Transport-dominated phenomena provide a challenge for common modebased model reduction approaches. We present a model reduction method, which is suited for these kinds of systems. It extends the proper orthogonal decomposition (POD) by introducing time-dependent shifts of the snapshot matrix. The approach, called shifted proper orthogonal decomposition (sPOD), features a determination of the multiple transport velocities and a separation of these. One-and two-dimensional test examples reveal the good performance of the sPOD for transport-dominated phenomena and its superiority in comparison to the POD.

We analyze the competition between antiferromagnetism and superconductivity in the two-dimensional Hubbard model by combining a functional renormalization group flow with a mean-field theory for spontaneous symmetry breaking. Effective interactions are computed by integrating out states above a scale Λ MF in one-loop approximation, which captures in particular the generation of an attraction in the dwave Cooper channel from fluctuations in the particle-hole channel. These effective interactions are then used as an input for a mean-field treatment of the remaining low-energy states, with antiferromagnetism, singlet superconductivity and triplet πpairing as the possible order parameters. Antiferromagnetism and superconductivity suppress each other, leaving only a small region in parameter space where both orders can coexist with a sizable order parameter for each. Triplet π-pairing appears generically in the coexistence region, but its feedback on the other order parameters is very small.

The coupling of atmospheric pressure ionization (API) sources like electrospray ionization (ESI) to vacuum based applications like mass spectrometry (MS) or ion beam deposition (IBD) is done by differential pumping, starting with a capillary or pinhole inlet. Because of its low ion transfer efficiency the inlet represents a major bottleneck for these applications. Here we present a nano-ESI vacuum interface optimized to exploit the hydrodynamic drag of the background gas for collimation and the reduction of space charge repulsion. Up to a space charge limit of 40 nA we observe 100% current transmission through a capillary with an inlet and show by MS and IBD experiments that the transmitted ion beams are well defined and free of additional contamination compared to a conventional interface. Based on computational fluid dynamics modelling and ion transport simulations, we show how the specific shape enhances the collimation of the ion cloud. Mass selected ion currents in the nanoampere range available further downstream in high vacuum open many perspectives for the efficient use of electrospray ion beam deposition (ES-IBD) as a surface coating method.

Transfer capillaries are the preferred means to transport ions, generated by electrospray ionization, from ambient conditions to vacuum. During the transfer of ions through the narrow, long tubes into vacuum, substantial losses are typical. However, recently it was demonstrated that these losses can be avoided altogether. To understand the experimental observation and provide a general model for the ion transport, here, we investigate the ion transport through capillaries by numerical simulation of interacting ions. The simulation encompasses all relevant factors, such as space charge, diffusion, gas flow, and heating. Special attention is paid to the influence of the gas flow on the transmission and especially the change imposed by heating. The gas flow is modeled by a one-dimensional gas dynamics description. A large number of ions are treated as point particles in this gas flow. This allows to investigate the influence of the capillary heating on the gas flow and by this on the ion transport. The results are compared with experimental findings. Graphical Abstract ᅟ.

We present a fully conservative, skew-symmetric finite difference scheme on transformed grids. The skew-symmetry preserves the kinetic energy by first principles, simultaneously avoiding a central instability mechanism and numerical damping. In contrast to other skew-symmetric schemes no special averaging procedures are needed. Instead, the scheme builds purely on point-wise operations and derivatives. Any explicit and central derivative can be used, permitting high order and great freedom to optimize the scheme otherwise. This also allows the simple adaption of existing finite difference schemes to improve their stability and damping properties.

An adjoint-based approach for the sensitivity analysis of complex reaction mechanisms is presented. It builds purely on the evaluation of the governing equations. No adjoint equations have to be derived explicitly. Instead, the required adjoint operator is constructed numerically. The approach can be utilised for various kinetic models and in existing codes with minimal implementation effort. All dependencies on the state and on model parameters are fully evaluated without simplifications. Sensitivities are calculated more efficiently and more robustly compared with the often-used brute-force method. The approach is demonstrated for a homogeneous (zero-dimensional) reactor with different complex reaction mechanisms including several reaction types.

A detailed study of the transfer of ions in transfer capillaries of electrospray ion sources is presented. The laminar flow field for various capillary sizes and wall temperatures is calculated. It forms the base of ion transfer simulation of a large number of ions with space charge. This allows to study the thermodynamical conditions of the ions during transfer, which are found to vary strongly with the capillary dimensions. The dependence of mass flow and ion current on the size of the capillary is presented. Simple scaling relations are derived and tested. The method also allows to predict a transfer bias between different ion species depending on the difference in ion mobility and the composition of transferred ions.

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