A Bramble-Pasciak-like method with applications in optimization

Saddle-point systems arise in many applications areas, in fact in any situation where an extremum principle arises with constraints. The Stokes problem describing slow viscous flow of an incompressible fluid is a classic example coming from partial differential equations and in the area of Optimization such problems are ubiquitous.\ud In this manuscript we show how new approaches for the solution of saddle-point systems arising in Optimization can be derived from the Bramble-Pasciak Conjugate Gradient approach widely used in PDEs and more recent generalizations thereof. In particular we derive a class of new solution methods based on the use of Preconditioned Conjugate Gradients in non-standard inner products and demonstrate how these can be understood through more standard machinery. We show connections to Constraint Preconditioning and give the results of numerical computations on a number of standard Optimization test examples

Gasification of biomass in supercritical water, challenges for the process design—lessons learned from the operation experience of the first dedicated pilot plant

Gasification of organic matter under the conditions of supercritical water (T > 374 °C, p > 221 bar) is an allothermal, continuous flow process suitable to convert materials with high moisture content (<20 wt.% dry matter) into a combustible gas. The gasification of organic matter with water as a solvent offers several benefits, particularly the omission of an energy-intensive drying process. The reactions are fast, and mean residence times inside the reactor are consequently low (less than 5 min). However, there are still various challenges to be met. The combination of high temperature and pressure and the low concentration of organic matter require a robust process design. Additionally, the low value of the feed and the product predestinate the process for decentralized applications, which is a challenge for the economics of an application. The present contribution summarizes the experience gained during more than 10 years of operation of the first dedicated pilot plant for supercritical water gasification of biomass. The emphasis lies on highlighting the challenges in process design. In addition to some fundamental results gained from comparable laboratory plants, selected experimental results of the pilot plant “VERENA” (acronym for the German expression “experimental facility for the energetic exploitation of agricultural matter”) are presented

Ferromagnetic coupling of mononuclear Fe centers in a self-assembled metal-organic network on Au(111)

The magnetic state and magnetic coupling of individual atoms in nanoscale structures relies on a delicate balance between different interactions with the atomic-scale surrounding. Using scanning tunneling microscopy, we resolve the self-assembled formation of highly ordered bilayer structures of Fe atoms and organic linker molecules (T4PT) when deposited on a Au(111) surface. The Fe atoms are encaged in a three-dimensional coordination motif by three T4PT molecules in the surface plane and an additional T4PT unit on top. Within this crystal field, the Fe atoms retain a magnetic ground state with easy-axis anisotropy, as evidenced by X-ray absorption spectroscopy and X-ray magnetic circular dichroism. The magnetization curves reveal the existence of ferromagnetic coupling between the Fe centers

Ground-state properties of rutile: electron-correlation effects

Electron-correlation effects on cohesive energy, lattice constant and bulk compressibility of rutile are calculated using an ab-initio scheme. A competition between the two groups of partially covalent Ti-O bonds is the reason that the correlation energy does not change linearly with deviations from the equilibrium geometry, but is dominated by quadratic terms instead. As a consequence, the Hartree-Fock lattice constants are close to the experimental ones, while the compressibility is strongly renormalized by electronic correlations.Comment: 1 figure to appear in Phys. Rev.

Decreasing Atmospheric CO2 During the Late Miocene Cooling

A pronounced late Miocene cooling (LMC) from ~7 to 5.7 Ma has been documented in extratropical and tropical sea surface temperature records, but to date, available proxy evidence has not revealed a significant pCO2 decline over this event. Here, we provide a new, high‐resolution pCO2 proxy record over the LMC based on alkenone carbon isotopic fractionation (εp) measured in sediments from the South Atlantic at Ocean Drilling Program (ODP) Site 1088. We apply a recent proxy calibration derived from a compilation of laboratory cultures, which more accurately reflects the proxy sensitivity to pCO2 changes during late Quaternary glacial‐interglacial cycles, together with new micropaleontological proxies to reconstruct past variations in algal growth rate, an important secondary influence on the εp. Our resulting pCO2 record suggests an approximately twofold to threefold decline over the LMC and confirms a strong coupling between climate and pCO2 through the late Miocene. Within this long‐term trend are pCO2 variations on sub‐myr timescales that may reflect 400‐kyr long‐eccentricity cycles, in which pCO2 minima coincide with several orbital‐scale maxima in published high‐resolution benthic δ18O records. These may correspond to ephemeral glaciations, potentially in the Northern Hemisphere. Our temperature and planktonic δ18O records from Site 1088 are consistent with substantial equatorward movement of Southern Ocean frontal systems during the LMC. This suggests that potential feedbacks between cooling, ocean circulation and deep ocean CO2 storage may warrant further investigation during the LMC