Uncertainty Quantification for Linear Hyperbolic Equations with Stochastic Process or Random Field Coefficients

In this paper hyperbolic partial differential equations with random coefficients are discussed. Such random partial differential equations appear for instance in traffic flow problems as well as in many physical processes in random media. Two types of models are presented: The first has a time-dependent coefficient modeled by the Ornstein--Uhlenbeck process. The second has a random field coefficient with a given covariance in space. For the former a formula for the exact solution in terms of moments is derived. In both cases stable numerical schemes are introduced to solve these random partial differential equations. Simulation results including convergence studies conclude the theoretical findings

3D Modelling of Flash Formation in Linear Friction Welded 30CrNiMo8 Steel Chain

Linear friction welding (LFW) is a solid-state welding process that has been thoroughly investigated for chain welding in recent years in order to replace the currently in use Flash Butt Welding (FBW) process. Modelling has proven to be an indispensable tool in LFW, thus providing necessary insight to the process, regardless of its final application. This article describes a 3D model developed in the commercial software DEFORM to study the LFW process of 30CrNiMo8 high strength steel in the Hero chain. Hence, a weakly coupled thermal and mechanical model were used, by means of the process experimental input such as displacement histories. The flash morphology and intervening mechanisms were analyzed. A thermal evaluation of different regions in the studied geometry was considered, and a correlation of the modeled and experimental width of the extrusion zone was established

Approximate Riemann Solvers and Robust High-Order Finite Volume Schemes for Multi-Dimensional Ideal MHD Equations

We design stable and high-order accurate finite volume schemes for the ideal MHD equations in multi-dimensions. We obtain excellent numerical stability due to some new elements in the algorithm. The schemes are based on three- and five-wave approximate Riemann solvers of the HLL-type, with the novelty that we allow a varying normal magnetic field. This is achieved by considering the semi-conservative Godunov-Powell form of the MHD equations. We show that it is important to discretize the Godunov-Powell source term in the right way, and that the HLL-type solvers naturally provide a stable upwind discretization. Second-order versions of the ENO- and WENO-type reconstructions are proposed, together with precise modifications necessary to preserve positive pressure and density. Extending the discrete source term to second order while maintaining stability requires non-standard techniques, which we present. The first- and second-order schemes are tested on a suite of numerical experiments demonstrating impressive numerical resolution as well as stability, even on very fine meshe

Clock-Feedthrough Compensation in MOS Sample-and-Hold Circuits

All MOS sample-and-hold circuits suffer to a greater or lesser extent from clock-feedthrough (CLFT), also called charge-injection. During the transition from sample to hold mode, charge is transferred from an MOS transistor switch onto the hold capacitor, thus the name charge-injection. This error can lead to considerable voltage change across the capacitor, and predicting the extent of the induced error potentials is important to circuit designers. Previous studies have shown a considerable dependency of CLFT on signal voltage, circuit impedances, clock amplitude and clock fall-time. The focus of this work was on the signal dependency of the CLFT error and on the CLFT induced signal distortion in open-loop sample-and-hold circuits. CLFT was found to have a strongly non-linear, signal dependent, component, which may cause considerable distortion of the sampled signal. The parameters influencing this distortion were established. It was discovered that distortion could be reduced by more than 20dB through careful adjustment of the clock fall-rate. Several circuit solutions that can help reduce the level of distortion arising from CLFT are presented. These circuits can also reduce the absolute level of CLFT. Simulations showed their effectiveness, which was also proven in silicon. The CLFT reduction methods used in these circuits are easily transferable to other switched-capacitor circuits and are suitable for applications where space is at a premium (as, for example, in analogue neural networks). A new saturation mode contribution to CLFT was found. It is shown to give rise to increased CLFT under high injection conditions

Optimal mixers restricted to subspaces and the stabilizer formalism

We present a novel formalism to both understand and construct mixers that preserve a given subspace. The method connects and utilizes the stabilizer formalism that is used in error correcting codes. This can be useful in the setting when the quantum approximate optimization algorithm (QAOA), a popular meta-heuristic for solving combinatorial optimization problems, is applied in the setting where the constraints of the problem lead to a feasible subspace that is large but easy to specify. The proposed method gives a systematic way to construct mixers that are resource efficient in the number of controlled not gates and can be understood as a generalization of the well-known X and XY mixers. The numerical examples provided show a dramatic reduction of CX gates when compared to previous results. Overall, we hope that this new perspective can lead to further insight into the development of quantum algorithms