4 × 10(13) cm(-2) at room temperature, indicating highly effective doping. Additionally it results in the opening of a charge transport gap as revealed by the temperature dependence of the resistance. The magnetotransport exhibits a conspicuous sign change from positive Lorentz magnetoresistance (MR) in undoped to large negative MR that we can attribute to the doping induced disorder. At low magnetic fields, we use quantum transport signals to quantify the transport properties. Analyses based on weak localization models allow us to determine an orders of magnitude decrease in the phase coherence and scattering times for doped samples, since the dopants act as effective scattering centers.

No abstract

This contribution focuses on the model order reduction of index 1 hyperbolic differential algebraic equations which are quadratic in state, at the example of district heating networks. We demonstrate that an appropriate splitting of the state space variables in the two categories massflow and temperature leads to a linear parameter varying system, allowing the use of tools from linear model order reduction. We measure a significant decrease of computational effort to simulate the underlying network dynamics while preserving stability.District heating networks are an important tool for carbon neutral urban heating due to their high flexibility towards the injection of energy [1]. Starting from a centralized power plant, heated water is guided through a pipeline network to consumers with varying consumption. Using a heat exchanger, the power demand is deposited at the consumers, and the cooled fluid is transported back to the power plant. The disperse energy input combined with the dynamical thermal transport to the connected houses makes them an interesting but challenging subject of optimization. Approaches towards finding the optimal use of the power resources such as model predictive control require simulating the network dynamics multiple times. The high number of transport pipelines and junctions in the order 10 3 makes them large scale dynamical systems, explaining the need for a reduced order model (ROM). Due to high Reynolds numbers we assume to be in the turbulent regime. The transport of thermal energy via water within a pipeline is modeled by one-dimensional Euler equations in the incompressible limitHere d is the pipeline diameter, T is the temperature of the hot fluid traveling with velocity v, and p is the pressure level at the junctions connecting different pipelines. The quantities isobaric heat capacity c p , density of the fluid ρ, and the friction factor λ are assumed to be constant. The latter arises in the Colebrook-White law accounting for frictional pressure loss in pipelines. The acceleration term originally occurring in (1) can be neglected compared to typical friction values. We assume the pipelines to be adequately isolated allowing to neglect the heat loss (k = 0) relative to the environment with temperature T e . Network model and parametric model order reductionFacing the network case, additional algebraic conditions at the junctions connecting incoming and outgoing pipelines occur. An upwind discretization of (2), together with these algebraic equations leads to a differential algebraic equation (DAE),whereHere n L , n P , n H , n T denote the number of loops, pipelines, consumers, and temperature cells. Eq. (3) describes the temperature transport with respect to the massflowm and the flow temperature u T , (4) measures temperatures located at the consumers as an output y. Following Kirchhoff's first law we claim the conservation of mass and thermal energy at junctions corresponding

No abstract