Conjugate gradient method for dual-dual mixed formulations

We deal with the iterative solution of linear systems arising from so-called dual-dual mixed finite element formulations. The linear systems are of a two-fold saddle point structure; they are indefinite and ill-conditioned. We define a special inner product that makes matrices of the two-fold saddle point structure, after a specific transformation, symmetric and positive definite. Therefore, the conjugate gradient method with this special inner product can be used as iterative solver. For a model problem, we propose a preconditioner which leads to a bounded number of CG-iterations. Numerical experiments for our model problem confirming the theoretical results are also reported.

     

Torelli Theorem for the Deligne–Hitchin Moduli Space

Fix integers g ≥ 3 and r ≥ 2, with r ≥ 3 if g = 3. Given a compact connected Riemann surface X of genus g, let denote the corresponding Deligne–Hitchin moduli space. We prove that the complex analytic space determines (up to an isomorphism) the unordered pair , where is the Riemann surface defined by the opposite almost complex structure on X.     

Structure–conductivity relations of simulated highly porous nanoparticle aggregate films

Electrical conductivity of porous films composed of nanoparticle aggregates is theoretically evaluated with respect to aggregate structure and film packing density. The aggregates are fractals composed of 5–30 primary particles with diameter of 10 nm. The film properties are derived from simulated boxes in the range of 0.5–1 μm. The electrical conductivity across the films of packing densities ranging from 0.01 to 0.15 was studied. All films prepared by an aerosol deposition technique, which uses nanoparticle aggregates, exhibited percolation behavior between planes parallel to the moving direction of the aggregates. They also followed the classical percolation relation for electrical conductivity while the critical percolation packing density depends on the aggregate size and structure used to build the films. Films using larger aggregates as building blocks have higher electrical conductance than smaller aggregates close to the percolation limit. For validation and supplementary information, two independent models are developed: one model follows the percolation theory to get detailed physical insights and another one computes the exact conductivities but at the cost of some details. This analysis gives new insights into the conduction backbone structures of these films with regard to neck contacts within an aggregate and grain boundary contacts between aggregates. The results shown are important for solar application of these films and especially for gas sensors where high sensitivity is often counteracted by low conductivity.     

On index formulas for manifolds with metric horns

In this paper was discuss the index problem for geometric differential operators (Spin–Dirac opreatorm Gauβ–Bonnet operator, Singnature operator) on manifolds with metric horns. On singular manifolds these operators in general do not unique closed extensions. But there always exist two extremal extensions D$sub:min$esub:and D$sub:max$esub: We describe the quotient D (D$sub:max$esub:)/D(D$sub:esub:) explicitely in geometric resp.topological terms of the base manifolds of the metric horns.

We derive index formulas for the3 Spin–Dirac and GauβBonnet operator. For the Singnature operator we present a partial result.     

Netlike partial cubes III. The median cycle property

A graph G has the Median Cycle Property (MCP) if every triple (u₀,u₁,u₂) of vertices of G admits a unique median or a unique median cycle, that is a gated cycle C of G such that for all i,j,k∈{0,1,2}, if x_i is the gate of u_i in C, then: {x_i,x_j}⊆I_G(u_i,u_j) if i≠j, and d_G(x_i,x_j)<d_G(x_i,x_k)+d_G(x_k,x_j). We prove that a netlike partial cube has the MCP if and only if it contains no triple of convex cycles pairwise having an edge in common and intersecting in a single vertex. Moreover a finite netlike partial cube G has the MCP if and only if G can be obtained from a set of even cycles and hypercubes by successive gated amalgamations, and equivalently, if and only if G can be obtained from K₁ by a sequence of special expansions. We also show that the geodesic interval space of a netlike partial cube having the MCP is a Pash-Peano space (i.e. a closed join space).     

Mechanism of Host–Guest Complex Formation and Identification of Intermediates through NMR Titration and Diffusion NMR Spectroscopy

The formation of host–guest (H‐G) complexes between 1,8‐bis[(diethylgallanyl)ethynyl]anthracene (H) and the N‐heterocycles pyridine and pyrimidine (G) was studied in solution using a combination of NMR titration and diffusion NMR experiments. For the latter, diffusion coefficients of potential host–guest structures in solution were compared with those of tailor‐made reference compounds of similar shape (synthesized and characterized by NMR, HRMS, and in part XRD). Highly dynamic behavior was observed in both cases, but with different host–guest species and equilibria. With increasing concentrations of the pyridine guest, the equilibrium H₂?H₂κ¹‐G₁?HG₂ is observed (in the second step a host dimer coordinates one guest molecule); for pyrimidine the equilibrium H₂→H₁κ²‐G₁?HG₂ is observed (the formation of a 1:1 aggregate is the second step).     

Nitrogen‐Doped Ordered Mesoporous Carbon Supported Bimetallic PtCo Nanoparticles for Upgrading of Biophenolics

Hydrodeoxygenation (HDO) is an attractive route for the upgrading of bio‐oils produced from lignocellulose. Current catalysts require harsh conditions to effect HDO, decreasing the process efficiency in terms of energy and carbon balance. Herein we report a novel and facile method for synthesizing bimetallic PtCo nanoparticle catalysts (ca. 1.5 nm) highly dispersed in the framework of nitrogen‐doped ordered mesoporous carbon (NOMC) for this reaction. We demonstrate that NOMC with either 2D hexagonal (p6m) or 3D cubic (Im m) structure can be easily synthesized by simply adjusting the polymerization temperature. We also demonstrate that PtCo/NOMC (metal loading: Pt 9.90 wt %; Co 3.31 wt %) is a highly effective catalyst for HDO of phenolic compounds and “real‐world” biomass‐derived phenolic streams. In the presence of PtCo/NOMC, full deoxygenation of phenolic compounds and a biomass‐derived phenolic stream is achieved under conditions of low severity.     

Spatially resolved ultra-trace analysis of elements combining resonance ionization with a MALDI-TOF spectrometer

A combined setup for spatially resolved mass analysis of trace amounts of elements and macromolecules is presented. Using a MALDI-TOF mass spectrometer, a laser spectroscopic setup for resonant ionization of neutral atoms has been implemented. This allows for an efficient and selective detection of trace elements by means of resonance ionization mass spectrometry (RIMS). The instrumental scheme is described, and methodological developments are presented. In a first application pure, laser desorption/ionization with TOF-MS was used to measure mass distributions of cosmic nanodiamonds. For further applications regarding the spatially resolved ultra-trace analysis of elements in solid samples, an implanted target was used to characterize both laser desorption/ionization and laser desorption/resonance ionization for the detection of trace elements within. A perspective of the setup is given and future investigations are outlined.     

Experimental and Theoretical Structure Elucidation of the [2 : 1] Complex Ion of Carbo[n]helicene with n=6, 7 and 8 and Ag+

Gas-phase complexes of [n]helicenes with n=6, 7 and 8 and the silver(I) cation are generated utilizing electrospray ionization mass spectrometry (ESI-MS). Besides the well-established [1 : 1] helicene/Ag⁺-complex in which the helicene provides a tweezer-like surrounding for the Ag⁺, there is also a [2 : 1] complex formed. Density functional theory (DFT) calculations in conjunction with energy-resolved collision-induced dissociation (ER-CID) experiments reveal that the second helicene attaches via π-π stacking to the first helicene, which is part of the pre-formed [1 : 1] tweezer complex with Ag⁺. For polycyclic aromatic hydrocarbons (PAHs) of planar structure, the [2 : 1] complex with silver(I) is typically structured as an Ag⁺-bound dimer in which the Ag⁺ would bind to both PAHs as the central metal ion (PAH–Ag⁺–PAH). For helicenes, the Ag⁺-bound dimer is of similar thermochemical stability as the π-π stacked dimer, however, it is kinetically inaccessible. Coronene (Cor) is investigated in comparison to the helicenes as an essentially planar PAH. In analogy to the π-π stacked dimer of the helicenes, the Cor−Ag⁺−Cor−Cor complex is also observed. Competition experiments using [n]helicene mixtures reveal that the tweezer complexes of Ag⁺ are preferably formed with the larger helicenes, with n=6 being entirely ignored as the host for Ag⁺ in the presence of n=7 or 8.     

Coherent electronic and nuclear dynamics for charge transfer in 1-ethyl-4-(carbomethoxy)pyridinium iodide

Although polaronic interactions and states abound in charge transfer processes and reactions, quantitative and separable determination of electronic and nuclear relaxation is still challenging. The present paper employs the amplitudes, polarizations, and phases of four-wave mixing signals to obtain unique dynamical information on relaxation processes following photoinduced charge transfer between iodide and 1-ethyl-4-(carbomethoxy)pyridinium ions. Pump-probe signal amplitudes reveal the coherent coupling of an underdamped 115 cm(-1) nuclear mode to the charge transfer excitation. Assignments of this recurrence to intramolecular vibrational modes of the acceptor and to modulation of the intermolecular donor-acceptor distance are discussed on the basis of a high-level density functional theory normal-mode analysis and previously observed wave packet dynamics of solvated molecular iodine. Nuclear relaxation of the acceptor induces sub-picosecond decay of the pump-probe polarization anisotropy from an initial value of 0.4 to an asymptotic value of -0.05. Electronic structure calculations suggest that relaxation along the torsional coordinate of the ethyl group is the origin of the anisotropy decay. Electric-field-resolved transient grating (EFR-TG) signal fields are obtained by spectral interferometry with a diffractive optic based interferometer. These measurements show that the signal phase and amplitude possess similar dynamics. Model calculations are used to demonstrate how the EFR-TG signal phase yields unique information on transient material resonances located outside the laser pulse spectrum. This effect can be rationalized in that the real and imaginary parts of the nonlinear polarization are related by the Kramers-Kronig transformation, which allows the dispersive component of the polarization response to exhibit spectral sensitivity over a larger frequency range than that defined by the absorption bandwidth.