## Fachbereich Elektrotechnik, Maschinenbau, Technikjournalismus

Long-term variability of solar irradiance and its implications for photovoltaic power in West Africa
(2020)

This paper addresses long-term changes in solar irradiance for West Africa (3° N to 20° N and 20° W to 16° E) and its implications for photovoltaic power systems. Here we use satellite irradiance (Surface Solar Radiation Data Set-Heliosat, Edition 2.1, SARAH-2.1) to derive photovoltaic yields. Based on 35 years of data (1983–2017) the temporal and regional variability as well as long-term trends of global and direct horizontal irradiance are analyzed. Furthermore, at four locations a detailed time series analysis is undertaken. The dry and the wet season are considered separately.

In complex, expensive optimization domains we often narrowly focus on finding high performing solutions, instead of expanding our understanding of the domain itself. But what if we could quickly understand the complex behaviors that can emerge in said domains instead? We introduce surrogate-assisted phenotypic niching, a quality diversity algorithm which allows to discover a large, diverse set of behaviors by using computationally expensive phenotypic features. In this work we discover the types of air flow in a 2D fluid dynamics optimization problem. A fast GPU-based fluid dynamics solver is used in conjunction with surrogate models to accurately predict fluid characteristics from the shapes that produce the air flow. We show that these features can be modeled in a data-driven way while sampling to improve performance, rather than explicitly sampling to improve feature models. Our method can reduce the need to run an infeasibly large set of simulations while still being able to design a large diversity of air flows and the shapes that cause them. Discovering diversity of behaviors helps engineers to better understand expensive domains and their solutions.

This work introduces a semi-Lagrangian lattice Boltzmann (SLLBM) solver for compressible flows (with or without discontinuities). It makes use of a cell-wise representation of the simulation domain and utilizes interpolation polynomials up to fourth order to conduct the streaming step. The SLLBM solver allows for an independent time step size due to the absence of a time integrator and for the use of unusual velocity sets, like a D2Q25, which is constructed by the roots of the fifth-order Hermite polynomial. The properties of the proposed model are shown in diverse example simulations of a Sod shock tube, a two-dimensional Riemann problem and a shock-vortex interaction. It is shown that the cell-based interpolation and the use of Gauss-Lobatto-Chebyshev support points allow for spatially high-order solutions and minimize the mass loss caused by the interpolation. Transformed grids in the shock-vortex interaction show the general applicability to non-uniform grids.

In an effort to assist researchers in choosing basis sets for quantum mechanical modeling of molecules (i.e. balancing calculation cost versus desired accuracy), we present a systematic study on the accuracy of computed conformational relative energies and their geometries in comparison to MP2/CBS and MP2/AV5Z data, respectively. In order to do so, we introduce a new nomenclature to unambiguously indicate how a CBS extrapolation was computed. Nineteen minima and transition states of buta-1,3-diene, propan-2-ol and the water dimer were optimized using forty-five different basis sets. Specifically, this includes one Pople (i.e. 6-31G(d)), eight Dunning (i.e. VXZ and AVXZ, X=2-5), twenty-five Jensen (i.e. pc-n, pcseg-n, aug-pcseg-n, pcSseg-n and aug-pcSseg-n, n=0-4) and nine Karlsruhe (e.g. def2-SV(P), def2-QZVPPD) basis sets. The molecules were chosen to represent both common and electronically diverse molecular systems. In comparison to MP2/CBS relative energies computed using the largest Jensen basis sets (i.e. n=2,3,4), the use of smaller sizes (n=0,1,2 and n=1,2,3) provides results that are within 0.11--0.24 and 0.09-0.16 kcal/mol. To practically guide researchers in their basis set choice, an equation is introduced that ranks basis sets based on a user-defined balance between their accuracy and calculation cost. Furthermore, we explain why the aug-pcseg-2, def2-TZVPPD and def2-TZVP basis sets are very suitable choices to balance speed and accuracy.

During the dawn of chemistry when the temperature of the young Universe had fallen below ∼4000 K, the ions of the light elements produced in Big Bang nucleosynthesis recombined in reverse order of their ionization potential. With its higher ionization potentials, He++ (54.5 eV) and He+ (24.6 eV) combined first with free electrons to form the first neutral atom, prior to the recombination of hydrogen (13.6 eV). At that time, in this metal-free and low-density environment, neutral helium atoms formed the Universe's first molecular bond in the helium hydride ion HeH+, by radiative association with protons (He + H+ → HeH+ + hν). As recombination progressed, the destruction of HeH+ (HeH+ + H → He + H+2) created a first path to the formation of molecular hydrogen, marking the beginning of the Molecular Age. Despite its unquestioned importance for the evolution of the early Universe, the HeH+ molecule has so far escaped unequivocal detection in interstellar space. In the laboratory, the ion was discovered as long ago as 1925, but only in the late seventies was the possibility that HeH+ might exist in local astrophysical plasmas discussed. In particular, the conditions in planetary nebulae were shown to be suitable for the production of potentially detectable HeH+ column densities: the hard radiation field from the central hot white dwarf creates overlapping Strömgren spheres, where HeH+ is predicted to form, primarily by radiative association of He+ and H. With the GREAT spectrometer onboard SOFIA, the HeH+ rotational ground-state transition at λ149.1 μm is now accessible. We report here its detection towards the planetary nebula NGC7027.

Differential-Algebraic Equations and Beyond: From Smooth to Nonsmooth Constrained Dynamical Systems
(2018)

In this article we introduce the concept and the first implementation of a lightweight client-server-framework as middleware for distributed computing. On the client side an installation without administrative rights or privileged ports can turn any computer into a worker node. Only a Java runtime environment and the JAR files comprising the workflow client are needed. To connect all clients to the engine one open server port is sufficient. The engine submits data to the clients and orchestrates their work by workflow descriptions from a central database. Clients request new task descriptions periodically, thus the system is robust against network failures. In the basic set-up, data up- and downloads are handled via HTTP communication with the server. The performance of the modular system could additionally be improved using dedicated file servers or distributed network file systems. We demonstrate the design features of the proposed engine in real-world applications from mechanical engineering. We have used this system on a compute cluster in design-of-experiment studies, parameter optimisations and robustness validations of finite element structures.

Since being introduced in the sixties and seventies, semi-implicit RosenbrockWanner (ROW) methods have become an important tool for the timeintegration of ODE and DAE problems. Over the years, these methods have been further developed in order to save computational effort by regarding approximations with respect to the given Jacobian [5], reduce effects of order reduction by introducing additional conditions [2, 4] or use advantages of partial explicit integration by considering underlying Runge-Kutta formulations [1]. As a consequence, there is a large number of different ROW-type schemes with characteristic properties for solving various problem formulations given in literature today.

This paper presents a new method of analysing the error of a sampled-data velocity stabilising system with a wide range of pulse width modulation. The analysis is based on multi-channel model obtained as a result of approximation of pulse-modulated signal at the output of a PWM converter. Approximation of piecewise-linear modulation characteristics of each channel has been obtained as a series expansion of Hermite polynomials where the expansion comprises two polynomials of the first and third orders. The transfer function of every channel and a closed-loop system has been obtained using multidimensional Z-transform. The analytical expression of an error under impact of a step input has been derived using a transfer function of the closed-loop system. A dc electric drive has been used as an example of high accuracy sample-data stabilising system to verify and demonstrate the proposed method.

We derive rates of convergence for limit theorems that reveal the intricate structure of the phase transitions in a mean-field version of the Blume-Emery-Griffith model. The theorems consist of scaling limits for the total spin. The model depends on the inverse temperature β and the interaction strength K. The rates of convergence results are obtained as (β,K) converges along appropriate sequences (βn,Kn) to points belonging to various subsets of the phase diagram which include a curve of second-order points and a tricritical point. We apply Stein's method for normal and non-normal approximation avoiding the use of transforms and supplying bounds, such as those of Berry-Esseen quality, on approximation error. We observe an additional phase transition phenomenon in the sense that depending on how fast Kn and βn are converging to points in various subsets of the phase diagram, different rates of convergences to one and the same limiting distribution occur.