Julius Reiss

A hydrodynamically optimized nano-electrospray ionization source and vacuum interface

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.

Renormalized mean-field analysis of antiferromagnetism and d-wave superconductivity in the two-dimensional hubbard model

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 Lambda_{MF} in one-loop approximation, which captures in particular the generation of an attraction in the d-wave 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 pi-pairing 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 pi-pairing appears generically in the coexistence region, but its feedback on the other order parameters is very small.

The Shifted Proper Orthogonal Decomposition: A Mode Decomposition for Multiple Transport Phenomena

Transport-dominated phenomena provide a challenge for common mode-based model reduction approaches. We present a model reduction method, which is suited for these kind 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 {\it 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.

Fully conservative finite-difference schemes of arbitrary order for compressible flow

Semi-conservative finite-difference schemes for the equations of compressible flow have been known and used for the last couple of years, [1, 2, 3]. These schemes are based on rewritting the Euleror Navier-Stokes equations in a discrete form which preserves their skew-symmetry. Thus the construction of conservative finite-difference schemes in space is easily possible with a wide variety of explicit differentiation schemes. However, schemes which are conservative both in space and time have not been widely developed. This is related to the unusual form of the skew-symmetric temporal derivative which arises in the momentum equation. Here we will show how to construct fully conservative discretizations of arbitrary order in space and time without such contraints.

A Family of Energy Stable, Skew-Symmetric Finite Difference Schemes on Collocated Grids

A simple scheme for incompressible, constant density flows is presented, which avoids odd-even decoupling for the Laplacian on collocated grids. Energy stability is implied by guaranteeing strict energy conservation. Momentum is conserved. Arbitrary order in space and time can easily be obtained. These conservation properties also hold on transformed grids.

Model reduction of reactive processes

Interpolation based model reduction is applied to a reactive process. A zero-dimensional, perfectly stirred, constant pressure reactor with complex chemistry, modeled by the GRI3.0 scheme, is considered. The aim of this work is to analyze how interpolatory model reduction performs for combustion processes, where the solution is very sensitive to the choice of input parameters. In this study the initial temperature is chosen as varying parameter.

Magnetic and superconducting correlations in the two‐dimensional Hubbard model

The interplay and competition of magnetic and superconducting correlations in the weakly interacting two-dimensional Hubbard Model is investigated by means of the functional renormalization group. At zero temperature the flow of interactions in one-loop approximation evolves into a strong coupling regime at low energy scales, signalling the possible onset of spontaneous symmetry breaking. This is further analyzed by a mean-field treatment of the strong renormalized interactions which takes into account magnetic and superconducting order simultaneously. The effect of strong correlations on single-particle properties in the normal phase is studied by calculating the flow of the self-energy.

Conservative Finite Differences as an Alternative to Finite Volume for Compressible Flows

Finite Volume schemes are the natural choice when simulating flows with shocks, since conservation is essential in the physics and as such in the simulation of this phenomenon. But finite difference schemes can be conservative as well. Conservation requires in such schemes a high internal consistency of the spatial and the temporal discretization. We present a skew-symmetric finite difference scheme, which is fully conservative due to its consistency, still easy to implement and numerically efficient. A variety of different flow configurations containing shocks and turbulence are presented.

Conservative, Skew–Symmetric Discretization of the Compressible Navier–Stokes Equations

We present a fully conservative finite difference scheme for the compressible Navier–Stokes equations. Due to its skew symmetry it is possible to have no physical or artificial damping. Therefore it is especially suited for simulating configurations where perfect conservation is needed along with low damping. The full conservation properties for compressible FD on arbitrarily transformed grids for discrete time and high order derivatives are to our knowledge new.

Adjoint-based analysis of thermoacoustic coupling

We derive adjoint equations for reactive multi-species, compressible flows. Examples for homogeneous and non-homogeneous flows are calculated. To validate the adjoint approach for this highly non-linear problem a comparison between the adjoint solution and a finite difference expression for the objective function is done. We find, that the adjoint approach works well for reactive flows in spite of the strong non-linearity.