A hyperbranched,rotaxane‐type mechanically interlocked polymer

Based on the dibenzo‐24‐crown‐8/1,2‐bis(pyridinium)ethane recognition motif, a hyperbranched mechanically interlocked polymer was prepared by polyesterification of an easily available dynamic trifunctional AB₂ pseudorotaxane monomer. It was characterized by various techniques including ¹H NMR, COSY, NOESY, GPC, viscosity, TGA, dynamic laser light scattering, AFM, and SEM. Its GPC M_n was determined to be 191 kDa with polydispersity 1.7 and its hydrodynamic diameter in a dilute solution in acetone was about 70 nm. This measured M_n value corresponds to about 93 repeating units. The study reported here presents not only a new polymer topology but also a novel and convenient way to prepare mechanically interlocked polymers. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 4067–4073, 2010     

A note on anisotropic,inhomogeneous, poro‐elastic media

A modification of the material law associated with the well‐known Biot system as suggested by Murad and Cushman (Int. J. Eng. Sci. 1996; 34(3):313–338) and first investigated by Showalter (J. Math. Anal. Appl. 2000; 251(1):310–340) is reconsidered, generalized and analysed in the light of a new approach to a comprehensive class of evolutionary problems. The framework allows a uniform approach to problems involving general anisotropic, inhomogeneous, non‐smooth media thus covering, for example, transmission problems in layered materials. Copyright © 2009 John Wiley & Sons, Ltd.     

Dynamic observations of interface motion during the oxidation of silicon

We describe real time observations of the behaviour of the silicon-oxide interface during oxidation in situ in an ultrahigh vacuum transmission electron microscope. We have formed clean, flat Si(111) surfaces by heating under UHV and allowed oxidation or oxygen etching to proceed in the microscope. We have examined the kinetics of both the oxidation and etching reactions using an imaging technique based on the use of forbidden reflections in silicon. We find that oxidation to form SiO₂ occurs by the reaction of discrete monolayers with no flow of surface steps. This is in dramatic contrast to oxygen etching, during which the volatile oxide SiO evaporates preferentially from step edges.     

Dynamics of peptides with fixed geometry: Kinetic energy terms and potential energy derivatives as functions of dihedral angles

Expressions are derived for computing the kinetic energy of a peptide with fixed geometry, in terms of dihedral angles as generalized coordinates; other expressions required for the solution of Lagrange's equations are also presented. The peptide is regarded as held stationary at one end. We also outline the computations that are needed in calculating the components of the third derivative of a potential energy function that consists of a sum of pairwise interatomic interactions.     

Letter to the Editor: Stockwell and Wavelet Transforms

Recent applied literature introduces the Stockwell transform (S-transform) as a new approach to time-frequency analysis. It is the purpose of this letter to encourage the interaction between the wavelet and the Stockwell communities by demonstrating that—up to minor modifications—the S-transform is a special case of the well-known continuous wavelet transform via a Morlet-type mother wavelet, with the features of a linear frequency scale, and an amplitude and modulation adjustment in phase space. The extensive research and applications obtained for the continuous wavelet transform can therefore be directly applied to the Stockwell domain.     

The First Turbulence and First Fossil Turbulence

A model is proposed connecting turbulence, fossil turbulence and the big-bang origin of the universe. While details are incomplete, the model is consistent with our knowledge of these processes and is supported by observations. Turbulence arises in a hot big-bang quantum gravitational dynamics scenario at Planck scales. Chaotic, eddy-like motions produce an exothermic Planck particle cascade from 10^?35 m at 10³² K to 10⁸ larger, 10⁴ cooler, quark-gluon scales. A Planck-Kerr instability gives high Reynolds number (Re ～ 10⁶) turbulent combustion, space-time-energy-entropy and turbulent mixing. Batchelor-Obukhov-Corrsin turbulent-temperature fluctuations are preserved as the first fossil turbulence by inflation stretching the patterns beyond the horizon ct of causal connection faster than light speed c in time t～ 10^?33 sec. Fossil big-bang temperature turbulence reenters the horizon and imprints nucleosynthesis of H-He densities that seed fragmentation by gravity at 10¹² s in the low Reynolds number plasma before its transition to gas at t～ 10¹³ s and T～ 3000 K. Multiscaling coefficients of the cosmic microwave background (CMB) temperature anisotropies closely match those for high Reynolds number turbulence, Bershadskii, A. and Sreenivasan, K.R., Phys. Lett. A 299 (2002) 149-152; Bershadskii, A. and Sreenivasan, K.R., Phys. Lett. A 319 (2003) 21-23. CMB spectra support the interpretation that big-bang turbulence fossils triggered fragmentation of the viscous plasma at supercluster to galaxy mass scales from 10⁴⁶ to 10⁴² kg, Gibson, C.H., Appl. Mech. Rev. 49 (5) (1996) 299-315; Gibson, C.H., J. Fluids Eng. 122 (2000) 830-835; Gibson, C.H., Combust. Sci. Technol. (2004, to be published).     

Turbulent boundary layer on a mildly curved convex surface

Mean flow and turbulence measurements have been made in a boundary layer which grows first on a flat' wall and then on a convex wall of radius of curvature approximately 100 times the boundary layer thickness. The turbulence data include profiles of the four non-zero components of the Reynolds stress tensor and three triple velocity products obtained at five stream-wise positions. A number of measurements were also made for comparison in the boundary layer on a flat wall under the same conditions. The effects of convex curvature are to reduce turbulent intensities, shear stress and wall friction by approximately 10% of their plane flow values; the triple velocity products are halved in the curved layer. The measurements supplement the small quantity of previously published data available for testing mathematical models of turbulence. The results show the same general trends that have been observed in earlier investigations but there are significant differences in detail, notably in respect of levels of the normal stresses.