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In recent years, the supply and demand of electricity has significantly increased. As a result, the interconnecting grid infrastructure has required (and will continue to require) further expansion, while allowing for rapid resolution of unforeseen failures. Energy grid operators strive for networks that satisfy different levels of security requirements. In the case of N-1 security for medium voltage networks, the goal is to ensure the continued provision of electricity in the event of a single-link failure. However, the process of determining if networks are N-1 secure is known to scale polynomially in the network size. This poses restrictions if we increase our demand of the network. In that case, more computationally hard cases will occur in practice and the computation time also increases significantly. In this work, we explore the potential of quantum computers to provide a more scalable solution. In particular, we consider gate-based quantum computing, quantum annealing, and photonic quantum computing.

The convergence between effective medium theory and pore-network modelling is examined. Electrical conductance on two and three-dimensional cubic resistor networks is used as an example of transport through composite materials or porous media. Effective conductance values are calculated for the networks using effective medium theory and pore-network models. The convergence between these values is analyzed as a function of network size. Effective medium theory results are calculated analytically and numerically. Pore-network results are calculated numerically using Monte Carlo sampling. The reduced standard deviations of the Monte Carlo sampled pore-network results are examined as a function of network size. Finally, a "quasi-two-dimensional" network is investigated to demonstrate the limitations of effective medium theory when applied to thin porous media. Power law fits are made to these data to develop simple models governing convergence. These can be used as a guide for future research that uses both effective medium theory and pore-network models., Comment: 28 pages, 10 figures

The starting point in quantitative susceptibility mapping (QSM) is a theoretical model that is used to map susceptibility distributions from magnetic field measurements. It requires regularisation techniques to avoid artefacts in the resulting image. The underlying problem is that the model was developed by starting with the so-called Lorentz sphere on a microscopic scale. After averaging over a macroscopic sample, it is assumed that the magnetic flux density vanishes in the center of the sample. For the macroscopic problem of a homogeneous sphere in a uniform field, we show that at the surface the normal component of the flux density is not continuous, which contradicts Maxwell's macroscopic theory. In this paper, we propose a model consistent with macroscopic magnetic field theory, in which we image magnetisation rather than susceptibility. This model is well-posed. Some simple but representative numerical examples show that it allows for high-resolution images.

The sensitivity of light and matter-wave interferometers to rotations is based on the Sagnac effect and increases with the area enclosed by the interferometer. In the case of light, the latter can be enlarged by forming multiple fibre loops, whereas the equivalent for matter-wave interferometers remains an experimental challenge. We present a concept for a multi-loop atom interferometer with a scalable area formed by light pulses. Our method will offer sensitivities as high as $2\cdot10^{-11}$ rad/s at 1 s in combination with the respective long-term stability as required for Earth rotation monitoring., Comment: 8 pages, 2 figures

The Solar Probe Cup (SPC) is a Faraday Cup instrument onboard NASA's Parker Solar Probe (PSP) spacecraft designed to make rapid measurements of thermal coronal and solar wind plasma. The spacecraft is in a heliocentric orbit that takes it closer to the Sun than any previous spacecraft, allowing measurements to be made where the coronal and solar wind plasma is being heated and accelerated. The SPC instrument was designed to be pointed directly at the Sun at all times, allowing the solar wind (which is flowing primarily radially away from the Sun) to be measured throughout the orbit. The instrument is capable of measuring solar wind ions with an energy/charge between 100 V and 6000 V (protons with speeds from $139-1072~km~s^{-1})$. It also measures electrons with an energy between 100 V and 1500 V. SPC has been designed to have a wide dynamic range that is capable of measuring protons and alpha particles at the closest perihelion (9.86 solar radii from the center of the Sun) and out to 0.25 AU. Initial observations from the first orbit of PSP indicate that the instrument is functioning well.

In the seventies, scientists observed discrepancies of the bending of light around the Sun based on Einstein's prediction of the curvature of star light due to the mass of the Sun. We claim that the interior electromagnetic properties of the Sun influence the curvature of the light path outside the Sun as well. In this paper, we investigate the additional deflection of light in the vacuum region surrounding the Sun by its electromagnetic parameters. Starting with Maxwell's equations, we show how the deflection of light passing the Sun depends on the electric permittivity and the magnetic permeability of the interior of the Sun. The electromagnetic field equations in Cartesian coordinates are transformed to the ones in an appropriately chosen Riemannian space. This coordinate transform is dictated by the introduction of a refractional potential. The geodetic lines with the shortest propagation time are constructed from this potential. As far as the deflection of light propagating along these geodetic lines is concerned, we show that the existence of a refractional potential influences the light path outside any object with a typical refractive index. Our results add new aspects to the bending of star light explained by general relativity. Some astrophysical observations, which cannot be explained by gravity in a satisfactory manner, are justified by the electromagnetic model. In particular, the frequency dependency of the light deflection is discussed. We show that the additional bending due to the refractive index is proportional to the third power of the inverse distance. The general relativity predicts that the bending due to the mass is proportional to the inverse distance., Comment: Following up comments from colleagues, we have revised Section II and III

In a changing climate, a key role may be played by the response of convective-type cloud and precipitation to temperature changes. Yet, it is unclear if precipitation intensities will increase mainly due to modified thermodynamic forcing or due to stronger convective dynamics. In gradual self-organization, convective events produce highest intensities late in the day. Tracking rain cells throughout their life cycles, we find that interacting events respond strongly to changes in boundary conditions. Conversely, events without interaction remain unaffected. Increased surface temperature indeed leads to more interaction and higher precipitation extremes. However, a similar intensification occurs when leaving temperature unchanged but simply granting more time for self-organization.Our study implies that the convective field as a whole acquires a memory of past precipitation and inter-cloud dynamics, driving extremes. Our results implicate that the dynamical interaction between convective clouds must be incorporated in global climate models to describe convective extremes and the diurnal cycle more realistically., Comment: 25 pages, 10 figures; removed typo in abstract

In this paper we study the equilibrium shape of an interface that represents the lateral boundary of a pore channel embedded in an elastomer. The model consists of a system of PDEs, comprising a linear elasticity equation for displacements within the elastomer and a nonlinear Poisson equation for the electric potential within the channel (filled with protons and water). To determine the equilibrium interface, a variational approach is employed. We analyze: i) the existence and uniqueness of the electrical potential, ii) the shape derivatives of state variables and iii) the shape differentiability of the corresponding energy and the corresponding Euler-Lagrange equation. The latter leads to a modified Young-Laplace equation on the interface. This modified equation is compared with the classical Young-Laplace equation by computing several equilibrium shapes, using a fixed point algorithm., Comment: 24 pages, 8 figures

We formally derive an effective catalyst layer model comprising the reduction of oxygen for periodically distributed pore geometries. By assumption, the pores are completely filled with water and the surrounding walls consist of catalyst particles which are attached to an electron conducting microstructure. The macroscopic transport equations are established by a multi-scale approach, based on microscopic phenomena at the pore level, and serve as a first step toward future optimization of catalyst layer designs.

A molten carbonate fuel cell (MCFC) is an electro-chemical energy conversion technology that runs on natural gas and employs a molten salt electrolyte. In order to keep the electrolyte in this state, the cell must be kept at a temperature above 500 C, eliminating the need for precious metals as the catalyst. There has been only a limited amount of research on modelling the transport processes inside this device, mainly due to its restricted applicability for mobile applications. In this work, three one-dimensional models of a MCFC cathode are presented based on different types of diffusion and convection. Comparisons between models are performed so as to assess their validity. Regarding ion transport, it is shown that there exists a limiting case for ion migration across the cathode that depends on the conductivity for the liquid potential. Finally, an optimization of the diffusivity across the cathode is carried out in an attempt to increase the cell performance and its longevity., Comment: Research report

A bottleneck simulation of road traffic on a loop, using the deterministic cellular automata (CA) Nagel-Schreckenberg model with zero dawdling probability, reveals three types of stationary wave solutions. They consist of i) two shock waves, one at each bottleneck boundary, ii) one shock wave at the boundary and one on the "open" road, and iii) the trivial solution, i.e. homogeneous, uniform flow. These solutions are selected dynamically from a range of kinematicly permissible stationary shocks. This is similar in fashion to the wave selection in a bottleneck simulation of the optimal-velocity (OV) model, which is explained by a travelling wave phase-plane analysis of the corresponding continuum model. It is yet another strong indication that CA and OV models share certain underlying dynamics, although the former are discrete in space and time while the latter are continuous., Comment: research report