Predicting thermal displacements in modular tool systems

In the last decade, there has been an increasing interest in compensating thermally induced errors to improve the manufacturing accuracy of modular tool systems. These modular tool systems are interfaces between spindle and workpiece and consist of several complicatedly formed parts. Their thermal behavior is dominated by nonlinearities, delay and hysteresis effects even in tools with simpler geometry and it is difficult to describe it theoretically. Due to the dominant nonlinear nature of this behavior the so far used linear regression between the temperatures and the displacements is insufficient. Therefore, in this study we test the hypothesis whether we can reliably predict such thermal displacements via nonlinear temperature-displacement regression functions. These functions are estimated first from learning measurements using the alternating conditional expectation (ACE) algorithm and then tested on independent data sets. First, we analyze data that were generated by a finite element spindle model. We find that our approach is a powerful tool to describe the relation between temperatures and displacements for simulated data. Next, we analyze the temperature-displacement relationship in a silent real experimental setup, where the tool system is thermally forced. Again, the ACE algorithm is powerful to estimate the deformation with high precision. The corresponding errors obtained by using the nonlinear regression approach are 10-fold lower in comparison to multiple linear regression analysis. Finally, we investigate the thermal behavior of a modular tool system in a working milling machine and again get promising results. The thermally induced errors can be estimated with 1-2 microm accuracy using this nonlinear regression analysis. Therefore, this approach seems to be very useful for the development of new modular tool systems.     

Towards a Microscopic Understanding of Nucleon Polarizabilities

We outline a microscopic framework to calculate nucleon Compton scattering from the level of quarks and gluons within the covariant Faddeev approach. We explain the connection with hadronic expansions of the Compton scattering amplitude and discuss the obstacles in maintaining electromagnetic gauge invariance. Finally we give preliminary results for the nucleon polarizabilities.     

Characterization of different substrates for Raman spectroscopic imaging of eukaryotic cells

For Raman spectroscopic analyses of the cells and other biological samples, the choice of the right substrate material is very important to avoid loss of information in characteristic spectral features because of competing background signals. In the current study, Raman spectroscopy is used to characterize several potential Raman substrates. Raman vibrational bands of the substrate material are discussed. The surface topography is analyzed by atomic force microscopy, and the root mean square surface roughness values are reported. Biocompatibility of the substrates is tested with Hep G2 cells evaluating cellular morphology as well as live/dead staining. Calcium fluoride, silicon, fused silica, borofloat glass, and silicon nitride membranes support cell growth and adherence. Silicon, borofloat glass, and fused silica give rise to Raman signals in the region of interest. Calcium fluoride substrate (UV grade) is suitable for Raman spectroscopic investigation of living cells. Nickel foil is suitable substrate for Raman spectroscopic investigation but cellular adherence and viability depend on the quality of the foil. Silicon nitride membranes coated with nickel chrome is a suitable Raman substrate in closed microfluidic systems. Copyright © 2016 John Wiley & Sons, Ltd.     

Unquenched complex dirac spectra at nonzero chemical potential: two-color QCD lattice data versus matrix model

We compare analytic predictions of non-Hermitian chiral random matrix theory with the complex Dirac operator eigenvalue spectrum of two-color lattice gauge theory with dynamical fermions at nonzero chemical potential. The Dirac eigenvalues come in complex conjugate pairs, making the action of this theory real and positive for our choice of two staggered flavors. This enables us to use standard Monte Carlo simulations in testing the influence of the chemical potential and quark mass on complex eigenvalues close to the origin. We find excellent agreement between the analytic predictions and our data for two different volumes over a range of chemical potentials below the chiral phase transition. In particular, we detect the effect of unquenching when going to very small quark masses.     

Über Verdazyliumsalze

Zusammenfassung Verdazyle reagieren mit FeCl₃ und anderen Metallhalogeniden in HCOOH unter Bildung von Doppelsalzen. Mit Tetranitromethan erhält man Verdazylium; C(NO₂)₃ ; und Verdazylium^;NO₃ ;. Verdazyliumsalze und Tetramethyl-p-phenylendiamin ergeben unter Elektronenübergang Verdazyle undWursters Blau. Dabei werden aus 2 diamagnetischen Verbindungen 2 paramagnetische Radikale gebildet. Die Absorptionsspektren verschiedenartig substituierter Verdazyliumsalze werden im Zusammenhang mit den Spektren der entsprechenden Verdazyle diskutiert.

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Verdazyls react with FeCl₃ and other metal halides in formic acid to give double-salts. Verdazylium;·C(NO₂)₃ ; and Verdazylium;NO₃ ; were obtained with tetranitromethane. Verdazyliumsalts and tetramethyl-p-phenylenediamine yield, in an electron transfer reaction, the corresponding verdazyls andWurster's-blue; i. e. two diamagnetic compounds react to give two stable paramagnetic species. The absorption spectra of different substituted verdazylium salts are discussed in relation to the spectra of the corresponding verdazyls.

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10. Mitt.:F. A. Neugebauer, Mh. Chem.97, 853 (1966).     

The nature of the chemical bond revisited. An energy partitioning analysis of diatomic molecules E2 (E=N–Bi, F–I), CO and BF

The nature of the chemical bonds in the diatomic molecules E₂ (E=N–Bi, F–I), CO and BF has been studied with an energy partitioning analysis using gradient-corrected density functional theory calculations. The results make it possible to estimate quantitatively the strength of covalent and electrostatic attractions and the Pauli repulsion between the atoms. The data suggest that some traditional explanations regarding the strength of the molecules should be modified. The energy partitioning analysis shows that the chemical bonds in the group 15 diatomic molecules have significant electrostatic character, which increases from 30.1% in N₂ to 58.3% in Bi₂. The contribution of the electrostatic attraction to the binding interactions in Sb₂ and Bi₂ is larger than the covalent bonding. The strength of the bonding in the triply bonded dinitrogen is less than that of the bonding. The calculations indicate that E is between 32.2% (Bi₂) and 40.0% (P₂) of the total orbital interaction energy (E_orb). The much stronger bond of N₂, as compared with the heavier group 15 E₂ homologues, is not caused by a particularly strong contribution by the bonding, but rather by the relatively large interactions. The comparison of N₂ with isoelectronic CO shows that the electrostatic character in the heteroatomic molecule is slightly smaller (28.8%) than in the homoatomic molecule. The contribution of the bonding in CO is larger (49.2%) than in N₂ (34.3%). The reason why CO has a stronger bond than N₂ is the significantly weaker Pauli repulsion in CO. The electrostatic character of the bonding in BF is slightly larger (32.0%) than in CO and N₂. BF has much weaker -bonding contributions that provide only 11.2% of the covalent interactions, which is why BF has a much weaker bond than CO and N₂. The chemical bonds in the dihalogen molecules have much higher covalent than electrostatic character. The E_orb term contributes between 74.4% (Br₂) and 79.7% (F₂) to the total attractive interactions. The relatively weak bond in F₂ comes from the rather large Pauli repulsion.Contribution to the Jacopo Tomasi Honorary Issue