Renormalization group and high-temperature series for the two-dimensional ising model

We employ high-temperature series to investigate a two-parameter class of renormalization group transformations for the two-dimensional Ising model on the triangular lattice. For the static case we identify an optimal organization of the high-temperature expansion and an optimal transformation matrix and thus find, in second order, =0.96 and the magnetic eigenvaluey=2-/2=1.76.From recursion relations for flip rates we find the dynamic exponent to be the same for all transformations in our two-parameter class,z=2.32.Our fixed-point flip rates do not describe a Markov process even though the corresponding master equation for the single-event probability displays no explicit memory effects. The non-Markovian nature shows up only in a violation of the Markovian detailed balance conditions.     

Collagen stability: insights from NMR spectroscopic and hybrid density functional computational investigations of the effect of electronegative substituents on prolyl ring conformations

Collagen-like peptides of the type (Pro-Pro-Gly)(10) fold into stable triple helices. An electron-withdrawing substituent at the H(gamma)(3) ring position of the second proline residue stabilizes these triple helices. The aim of this study was to reveal the structural and energetic origins of this effect. The approach was to obtain experimental NMR data on model systems and to use these results to validate computational chemical analyses of these systems. The most striking effects of an electron-withdrawing substituent are on the ring pucker of the substituted proline (Pro(i)) and on the trans/cis ratio of the Xaa(i-1)-Pro(i) peptide bond. NMR experiments demonstrated that N-acetylproline methyl ester (AcProOMe) exists in both the C(gamma)-endo and C(gamma)-exo conformations (with the endo conformation slightly preferred), N-acetyl-4(R)-fluoroproline methyl ester (Ac-4R-FlpOMe) exists almost exclusively in the C(gamma)-exo conformation, and N-acetyl-4(S)-fluoroproline methyl ester (Ac-4S-FlpOMe) exists almost exclusively in the C(gamma)-endo conformation. In dioxane, the K(trans/cis) values for AcProOMe, Ac-4R-FlpOMe, and Ac-4S-FlpOMe are 3.0, 4.0, and 1.2, respectively. Density functional theory (DFT) calculations with the (hybrid) B3LYP method were in good agreement with the experimental data. Computational analysis with the natural bond orbital (NBO) paradigm shows that the pucker preference of the substituted prolyl ring is due to the gauche effect. The backbone torsional angles, phi and psi, were shown to correlate with ring pucker, which in turn correlates with the known phi and psi angles in collagen-like peptides. The difference in K(trans/cis) between AcProOMe and Ac-4R-FlpOMe is due to an n-->pi interaction associated with the Bürg-Dunitz trajectory. The decrease in K(trans/cis) for Ac-4S-FlpOMe can be explained by destabilization of the trans isomer because of unfavorable electronic and steric interactions. Analysis of the results herein along with the structures of collagen-like peptides has led to a theory that links collagen stability to the interplay between the pyrrolidine ring pucker, phi and psi torsional angles, and peptide bond trans/cis ratio of substituted proline residues.     

Die sterischen Bedingungen der Fragmentierungsreaktion III. Teil. Stereoisomere 4-, 5- und 7-Decahydrochinolyl-toluolsulfonate Fragmentierungsreaktionen, 16. Mitteilung

In a heterolytic fragmentation reaction of the type a-b-c-d-X → a - b + c = d + : X the geometry of the d - X bond and that of the electron-donating group a relative to the b - c bond are critical. This follows from a study of solvolysis rates and products of stereoisomeric 1-methyl-4-, -5- and -7-decahydroquinolyl p-toluenesulphonates in 80 Vol.% ethanol.     

Characterization of an optical multilayer hydrophone with constant frequency response in the range from 1 to 75 MHz

The performance of an optical multilayer hydrophone for ultrasound measurements is investigated both in theoretical terms and experimentally. The optical measurement system comprises a thin high-finesse dielectric interference filter structure that is deposited onto a plane glass plate. An incident acoustic pressure wave deforms the layer system, and the induced variation of the optical reflectance is determined. Applying the concept of an optical off-axis detection scheme offers good sensitivity and a simple and low-cost setup. A primary interferometric calibration technique is applied to experimentally determine the pressure-voltage transfer function in the range from 1 to 75 MHz. Within the measurement uncertainty a constant transfer factor is obtained for the whole frequency range. Measurements of broadband ultrasound pulses are influenced neither by acoustic resonances of the very thin sensing element nor by diffraction phenomena that are known to cause waveform distortions in small probe hydrophone measurements. High temporal and spatial resolution is combined with high durability of the probe, which is why the optical multilayer hydrophone is well suited for use as a reference for secondary hydrophone calibration.