Modeling and simulation of first and second sound in solids

We investigate the propagation of mechanical and thermal waves in solids at cryogenic temperatures. The latter are known as the second sound phenomenon. It occurs, e.g., in dielectric solids and differs greatly from the classical case in which the heat transport proceeds by diffusion. Since Fourier’s law of heat conduction fails for modeling second sound, we apply a non-classical one. During the last two decades, the non-classical thermoelastodynamic theory of Green and Naghdi enjoys steadily growing research activities.     

Weitere Evidenz für die mikroskopische Gleichzeitigkeit des Bruches zweier Bindungen bei einer E2-Reaktion: H-Isotopeneffekte und Substituentenwirkungen bei der Reaktion von 2,2-Diphenyläthyl-benzolsulfonat mit Methoxid-Ion

Second order rate constants are determined for the E2 reactions of 2,2-diphenyl-ethyl benzenesulfonates Ph₂C^xHCH₂O · O₂S–C₆H₄–X with CH₃ONa in methyl cellosolve solution (^xH = H or D, X = p-CH₃O, p-CH₃, H or p-NO₂). The HAMMETT ? values are of the same order of magnitude as those found in the first order solvolyses of methyl, ethyl or isopropyl benzenesulfonates. The primary deuterium isotope effects k_H/k_D are 5.27, 5.42 and 6.70 for X = p-CH₃O, H and p-NO₂. The ? values as well as the increase of k_H/k_D with introduction of p-NO₂ supply evidence for simultaneous C_αO and C_βH bond cleavages also in the E2 reactions of these compounds.     

Der A2+-Mechanismus der säurekatalytischen Hydrolyse von Epoxiden und anderen cyklischen Oxa- Verbindungen

It is suggested that the acid catalyzed hydrolyses of isobutene oxide and propene oxide proceed via rate-determining bimolecular reaction between a carbonium ion and solvent water (A2⁺ mechanism). The carbonium ion is formed by ring opening of the protonated epoxide, in a relatively fast preceding step. This mechanism is in agreement with all experimental facts known today. There is evidence for a similar mechanism in the acid catalyzed hydrolyses of cyclic acetals.     

Alstonia scholaris: Struktur des Indolalkaloides Narelin

Alstonia scholaris: The structure of the indole alkaloid nareline Besides the known akuammidine, picralinal, picrinine and pseudoakuammigine a new indole alkaloid called nareline (M=352) was isolated from Alstonia scholaris R. BR. , which belongs to the plant family of Apocynaceae. Its structure 2 was deduced by single crystal X-ray diffraction. 2 represents the absolute configuration. The spectroscopic data of 2 and its derivatives (Scheme 1) as well as their chemical behavior support this structure. In biogenetic sense nareline is related to the bases akuammiline ( 4 ) and picraline ( 5 ) (Scheme 2). In contrast to those the C-atom 5 is exocyclic and represents an aldehyde group which forms together with the oxygen atom of the N (4)-hydroxylamine group a cyclic half acetale. - By oxidation (CrO₃/CH₃COOH) of 2 the oxindol derivative 19 (oxonareline) is formed which contains a cyclic acetal as a partial structure element (Scheme 4).     

Objective comparison of concentration profiles in solids by means of mathematical statistics

To compare concentration profiles in solids in an objective manner, a multi-dimensional generalization of the comparison of two means by Student'st-test is proposed. The approach is based on piecewise modelling the profiles using rougha priori information, estimating the model parameters and their covariance matrix and comparing the estimated parameters by use of multidimensional test variables. The piecewise modelling is treated in the most important cases in such a way that the partial functions are straight lines or cubic polynoms (splines) with continuity at all knots in each case. It enables us to compare whole profiles as well as the most relevant parts of them. Two ways of estimating the covariance matrix as a generalization of the variance estimation are discussed. The approach is useful for any kind of line profiles if rough information on the profile type is available. As an example SIMS depth-profiles of aluminum obtained from thin-layer systems after different technological heat treatments are considered. These profiles are modeled by three straight lines.