Practical aspects of shimming a high resolution magic angle spinning probe

High resolution magic angle spinning (HRMAS) has become an extremely versatile tool to study heterogeneous systems. HRMAS relies on magic angle spinning of the sample to average out to zero magnetic susceptibility differences in the sample and to obtain resonance linewidths approaching those of liquid state NMR. Shimming such samples therefore becomes an important issue. By analyzing the different sources of magnetic field perturbations present in a sample under MAS conditions, we propose a simple protocol to obtain optimum shim settings in HRMAS. In the case of aqueous samples, we show that the lock level cannot be used as a reliable indicator of the quality of the shims at high spinning speeds. This effect is explained by the presence of temperature gradients imparted by the sample rotation.     

Ambient noise cross correlation in free space: theoretical approach

It has been experimentally demonstrated that the Green's function between two points could be recovered using the cross-correlation function of the ambient noise measured at these two points. This paper investigates the theory behind this result in the simple case of a homogeneous medium with attenuation.     

On quadratic fields with large 3-rank

Davenport and Heilbronn defined a bijection between classes of binary cubic forms and classes of cubic fields, which has been used to tabulate the latter. We give a simpler proof of their theorem then analyze and improve the table-building algorithm. It computes the multiplicities of the general cubic discriminants (real or imaginary) up to in time and space , or more generally in time and space for a freely chosen positive . A variant computes the -ranks of all quadratic fields of discriminant up to with the same time complexity, but using only units of storage. As an application we obtain the first real quadratic fields with , and prove that is the smallest imaginary quadratic field with -rank equal to .

     

High‐throughput characterization of pattern formation in symmetric diblock copolymer films

Surface‐pattern formation in thin block copolymer films was investigated by utilizing a high‐throughput methodology to validate the combinatorial measurement approach and to demonstrate the value of the combinatorial method for scientific investigation. We constructed measurement libraries from images of subregions of block copolymer films having gradients in film thickness and a range of molecular mass, M. A single gradient film covers a wide range of film morphologies and contains information equivalent to a large number of measurements of films having a fixed thickness, h. Notably, the scale of the surface patterns is generally much larger than the molecular dimensions so that the interpretation of the patterns is more subtle than ordering in bulk block copolymer materials, and there is no predictive theory of this type of surface‐pattern formation. We observed a succession of surface patterns that repeat across the film with increasing h [extended smooth regions, regions containing circular islands, labyrinthine (“spinodal”) patterns, holes, and smooth regions again]. The extended smooth regions and the labyrinthine patterns appear to be novel features revealed by our combinatorial study, and these patterns occurred as bands of h that were quantized by integral multiples of the bulk lamellar period, L_o. The magnitude of the height gradient influenced the width of the bands, and the smooth regions occupied an increasing fraction of the film‐surface area with an increasing film gradient. The average size of the spinodal patterns, λ, was found to scale as λ ～ L or λ ～ M^?1.65 and reached a limiting size at long annealing times. The hole and island features had a size comparable to λ, and their size likewise decreased with increasing M. The smooth regions were attributed to an increase in the surface‐chain density in the outer brushlike block copolymer layer with increasing h, and the scaling of λ with M was interpreted in terms of the increasing surface elasticity with M. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2141–2158, 2001     

A generalization of a theorem on biseparating maps

In J. Math. Anal. Appl. 12 (1995) 258–265, Araujo et al. proved that for any linear biseparating map  from C(X) onto C(Y), where X and Y are completely regular, there exist ω in C(Y) and an homeomorphism h from the realcompactification vX of X onto vY, such that

The compact version of this result was proved before by Jarosz in Bull. Canad. Math. Soc. 33 (1990) 139–144. In Contemp. Math., Vol. 253, 2000, pp. 125–144, Henriksen and Smith asked to what extent the result above can be generalized to a larger class of algebras. In the present paper, we give an answer to that question as follows. Let A and B be uniformly closed Φ-algebras. We first prove that every order bounded linear biseparating map from A onto B is automatically a weighted isomorphism, that is, there exist ω in B and a lattice and algebra isomorphism ψ between A and B such that

(a)=ωψ(a) for all aA.

We then assume that every universally σ-complete projection band in A is essentially one-dimensional. Under this extra condition and according to a result from Mem. Amer. Math. Soc. 143 (2000) 679 by Abramovich and Kitover, any linear biseparating map from A onto B is automatically order bounded and, by the above, a weighted isomorphism. It turns out that, indeed, the latter result is a generalization of the aforementioned theorem by Araujo et al. since we also prove that every universally σ-complete projection band in the uniformly closed Φ-algebra C(X) is essentially one-dimensional.     

Noise Figure Reduction in Externally Modulated Analog Fiber-Optic Links

An octave-bandwidth microwave photonic link with a third-order limited spurious-free dynamic range of 121 dB in a 1-Hz bandwidth has been demonstrated. The link noise figure of 9 dB at a modulation frequency of 2 GHz was achieved by using a bias-shifted Mach-Zehnder modulator with an optical input power of 500 mW. This level of performance was realized without electronic or optical linearization     

Everything over IP — an overview of the strategic change in voice and data networks

This paper investigates the changes that are required in networking technology for ‘everything over IP’ to become a reality. Initially the changes that are taking place in the telecommunications industry are reviewed. This review ranges from a discussion about the companies installing massive global IP networks to the emergence of novel routeing technologies, e.g. multi-protocol label switching (MPLS) and terabit router technologies. The role of existing telecommunications operators is then discussed, along with the reasons why they are developing interworking and intelligence layers based on distributed computing principles to support all their networks — mobile, fixed, broadband and IP.     

Role of interfacial chemistry on the rheology and thermo-mechanical properties of clay-polymer nanocomposites for building applications

This study is directed towards investigating the role of the surface treatment of clay particles on the rheological and thermomechanical behaviour of clay-epoxy blends. Nanocomposites were prepared by mixing small amounts (5–10 mass %) of commercial organoclays or raw clays with an epoxy system commonly used in civil engineering. Rheological characterisations in the liquid state revealed a pronounced thixotropic character of the organoclay-based systems, which all exhibited a shear-thinning behaviour above a critical stress threshold (yield stress), depending on both the intensity of interfacial interactions and the degree of filler dispersion. On the other hand, systems based on raw clay particles behaved like Newtonian fluids, in the same way as the unreinforced polymer matrix. Complementary dynamic mechanical analyses (DMA) performed on the cured cross-linked nanocomposites also showed significant changes in the viscoelastic behaviour of the epoxy matrix due to the introduction of organoclays, whereas only minor variations were observed following the introduction of raw fillers. These results were consistent with nanoscale morphological characterisations performed by conventional X-ray diffraction (XRD) on the various hybrid systems. In this context, rheology and DMA appear as attractive alternative methods for assessing the filler dispersion at a macroscopic (and possibly more relevant) scale. This research is of practical interest for civil engineers, since clay reinforced-epoxies could in the future be used as coating materials with enhanced barrier performances, in order to protect infrastructures against environmental ageing or corrosion.