Angles, Scales and Parametric Renormalization

We discuss the structure of renormalized Feynman rules. Regarding them as maps from the Hopf algebra of Feynman graphs to ${\mathbb{C}}$ originating from the evaluation of graphs by Feynman rules, they are elements of a group ${G=\mathrm{Spec}_{\mathrm{Feyn}}(H)}$ . We study the kinematics of scale and angle-dependence to decompose G into subgroups ${G_{\mathrm{\makebox{1-s}}}}$ and ${G_{\mathrm{fin}}}$ . Using parametric representations of Feynman integrals, renormalizability and the renormalization group underlying the scale dependence of Feynman amplitudes are derived and proven in the context of algebraic geometry.     

Compact formulations of the Steiner Traveling Salesman Problem and related problems

The Steiner Traveling Salesman Problem (STSP) is a variant of the TSP that is particularly suitable when routing on real-life road networks. The standard integer programming formulations of both the TSP and STSP have an exponential number of constraints. On the other hand, several compact formulations of the TSP, i.e., formulations of polynomial size, are known. In this paper, we adapt some of them to the STSP, and compare them both theoretically and computationally. It turns out that, just by putting the best of the formulations into the CPLEX branch-and-bound solver, one can solve instances with over 200 nodes. We also briefly discuss the adaptation of our formulations to some related problems.     

A Titanium(IV)‐Based Metal–Organic Framework Featuring Defect‐Rich Ti‐O Sheets as an Oxidative Desulfurization Catalyst

While titanium‐based metal–organic frameworks (MOFs) have been widely studied for their (photo)catalytic potential, only a few Ti^IV MOFs have been reported owing to the high reactivity of the employed titanium precursors. The synthesis of COK‐47 is now presented, the first Ti carboxylate MOF based on sheets of Ti^IVO₆ octahedra, which can be synthesized with a range of different linkers. COK‐47 can be synthesized as an inherently defective nanoparticulate material, rendering it a highly efficient catalyst for the oxidation of thiophenes. Its structure was determined by continuous rotation electron diffraction and studied in depth by X‐ray total scattering, EXAFS, and solid‐state NMR. Furthermore, its photoactivity was investigated by electron paramagnetic resonance and demonstrated by catalytic photodegradation of rhodamine 6G.     

Local density of states of one-dimensional Mott insulators and charge-density wave states with a boundary

We determine the local density of states of one-dimensional incommensurate charge-density wave states in the presence of a strong impurity potential, which is modeled by a boundary. We find that the charge-density wave gets pinned at the impurity, which results in a singularity in the Fourier transform of the local density of states at momentum 2k_{F}. At energies above the spin gap we observe dispersing features associated with the spin and charge degrees of freedom, respectively. In the presence of an impurity magnetic field we observe the formation of a bound state localized at the impurity. All of our results carry over to the case of 1D Mott insulators by exchanging the roles of spin and charge degrees of freedom. We discuss the implications of our result for scanning tunneling microscopy experiments on spin-gap systems such as two-leg ladder cuprates.     

Frictional duality observed during nanoparticle sliding

One of the most fundamental questions in tribology concerns the area dependence of friction at the nanoscale. Here, experiments are presented where the frictional resistance of nanoparticles is measured by pushing them with the tip of an atomic force microscope. We find two coexisting frictional states: While some particles show finite friction increasing linearly with the interface areas of up to 310 000 nm(2), other particles assume a state of frictionless sliding. The results further suggest a link between the degree of surface contamination and the occurrence of this duality.     

Passively mode-locked Yb:YAG thin-disk laser with pulse energies exceeding 13 microJ by use of an active multipass geometry

We demonstrate the generation of high-energy picosecond pulses directly from a thin-disk laser oscillator by employing a self-imaging active multipass geometry. Stable single-pulse operation has been obtained with an average output power in excess of 50 W, excluding a cw background of 8%, at a repetition rate of 3.8 MHz. Self-starting passive mode locking was accomplished using a semiconductor saturable absorber mirror. The maximum pulse energy was 13.4 microJ at a pulse duration of 1.36 ps with a time-bandwidth product of 0.34. Single-pass external frequency doubling with a conversion efficiency of 60% yielded >28 W of average power at 515 nm.     

Melting and freezing of argon in a granular packing of linear mesopore arrays

Freezing and melting of Ar condensed in a granular packing of template-grown arrays of linear mesopores (SBA-15, mean pore diameter 8 nm) has been studied by specific heat measurements C as a function of fractional filling of the pores. While interfacial melting leads to a single melting peak in C, homogeneous and heterogeneous freezing along with a delayering transition for partial fillings of the pores result in a complex freezing mechanism explainable only by a consideration of regular adsorption sites (in the cylindrical mesopores) and irregular adsorption sites (in niches of the rough external surfaces of the grains and at points of mutual contact of the powder grains). The tensile pressure release upon reaching bulk-liquid-vapor coexistence quantitatively accounts for an upward shift of the melting and freezing temperature observed while overfilling the mesopores.     

Postsynthetic Metal and Ligand Exchange in MFU‐4l: A Screening Approach toward Functional Metal–Organic Frameworks Comprising Single‐Site Active Centers

The isomorphous partial substitution of Zn²⁺ ions in the secondary building unit (SBU) of MFU‐4l leads to frameworks with the general formula [M_xZn_(5–x)Cl₄(BTDD)₃], in which x≈2, M=Mn^II, Fe^II, Co^II, Ni^II, or Cu^II, and BTDD=bis(1,2,3‐triazolato‐[4,5‐b],[4′,5′‐i])dibenzo‐[1,4]‐dioxin. Subsequent exchange of chloride ligands by nitrite, nitrate, triflate, azide, isocyanate, formate, acetate, or fluoride leads to a variety of MFU‐4l derivatives, which have been characterized by using XRPD, EDX, IR, UV/Vis‐NIR, TGA, and gas sorption measurements. Several MFU‐4l derivatives show high catalytic activity in a liquid‐phase oxidation of ethylbenzene to acetophenone with air under mild conditions, among which Co‐ and Cu derivatives with chloride side‐ligands are the most active catalysts. Upon thermal treatment, several side‐ligands can be transformed selectively into reactive intermediates without destroying the framework. Thus, at 300 °C, Co^II‐azide units in the SBU of Co‐MFU‐4l are converted into Co^II‐isocyanate under continuous CO gas flow, involving the formation of a nitrene intermediate. The reaction of Cu^II‐fluoride units with H₂ at 240 °C leads to Cu^I and proceeds through the heterolytic cleavage of the H₂ molecule.     

NMR-based differentiation of conventionally from organically produced chicken eggs in Germany

Both the German and European organic food markets are growing fast, and there is also a rising demand for organic chicken eggs. Consumers are willing to pay higher prices for organic eggs produced in an animal-appropriate environment considering animal welfare. Strict labelling requirements do not prevent chicken eggs from being a subject of food fraud. Conventionally produced (barn/free-range) eggs can easily be mislabeled as organic eggs. Especially because the demand for organically produced chicken eggs is likely to exceed supply in the future, mislabeling appears to be a realistic scenario. Therefore, there is a need for analytical methods that are suitable to classify eggs as being either conventionally or organically produced. Nuclear magnetic resonance (NMR) spectroscopy in combination with multivariate data analysis is a suitable tool to screen eggs according to the different systems of husbandry. Sample preparation is based on a fat extraction method, which was optimised for application to freeze-dried egg yolk. Samples were analysed using typical q-NMR parameters. A nontargeted approach was used for the analysis of the ¹H NMR data. Principal component analysis (PCA) was applied followed by a linear discriminant analysis (PCA-LDA) and Monte Carlo cross-validation. In total, 344 chicken eggs (214 barn/free-range eggs and 130 eggs from organic farms), most of them originating from Germany, were used to build and validate the prediction model. The results showed that the prediction model allowed for the correct classification of about 93% of the organic eggs.