The singularity in weakly nonlinear fracture mechanics

Material failure by crack propagation essentially involves a concentration of large displacement-gradients near a crack's tip, even at scales where no irreversible deformation and energy dissipation occurs. This physical situation provides the motivation for a systematic gradient expansion of general nonlinear elastic constitutive laws that goes beyond the first order displacement-gradient expansion that is the basis for linear elastic fracture mechanics (LEFM). A weakly nonlinear fracture mechanics theory was recently developed by considering displacement-gradients up to second order. The theory predicts that, at scales within a dynamic lengthscale ℓ from a crack's tip, significant logr displacements and 1/r displacement-gradient contributions arise. Whereas in LEFM the 1/r singularity generates an unbalanced force and must be discarded, we show that this singularity not only exists but is also necessary in the weakly nonlinear theory. The theory generates no spurious forces and is consistent with the notion of the autonomy of the near-tip nonlinear region. The J-integral in the weakly nonlinear theory is also shown to be path-independent, taking the same value as the linear elastic J-integral. Thus, the weakly nonlinear theory retains the key tenets of fracture mechanics, while providing excellent quantitative agreement with measurements near the tip of single propagating cracks. As ℓ is consistent with lengthscales that appear in crack tip instabilities, we suggest that this theory may serve as a promising starting point for resolving open questions in fracture dynamics.     

Two new polyketides from Hawaiian endophytic fungus Pestalotiopsis sp. FT172

Two new polyketides, pestalotiotones A (1) and B (2) were isolated from the cultured broth of Pestalotiopsis sp. FT172. The structures of compounds 1 and 2 were determined by analysis of HRMS and NMR spectroscopic data. The absolute configurations of compound 1 were assigned by Mosher reaction, J-based configuration analysis, and DP4 NMR calculations. Both compounds were tested against cancer cell lines, pathogenic fungi and bacteria.     

Persistent spectral-hole burning in the wide-gap semiconductor SiC doped with vanadium

Persistent spectral-hole burning was performed in the gamma line of V(4+) in the wide-gap semiconductor 6HSiC. Spectral holes burned at 11 K were stable to temperatures of at least 320 K for several days. The hole-burning mechanism consists of two-step photoionization of V(4+) (self-gated spectral-hole burning). The spectral holes could be erased optically, either by pumping of electrons back from stable traps or, presumably, by a charge-transfer transition from the valence band to the V(5+) ions.     

Bestimmung des germaniums mit hilfe eines radioaktiven germaniumisotops

Microchimica Acta - Die Überprüfung eines Analysenganges auf Germanium wurde mit Hilfe von radioaktivem Germanium 71 durchgeführt. Es zeigte sich, daß der Analysengang nicht...     

Aktivierungsanalytische Bestimmung von Verunreinigungen in Aluminium. V

Zusammenfassung Es wird ein Analysengang beschrieben, der es ermöglicht, nach Neutronenaktivierung die Elemente Antimon, Zinn, Scandium, Hafnium, Chrom, Kobalt, Eisen, Zink und Indium, die als Verunreinigungen im Aluminium auftreten und langlebige Isotope bilden, voneinander zu trennen und quantitativ zu bestimmen. Hierzu werden vorerst durch Destillation der Bromide Antimon und Zinn abgetrennt. Eine Trennung des Antimons vom Zinn beruht auf Sulfidfällung aus homogener Lösung. Die weitere Trennung erfolgt über den Ionenaustauscher Dowex 1×8 in 7-m HCl. Im Effluenten befinden sich Scandium, Hafnium und Chrom. Scandium und Hafnium werden daraus durch Tributylphosphatextraktion abgetrennt. Anschließend werden aus dem Austauscher mit 4-m HCl das Kobalt, schließlich mit Wasser das Eisen, Zink und Indium eluiert. Durch Chloridextraktion mit Diisopropyläther wird daraus das Eisen abgetrennt und anschließend durch Hydroxidfällung in ammoniakalischer Lösung das Indium vom Zink getrennt.Im Anschluß an den Analysengang werden zwei Schnellbestimmungsmethoden für Scandium und Antimon angegeben, die auf Extraktionsmethoden beruhen.

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Summary An analytical scheme is described which, following neutron activation, makes it possible to separate and quantitatively determine the elements antimony, tin, scandium, hafnium, chromium, cobalt, iron, zinc, indium which occur as impurities in aluminium and form long-lived isotopes. The first step removes antimony and tin by distillation of the bromides. The antimony is separated from the tin by sulfide precipitation from homogeneous solution. The further separation is accomplished by means of the ion exchanger Dowex 1×8 in 7M HCl. The effluents contain scandium, hafnium, and chromium. Scandium and hafnium are removed by extraction with tributyl phosphate. Then the cobalt is eluted from the exchange resin with 4M HCl, and finally the iron, zinc and indium are eluted with water. The iron is taken out by extracting the chloride mixture with diisopropyl ether, and then the indium is separated from zinc by hydroxide precipitation in ammoniacal solution.In connection with the analysis scheme, two rapid methods for scandium and antimony that are based on extraction procedures are described.

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Résumé On décrit un procédé d'analyse qui permet, après activation neutronique, de séparer les uns des autres et de doser les éléments antimoine, étain, scandium, hafnium, chrome, cobalt, fer, zinc et indium qui apparaissent comme impuretés dans l'aluminium et qui forment des isotopes de longue période. A cet effet, on sépare d'abord par distillation des bromures, l'antimoine et le zinc. Une séparation de l'antimoine d'avec le zinc repose sur la précipitation du sulfure en solution homogène. L'autre procédé s'effectue sur échangeur d'ions Dowex 1×8 dans HCl 7M. Le scandium, le hafnium et le chrome se trouve dans la partie éluée. On en sépare le scandium et le hafnium par extraction par le phosphate de tributyle. Enfin, le cobalt est élué de l'échangeur par HCl, puis le fer, le zinc et l'indium sont élués par l'eau. Le fer en est séparé par extraction du chlorure par l'éther diisopropylique et, finalement, l'indium est séparé du zinc par précipitation de l'hydroxyde en solution ammoniacale.A la fin du procédé d'analyse, on indique deux méthodes de dosage rapide pour le scandium et l'antimoine, reposant sur deux procédés d'extraction.

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IV. Mitteilung: Radiochimica Acta (im Druck).     

Lösungsmittelextraktion der Elemente Ruthenium und Osmium

Zusammenfassung An den beiden Elementen Ruthenium und Osmium wurden Lösungs-mittelextraktionsversuche vorgenommen. Es wurde eine Vorschrift zur Extraktion von Ruthenium(VII) mit Tetraphenylarsoniumchlorid-Chloroform ausgearbeitet. 96 bis 98% des Rutheniums konnten in einem Arbeitsgang extrahiert werden.Für die Extraktion des Osmiums mit dem flüssigen Anionenaustauscher LA-1 wurde eine Vorschrift ausgearbeitet, die einen Verteilungskoeffizienten von 24 ergibt.Durch die beiden angeführten Extraktionsmethoden läßt sich eine Trennung der beiden Elemente Ruthenium und Osmium bequem durchführen.

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Summary Solvent extraction trials were made with both ruthenium and osmium. A procedure was developed for the extraction of ruthenium(VII) with tetraphenylarsonium chlorid-chloroform. It was possible to extract 96 to 98% of the ruthenium in a single operation. A method for extraction of osmium with the liquid anion exchanger LA-1 was worked out. The two elements ruthenium and osmium can be readily separated by means of the two extraction methods.

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Résumé On a entrepris des recherches sur l'extraction par un solvant de deux éléments, le ruthénium et l'osmium. On a mis au point un mode opératoire pour extraire le ruthénium-VII par le système chlorure de tétraphénylarsonium-chloroforme. On peut extraire ainsi 96 à 98% du ruthénium.On a mis au point un mode opératoire pour l'extraction de l'osmium par l'échangeur anionique liquide LA-I, qui donne un coefficient de partage de 24.On peut réaliser commodément une séparation des deux éléments, ruthénium et osmium, au moyen des deux méthodes d'extraction indiquées.

     

Solvation phenomena in dilute multicomponent solutions I. Formal results and molecular outlook

We derive second-order thermodynamically consistent truncated composition expansions for the species residual partial molar properties--including volume, enthalpy, entropy, and Gibbs free energy--of dilute ternary systems aimed at the molecular account of solvation phenomena in compressible media. Then, we provide explicit microscopic interpretation of the expansion coefficients in terms of direct and total correlation function integrals over the microstructure of the corresponding infinite dilution reference system, as well as their pressure and temperature derivatives, allowing for the direct prediction of the species partial molar properties from the knowledge of the effective intermolecular interactions. Finally, we apply these formal results (a) to derive consistent expressions for the corresponding properties of the binary system counterparts, (b) to illustrate how the formal expressions converge, at the zero density limit, to those for multicomponent mixtures of imperfect gases obeying the virial equation of state Z = 1 + BPkT, and (c) to discuss, and highlight with examples from the literature, the thermodynamic inconsistencies encountered in the currently available first-order truncated expansions, by pinpointing the mathematical origin and physical meaning of the inconsistencies that render the first-order truncated expansions invalid.     

Switching Diarylethenes Reliably in Both Directions with Visible Light

A diarylethene photoswitch was covalently connected to two small triplet sensitizer moieties in a conjugated and nonconjugated fashion and the photochromic performance of the resulting compounds was investigated. In comparison with the parent diarylethene (without sensitizers) and one featuring saturated linkages, the conjugated photoswitch offers superior fatigue resistance upon visible‐light excitation due to effective triplet energy transfer from the biacetyl termini to the diarylethene core. Our design makes it possible to switch diarylethenes with visible light in both directions in a highly efficient and robust fashion based on extending π‐conjugation and by‐product‐free ring‐closure via the triplet manifold.     

Harmonic functions of linear growth on solvable groups

We answer a question posed by Bonilla and Grosse-Erdmann by showing that the operators P(D) on the space of entire functions H(C), where D is the differentiation operator and P is a polynomial, do not possess a frequently hypercyclic subspace.