Dynamic supercoiling bifurcations of growing elastic filaments

Certain bacteria form filamentous colonies when the cells fail to separate after dividing. In Bacillus subtilis, Bacillus thermus, and Cyanobacteria, the filaments can wrap into complex supercoiled structures as the cells grow. The structures may be solenoids or plectonemes, with or without branches in the latter case. Any microscopic theory of these morphological instabilities must address the nature of pattern selection in the presence of growth, for growth renders the problem nonautonomous and the bifurcations dynamic. To gain insight into these phenomena, we formulate a general theory for growing elastic filaments with bending and twisting resistance in a viscous medium, and study an illustrative model problem: a growing filament with preferred twist, closed into a loop. Growth depletes the twist, inducing a twist strain. The closure of the loop prevents the filament from unwinding back to the preferred twist; instead, twist relaxation is accomplished by the formation of supercoils. Growth also produces viscous stresses on the filament which even in the absence of twist produce buckling instabilities. Our linear stability analysis and numerical studies reveal two dynamic regimes. For small intrinsic twist the instability is akin to Euler buckling, leading to solenoidal structures, while for large twist it is like the classic writhing of a twisted filament, producing plectonemic windings. This model may apply to situations in which supercoils form only, or more readily, when axial rotation of filaments is blocked. Applications to specific biological systems are proposed.     

Growth kinetics of iron boride layers: Dimensional analysis

Dimensional analysis is presented as a powerful tool in the study of the paste boriding process. In particular, a dimensional method is used to study the growth kinetics of the boride layers FeB and Fe₂B. Experiments were performed in AISI 1045 steel and AISI M2 steel, to test the suggested model. Samples of 1045 steel were prepared and treated using boron paste thickness of 3-5 mm, at temperatures of 1193, 1223 and 1273 K, with 2, 4 and 6 h of treatment time. The M2 specimens had boron paste thickness of 3 and 4 mm and temperatures of 1223, 1253 and 1273 K for 2 and 6 h. Results indicate that the growth of boron layers obeys power laws of the form y = αx^β, where α and β constants are a function of the material and the interface of interest. Validation of the model was carried out using experimental data with an average error percentage of 7.6% for Fe₂B in 1045 steel, 15.8% for FeB and 3.4% for Fe₂B in M2 steel.     

Fluorinations with complex metal fluorides. Part 6 [1] fluorination of yridine and related compounds with caesium tetrafluorocobaltate(III) [2]

Pyridine has been fluorinated over caesium tetrafluorocobaltate(III) (CsCo^IIIF₄) at 300–400°C to give a mixture of undecafluoro-N-methylpyrrolidine, bis(trifluoromethyl)amine, pentafluoropyridine and several polyfluoropyridines; the product composition depended to some extent on the geometry of the reactor. The fluorinations of pentafluoropyridine, piperidine and undecafluoropiperidine were also investigated.     

Pythagorean euclidean four point properties

Characterizations of real inner product spaces among a class of metric spaces have been obtained based on homogeneity of metric pythagorean orthogonality, a metrization of the concept of pythagorean orthogonality as defined in normed linear spaces. In the present paper a considerable weakening of this hypothesis is shown to characterize real inner product spaces among complete, convex, externally convex metric spaces, generalizing a result of Kapoor and Prasad [9], and providing a connection with the many characterizations of such spaces using euclidean four point properties.     

Search for cosmic γ-ray bursts in the (1÷50) GeV energy range

Summary A search for cosmic gamma-ray bursts in the GeV energy range has been performed by means of the EAS-TOP Extensive Air Shower array at Campo Imperatore (Gran Sasso Laboratories) during the period March–December 1990. In 2566.5 hours of measurement the obtained upper limit to the rate of bursts of amplitude >2% of the cosmic-ray intensity and time duration τ=1 s, isR≤7.9y⁻¹ (90% c.l.). Assuming for γ-rays a differential energy spectrumS(E ₀ )≈E ₀ ^−2.5 , the corresponding upper limit to the energy flux of γ-rays with energy >5 GeV in bursts of duration τ≤1 s is Φ<8.3·10⁻⁵erg cm⁻².     

Complete assignment of the 1H and 13C NMR Spectra of 11,12-Dimethoxy[1]benzothieno[3,2-a]-4,7-phenanthroline and its 8-Chloro Analogue: Concerted Use of Two-Dimensional NMR Techniques

The ¹H and ¹³C nmr spectra of 11,12-dimethoxy[1]benzothieno[3,2-a]-4,7-phenanthroline and its 8-chloro precursor were totally assigned using a combination of two-dimensional nmr techniques. After correlation of the majority of the proton signals by a COSY spectrum and one-bond heteronuclear correlation, the full assignment of the ¹H and ¹³C nmr spectra of the novel heterocyclic compounds required the application of long-range CH coupling information particularly for quaternary carbon resonance assignments and the orientations of individual spin systems relative to one another. Key long-range heteronuclear couplings in both compounds served to confirm the one-bond heteronuclear correlations. Unequivocal interpretation of the spectral data leads to the complete assignments of the resonances.