Formation of Highly Ordered Molecular Porous 2D Networks from Cyano-Functionalized Porphyrins on Cu(111)

We investigated the adsorption of three related cyano-functionalized tetraphenyl porphyrin derivatives on Cu(111) by scanning tunneling microscopy (STM) in ultra-high vacuum (UHV) with the goal to identify the role of the cyano group and the central Cu atom for the intermolecular and supramolecular arrangement. The porphyrin derivatives studied were Cu-TCNPP, Cu-cisDCNPP, and 2H-cisDCNPP, that is, Cu-5,10,15,20-tetrakis-(p-cyano)-phenylporphyrin, Cu-meso-cis-di(p-cyano)-phenylporphyrin and 2H-meso-cis-di(p-cyano)-phenylporphyrin, respectively. Starting from different structures obtained after deposition at room temperature, all three molecules form the same long-range ordered hexagonal honeycomb-type structure with triangular pores and three molecules per unit cell. For the metal-free 2H-cisDCNPP, this occurs only after self-metalation upon heating. The structure-forming elements are pores with a distance of 3.1 nm, formed by triangles of porphyrins fused together by cyano-Cu-cyano interactions with Cu adatoms. This finding leads us to suggest that two cyano-phenyl groups in the “cis” position is the minimum prerequisite to form a highly ordered 2D porous molecular pattern. The experimental findings are supported by detailed density functional theory calculations to analyze the driving forces that lead to the formation of the porous hexagonal honeycomb-type structure.     

Lasing in thulium-doped polarizing photonic crystal fiber

We describe lasing of a thulium-doped polarizing photonic crystal fiber. A 4 m long fiber with 50 μm diameter core, 250 μm diameter cladding, and d/Λ ratio of 0.18 was pumped with a 793 nm diode and produced a polarized output with a polarization extinction ratio (PER) of 15 dB and an M(2) of <1.15. An intracavity polarizer and half-wave plate minimally increased the PER to 16 dB. The output power had 35% slope efficiency relative to the absorbed pump power. The maximum cw output power was limited to 4 W due to the quantum defect heating of the fiber.     

Analysis of first stage ignition delay times of dimethyl ether in a laminar flow reactor

The combustion chemistry of the first stage ignition and chemistry/flow interactions are studied for dimethyl ether (DME) with a mathematical analysis of two systems: a plug flow reactor study is used to reduce the reaction chemistry systematically. A skeletal reaction mechanism for the low temperature chemistry of DME until the onset of ignition is derived on the basis of the detailed DME mechanism of the Lawrence Livermore National Laboratory – see Curran, Fischer and Dryer, Int. J. Chem. Kinetics, Vol. 32 (2000). It is shown that reasonably good results for ignition delay times can be reached using a simple system of three ordinary differential equations and that the resulting analytical solution depends only on two reaction rates and the initial fuel concentration. The stepwise reduction of the system based on assumptions yields an understanding on why these reactions are so important. Furthermore, the validation of the assumptions yields insight into the influence of the fuel and the oxygen concentration on the temperature during the induction phase. To investigate the influence of chemistry/flow interactions, a 2D model with a laminar Hagen–Poiseuille flow and 2D-polynomial profiles for the radial species concentration is considered. For the 2D model, it is found that only the diffusion coefficients and the reactor radius need to be taken into consideration additionally to describe the system sufficiently. Also, the coupling of flow and chemistry is clarified in the mathematical analysis. The insight obtained from the comparison of the 2D model and the plug flow model is used to establish an average velocity for the conversion of ignition locations to ignition delay times in a laminar flow reactor. Finally, the 2D analytical solution is compared against new experimental data, obtained in such a laminar flow reactor for an undiluted DME/air mixture with an equivalence ratio of φ = 0.835 and a temperature range of 555 to 585 K at atmospheric pressure.     

Three-dimensional green water velocity on a model structure

Flow kinematics of green water due to plunging breaking waves impinging on a simplified, 3D model structure was investigated in the laboratory. Two breaking wave conditions were tested: one with waves impinging on the vertical wall of the model at still water level, and the other with waves impinging on the horizontal deck surface. The bubble image velocimetry (BIV) technique was used to measure flow velocities. Measurements were taken on both vertical and horizontal planes. Evolution of green water flow kinematics in time and space was revealed and was found to be quite different between the two wave conditions, even though the incoming waves are essentially identical. The time history of maximum velocity is demonstrated and compared. In both cases, the maximum velocity occurs near the green water front and beneath the free surface. The maximum horizontal velocity for the deck impinging case is 1.44C with C being the wave phase speed, which is greater than 1.24C for the wall impingement case. The overall turbulence level is about 0.3 of the corresponding maximum velocity in each wave condition. The results were also compared with 2D experimental results to examine the 3D effect. It was found that the magnitude of the maximum vertical velocity during the runup process is 1.7C in the 3D model study and 2.9C in the 2D model study, whereas the maximum horizontal velocity on the deck is similar, 1.2C in both 3D and 2D model studies.     

Cayley graph expanders and groups of finite width

We present new infinite families of expander graphs of vertex degree 4, which is the minimal possible degree for Cayley graph expanders. Our first family defines a tower of coverings (with covering indices equal to 2) and our second family is given as Cayley graphs of finite groups with very short presentations with only two generators and four relations. Both families are based on particular finite quotients of a group G of infinite upper triangular matrices over the ring .We present explicit vector space bases for the finite abelian quotients of the lower exponent-2 groups of G by upper triangular subgroups and prove a particular 3-periodicity of these quotients. We also conjecture that the group G has finite width 3 and finite average width 8/3.     

An anytime multistep anticipatory algorithm for online stochastic combinatorial optimization

The one-step anticipatory algorithms (1s-AA) is an online algorithm making decisions under uncertainty by ignoring the non-anticipativity constraints in the future. It was shown to make near-optimal decisions on a variety of online stochastic combinatorial problems in dynamic fleet management and reservation systems. Here we consider applications in which 1s-AA is not as close to the optimum and propose Amsaa, an anytime multi-step anticipatory algorithm. Amsaa combines techniques from three different fields to make decisions online. It uses the sampling average approximation method from stochastic programming, search algorithms for Markov decision processes from artificial intelligence, and discrete optimization algorithms. Amsaa was evaluated on a stochastic project scheduling application from the pharmaceutical industry featuring endogenous observations of the uncertainty. The experimental results show that Amsaa significantly outperforms state-of-the-art algorithms on this application under various time constraints.     

Hilbert scales and Sobolev spaces defined by associated Legendre functions

In this paper we study the Hilbert scales defined by the associated Legendre functions for arbitrary integer values of the parameter. This problem is equivalent to studying the left-definite spectral theory associated to the modified Legendre equation. We give several characterizations of the spaces as weighted Sobolev spaces and prove identities among the spaces corresponding to the lower regularity index.     

80th anniversary of Anatoly M. Kharitonov

Anniversary Dates

80th anniversary of Anatoly M. Kharitonov     

Triazolo-linked cinchona alkaloid carbamate anion exchange-type chiral stationary phases: Synthesis by click chemistry and evaluation

Immobilization strategy based on Huisgen 1,3-dipolar cycloaddition (click chemistry) of 10,11-didehydrocinchona tert-butylcarbamates to azido-grafted silica gels has been evaluated for preparation of novel chiral stationary phases (CSP 1-3). The resultant 1,2,3-triazole-linked CSPs were tested under various mobile phase conditions (polar organic and reversed phase mode) with a representative set of structurally diverse racemic acids including N-protected aminoacids, aromatic and aryloxycarboxylic acids as well as binaphthol phosphate. The chiral recognition performance of the C3-triazole-linked CSPs was found to mirror largely that of the known C3-thioether-linked CSP in terms of elution order, enantioselectivity and retention behavior. In an effort to assess the non-specific binding expressed as retention increment of these triazole-linked CSPs, the parent azidopropyl- and triazole-modified silica materials (thus not containing the chiral head ligand) were studied independently. Compared with the corresponding CSPs, the analyte retention on the azidopropyl control column was very low, and practically negligible on the corresponding triazole-modified reference column. Only minor losses in analyte retention behavior (<5%) were observed with triazole-linked CSPs after two month of continuous use with polar-organic and reversed-phase-type mobile phases, highlighting the excellent stability of the 1,2,3-triazole linker.