Notes on lattice points of zonotopes and lattice-face polytopes

Minkowski's second theorem on successive minima gives an upper bound on the volume of a convex body in terms of its successive minima. We study the problem to generalize Minkowski's bound by replacing the volume by the lattice point enumerator of a convex body. In this context we are interested in bounds on the coefficients of Ehrhart polynomials of lattice polytopes via the successive minima. Our results for lattice zonotopes and lattice-face polytopes imply, in particular, that for 0-symmetric lattice-face polytopes and lattice parallelepipeds the volume can be replaced by the lattice point enumerator.Comment: 16 pages, incorporated referee remarks, corrected proof of Theorem 1.2, added new co-autho

A model of an electrochemical flow cell with porous layer

In this paper we discuss three different mathematical models for fluid-porous interfaces in a simple channel geometry that appears e.g. in thin-layer channel flow cells. Here the difficulties arise from the possibly different orders of the corresponding differential operators in the different domains. A finite volume discretization of this model allows to calculate the limiting current of the H_2 oxidation in a porous electrode with platinum catalyst particles

Full-Stack, Real-System Quantum Computer Studies: Architectural Comparisons and Design Insights

In recent years, Quantum Computing (QC) has progressed to the point where small working prototypes are available for use. Termed Noisy Intermediate-Scale Quantum (NISQ) computers, these prototypes are too small for large benchmarks or even for Quantum Error Correction, but they do have sufficient resources to run small benchmarks, particularly if compiled with optimizations to make use of scarce qubits and limited operation counts and coherence times. QC has not yet, however, settled on a particular preferred device implementation technology, and indeed different NISQ prototypes implement qubits with very different physical approaches and therefore widely-varying device and machine characteristics. Our work performs a full-stack, benchmark-driven hardware-software analysis of QC systems. We evaluate QC architectural possibilities, software-visible gates, and software optimizations to tackle fundamental design questions about gate set choices, communication topology, the factors affecting benchmark performance and compiler optimizations. In order to answer key cross-technology and cross-platform design questions, our work has built the first top-to-bottom toolflow to target different qubit device technologies, including superconducting and trapped ion qubits which are the current QC front-runners. We use our toolflow, TriQ, to conduct {\em real-system} measurements on 7 running QC prototypes from 3 different groups, IBM, Rigetti, and University of Maryland. From these real-system experiences at QC's hardware-software interface, we make observations about native and software-visible gates for different QC technologies, communication topologies, and the value of noise-aware compilation even on lower-noise platforms. This is the largest cross-platform real-system QC study performed thus far; its results have the potential to inform both QC device and compiler design going forward.Comment: Preprint of a publication in ISCA 201

Biogas Crops – Part II: Balance of Greenhouse Gas Emissions and Energy from Using Field Crops for Anaerobic Digestion

Several field crops, cultivated under north-eastern German conditions, are analysed for their ecological benefit if used for anaerobic digestion. The analyses is based on the assessment of cumulated energy demand necessary for the cultivation at different fertilisation levels, transport and storage of these crops as well as on the assessment of greenhouse gas emissions deriving from these processes. Although the values obtained are quite similar to each other this picture completely changes if considering the methane formation potential and hence the electricity available from these renewable energy sources. Cereals like rye, triticale, barley and maize as well as alfalfa show relatively low values of GHG emissions, and cumulated energy demand whereas hemp and Jerusalem artichoke have a considerable worse balance. In the case of high fertiliser input during cultivation the value of GHG emissions for Jerusalem artichoke even approaches the value for electricity produced within the German power-mix. Open-top tanks for digested energy crops may be a serious source of additional methane emissions

Mathematical modeling of channel-porous layer interfaces in PEM fuel cells

In proton exchange membrane (PEM) fuel cells, the transport of the fuel to the active zones, and the removal of the reaction products are realized using a combination of channels and porous diffusion layers. In order to improve existing mathematical and numerical models of PEM fuel cells, a deeper understanding of the coupling of the flow processes in the channels and diffusion layers is necessary. After discussing different mathematical models for PEM fuel cells, the work will focus on the description of the coupling of the free flow in the channel region with the filtration velocity in the porous diffusion layer as well as interface conditions between them. The difficulty in finding effective coupling conditions at the interface between the channel flow and the membrane lies in the fact that often the orders of the corresponding differential operators are different, e.g., when using stationary (Navier-)Stokes and Darcy's equation. Alternatively, using the Brinkman model for the porous media this difficulty does not occur. We will review different interface conditions, including the well-known Beavers-Joseph-Saffman boundary condition and its recent improvement by Le Bars and Worster

Biogas Crops - Part I: Specifications and Suitability of Field Crops for Anaerobic Digestion

In Germany, the growing number of agricultural biogas plants causes an increasing demand for crops as a feedstock in both mono‑ and co‑digestion processes. Laboratory scale batch anaerobic digestion tests under mesophilic conditions according to the German Standard Procedure VDI 4630 were conducted to investigate the suitability of different plant species like barley (Hordeum vulgare), rye (Secale cereale), triticale (X Triticosecale), alfalfa (Medicago sativa), hemp (Cannabis sativa), Jerusalem artichoke (Helianthus tuberosus) and maize (Zea mays) for biogas production. Emphasis was placed on growing stage and maturity, respectively as well as on whole crop silage preparation without additives as a preservation method for biogas crops. Results presented indicate that biogas yield is clearly influenced by plant species and harvest stage. Ensiled matter shows a positive effect on biomethanation with higher biogas yields and methane contents than fresh matter investigated. Hence, storage as silages can be considered as pre‑treatment which has also potential to improve methane production from plant matter. Analyses of digested materials reveal considerable reduction of organic matter of all crops investigated

Corneal Intrastromal Implantation Surgery by means of MyoRing Corneal Implant for the Treatment of Keratoconus: A Review

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Directed transport born from chaos in asymmetric antidot structures

It is shown that a polarized microwave radiation creates directed transport in an asymmetric antidot superlattice in a two dimensional electron gas. A numerical method is developed that allows to establish the dependence of this ratchet effect on several parameters relevant for real experimental studies. It is applied to the concrete case of a semidisk Galton board where the electron dynamics is chaotic in the absence of microwave driving. The obtained results show that high currents can be reached at a relatively low microwave power. This effect opens new possibilities for microwave control of transport in asymmetric superlattices.Comment: 8 pages, 10 figure

An assessment of discretizations for convection-dominated convection-diffusion equations

The performance of several numerical schemes for discretizing convection-dominated convection-diffusion equations will be investigated with respect to accuracy and efficiency. Accuracy is considered in measures which are of interest in applications. The study includes an exponentially fitted finite volume scheme, the Streamline-Upwind Petrov--Galerkin (SUPG) finite element method, a spurious oscillations at layers diminishing (SOLD) finite element method, a finite element method with continuous interior penalty (CIP) stabilization, a discontinuous Galerkin (DG) finite element method, and a total variation diminishing finite element method (FEMTVD). A detailed assessment of the schemes based on the Hemker example will be presented