A topological representation of lattices

Presented by R. S. Pierce.     

An augmented Lagrangian method for optimization problems with structured geometric constraints

This paper is devoted to the theoretical and numerical investigation of an augmented Lagrangian method for the solution of optimization problems with geometric constraints. Specifically, we study situations where parts of the constraints are nonconvex and possibly complicated, but allow for a fast computation of projections onto this nonconvex set. Typical problem classes which satisfy this requirement are optimization problems with disjunctive constraints (like complementarity or cardinality constraints) as well as optimization problems over sets of matrices which have to satisfy additional rank constraints. The key idea behind our method is to keep these complicated constraints explicitly in the constraints and to penalize only the remaining constraints by an augmented Lagrangian function. The resulting subproblems are then solved with the aid of a problem-tailored nonmonotone projected gradient method. The corresponding convergence theory allows for an inexact solution of these subproblems. Nevertheless, the overall algorithm computes so-called Mordukhovich-stationary points of the original problem under a mild asymptotic regularity condition, which is generally weaker than most of the respective available problem-tailored constraint qualifications. Extensive numerical experiments addressing complementarity- and cardinality-constrained optimization problems as well as a semidefinite reformulation of MAXCUT problems visualize the power of our approach.

     

Fast Photoresponse and Long Lifetime UV Photodetectors and Field Emitters Based on ZnO/Ultrananocrystalline Diamond Films

We have designed photodetectors and UV field emitters based on a combination of ZnO nanowires/nanorods (ZNRs) and bilayer diamond films in a metal–semiconductor–metal (MSM) structure. The ZNRs were fabricated on different diamond films and systematic investigations showed an ultra‐high photoconductive response from ZNRs prepared on ultrananocrystalline diamond (UNCD) operating at a lower voltage of 2 V. We found that the ZNRs/UNCD photodetector (PD) has improved field emission properties and a reduced turn‐on field of 2.9 V μm^?1 with the highest electron field emission (EFE) by simply illuminating the sample with ultraviolet (UV) light. The photoresponse (I_photo/I_dark) behavior of the ZNRs/UNCD PD exhibits a much higher photoresponse (912) than bare ZNRs (229), ZNRs/nanocrystalline diamond (NCD; 518), and ZNRs/microcrystalline diamond (MCD; 325) under illumination at λ=365 nm. A photodetector with UNCD films offers superior stability and a longer lifetime compared with carbon materials and bare ZNRs. The lifetime stability of the ZNRs/UNCD‐based device is about 410 min, which is markedly superior to devices that use bare ZNRs (92 min). The ZNRs/UNCD PD possesses excellent photoresponse properties with improved lifetime and stability; in addition, ZNRs/UNCD‐based UV emitters have great potential for applications such as cathodes in flat‐panel displays and microplasma display devices.     

Lithium intercalation into disordered carbon/SiCN composite. Part 2: Raman spectroscopy and <Superscript>7</Superscript>Li MAS NMR investigation of lithium storage sites

Within this work, we analyze the lithium storage sites within carbon/silicon carbonitride (SiCN) composites. Commercial carbons, HD3 (hard carbon) and LD1N and LD2N (soft carbons), of varying porosity are impregnated with polysilazane (HTT 1800) and pyrolysed at 1100 °C. It is found in the first part of this study (Graczyk-Zajac et al. J Solid State Electrochem 19:2763–2769, 2015) that the initial porosity of the carbon phase plays an important role in determining the lithium insertion capacity and rate capability of the composite material. By applying Raman spectroscopy and solid-state ⁷Li MAS NMR on pristine, lithiated, and delithiated samples, we investigate the lithium storage sites within the composite materials. By means of Raman spectroscopy, it has been found that lithium storage in hard carbon-derived composites occurs in a significant extent via adsorption-like process within unorganized carbon, whereas for the soft carbon composites, storage in turbostratic carbon is identified. ⁷Li solid-state NMR confirms these findings revealing that more than 33 % of lithium stored in HD3/SiCN is adsorbed in ionic form at the surface and in pores of the composite, while around 38 % is stored between carbon layers. LD1N and LD2N composites store more than 50 % of lithium in the intercalation-type sites.     

Bayesian inference using a noninformative prior for linear Gaussian random coefficient regression with inhomogeneous within-class variances

A Bayesian inference for a linear Gaussian random coefficient regression model with inhomogeneous within-class variances is presented. The model is motivated by an application in metrology, but it may well find interest in other fields. We consider the selection of a noninformative prior for the Bayesian inference to address applications where the available prior knowledge is either vague or shall be ignored. The noninformative prior is derived by applying the Berger and Bernardo reference prior principle with the means of the random coefficients forming the parameters of interest. We show that the resulting posterior is proper and specify conditions for the existence of first and second moments of the marginal posterior. Simulation results are presented which suggest good frequentist properties of the proposed inference. The calibration of sonic nozzle data is considered as an application from metrology. The proposed inference is applied to these data and the results are compared to those obtained by alternative approaches.     

Experimental and theoretical characterization of the aromatization, epimerization, and fragmentation reactions of bi-2H-azirin-2-yls prepared from 1,4-diazidobuta-1,3-dienes

1,4‐Diazidobuta‐1,3‐dienes (Z,Z)‐ 10 , 17 , and 21 were photolyzed and thermolyzed to yield the pyridazines 13 , 20 , and 23 , respectively. To explain these aromatic final products, the generation of highly strained bi‐2H‐azirin‐2‐yls 12 , 19 , and 22 and their valence isomerization were postulated. In the case of meso‐ and rac‐ 22 , nearly quantitative formation from diazide 21 , isolation as stable solids, and complete characterization were possible. On the thermolysis of 22 , aromatization to 23 was only a side reaction, whereas equilibration of meso‐ and rac‐ 22 and fragmentation, which led to alkyne 24 and acetonitrile, dominated. Prolonged irradiation of 22 gave mainly the pyrimidine 25 . The change of the configuration at C‐2 of the 2H‐azirine unit was observed not only in the case of bi‐2H‐azirin‐2‐yls 22 but also for simple spirocyclic 2H‐azirines 29 at a relatively low temperature (75 °C). The fragmentation of rac‐ 22 to give alkyne 24 and two molecules of acetonitrile was also studied by high‐level quantum chemical calculations. For a related model system 30 (methyl instead of phenyl groups), two transition states TS‐ 30 – 31 of comparable energy with multiconfigurational electronic states could be localized on the energy hypersurface for this one‐step conversion. The symmetrical transition state complies with the definition of a coarctate mechanism.