Fluctuations in the quark-meson model for QCD with isospin chemical potential

We study the two-flavor quark-meson (QM) model with the functional renormalization group (FRG) to describe the effects of collective mesonic fluctuations on the phase diagram of QCD at finite baryon and   isospin chemical potentials, _μB${\mu }_B$ and _μI${\mu }_I$. With only isospin chemical potential there is a precise equivalence between the competing dynamics of chiral versus pion condensation and that of collective mesonic and baryonic fluctuations in the quark-meson-diquark model for two-color QCD at finite baryon chemical potential. Here, finite _μB=3μ${\mu }_B=3\mu$ introduces an additional dimension to the phase diagram as compared to two-color QCD, however. At zero temperature, the (_μI,μ${\mu }_I,\mu$) plane of this phase diagram is strongly constrained by the “Silver Blaze problem.” In particular, the onset of pion condensation must occur at _μI=_mπ/2${\mu }_I=m_{\pi }/2$, independent of μ   as long as μ+_μI$\mu +{\mu }_I$ stays below the constituent quark mass of the QM model or the liquid-gas transition line of nuclear matter in QCD. In order to maintain this relation beyond mean field it is crucial to compute the pion mass from its timelike correlator with the FRG in a consistent way.     

Bestimmung der Empfindlichkeit bei Tc-99-NMR-Messungen an einem 250-MHz-Spektrometer

By means of different concentrations the signal-to-noise ratios of Tc-99-NMR spectra were determined applying well measurable Tc-samples [tetrabutylammoniwn pertechnetate, TBA (TcO₄)J and a 250 MHz-spectrometer. The signal-to-noise ratios of the spectra were determined by using the integrated routines of the firm's software and accumulating different number of scans. By fittings of data of the signal-to-noise ratio dependence and by extrapolation the minimum Tc-concentralion could be empirically found out. Applying a duration of measurements of 12 hours about 10^?7 molar concentrations can be determined.     

Multiplicative Invariants and Semigroup Algebras

Let G be a finite group acting by automorphism on a lattice A, and hence on the group algebra S=k[A]. The algebra of G-invariants in S is called an algebra of multiplicative invariants. We present an explicit version of a result of Farkas stating that multiplicative invariants of finite reflection groups are semigroup algebras.     

Kinetics of phase transformation from hBN to cBN in the presence of Mg3BN3 catalyst

Abstract

Transformation kinetics from hBN to cBN has been studied at 6 GPa with changing reaction temperature and content of catalyst mixed with hBN powder. At lower catalyst content (3–10 wt %), rate of transformation was extraordinary rapid between 1300 and 1350 C. At higher catalyst content (30–50 wt %), rate of transformation was decreased. Normal nucleation kinetics was observed at about 1500 C. The rapid transformation temperature region correlates characteristic behavior of the sintering process.     

On a functional equation by Baak,Boo and Rassias

In Baak et al. (J Math Anal Appl 314(1):150–161, 2006) the authors considered the functional equation

$$\begin{aligned} r f\left( \frac{1}{r}\,\sum _{j=1}^{d}x_j\right)+ & {} \sum _{i(j)\in \{0,1\} \atop \sum _{1\le j\le d} i(j)=\ell }r f\left( \frac{1}{r}\,\sum _{j=1}^d (-1)^{i(j)}x_j\right) \\= & {} \left( {d-1\atopwithdelims ()\ell }-{d-1\atopwithdelims ()\ell -1} +1\right) \sum _{j=1}^{d} f(x_j) \end{aligned}$$

where \(d,\ell \in \mathbb {N}\), \(1<\ell <d/2\) and \(r\in \mathbb {Q}{\setminus }\{0\}\). The authors determined all odd solutions \(f:X\rightarrow Y\) for vector spaces X, Y over \(\mathbb {Q}\). In Oubbi (Can Math Bull 60:173–183, 2017) the author considered the same equation but now for arbitrary real \(r\not =0\) and real vector spaces X, Y. Generalizing similar results from (J Math Anal Appl 314(1):150–161, 2006) he additionally investigates certain stability questions for the equation above, but as for that equation itself for odd approximate solutions only. The present paper deals with the general solution of the equation and the corresponding stability inequality. In particular it is shown that under certain circumstances non-odd solutions of the equation exist.

     

Linear parameter varying control design for rotating systems supported by journal bearings

Linear parameter varying (LPV) control is a model-based control technique that takes into account time-varying parameters of the plant. In the case of rotating systems supported by lubricated bearings, the dynamic characteristics of the bearings change in time as a function of the rotating speed. Hence, LPV control can tackle the problem of run-up and run-down operational conditions when dynamic characteristics of the rotating system change significantly in time due to the bearings and high vibration levels occur. In this work, the LPV control design for a flexible shaft supported by plain journal bearings is presented. The model used in the LPV control design is updated from unbalance response experimental results and dynamic coefficients for the entire range of rotating speeds are obtained by numerical optimization. Experimental implementation of the designed LPV control resulted in strong reduction of vibration amplitudes when crossing the critical speed, without affecting system behavior in sub- or super-critical speeds.     

Hard X‐ray phase‐contrast tomography of non‐homogeneous specimens: grating interferometry versus propagation‐based imaging

X‐ray phase‐contrast imaging is an effective approach to drastically increase the contrast and sensitivity of microtomographic techniques. Numerous approaches to depict the real part of the complex‐valued refractive index of a specimen are nowadays available. A comparative study using experimental data from grating‐based interferometry and propagation‐based phase contrast combined with single‐distance phase retrieval applied to a non‐homogeneous sample is presented (acquired at beamline ID19‐ESRF). It is shown that grating‐based interferometry can handle density gradients in a superior manner. The study underlines the complementarity of the two techniques for practical applications.