Variational Integrators for Interconnected Lagrange–Dirac Systems

Interconnected systems are an important class of mathematical models, as they allow for the construction of complex, hierarchical, multiphysics, and multiscale models by the interconnection of simpler subsystems. Lagrange–Dirac mechanical systems provide a broad category of mathematical models that are closed under interconnection, and in this paper, we develop a framework for the interconnection of discrete Lagrange–Dirac mechanical systems, with a view toward constructing geometric structure-preserving discretizations of interconnected systems. This work builds on previous work on the interconnection of continuous Lagrange–Dirac systems (Jacobs and Yoshimura in J Geom Mech 6(1):67–98, 2014) and discrete Dirac variational integrators (Leok and Ohsawa in Found Comput Math 11(5), 529–562, 2011). We test our results by simulating some of the continuous examples given in Jacobs and Yoshimura (2014).     

Nonlinear Taylor stability of viscoelastic fluids

Using Stuart's energy method, the torque on the inner cylinder, for a second order fluid, in the supercritical regime is calculated. It is found that when the second normal stress difference is negative, the flow is more stable than for a Newtonian fluid and the torque is reduced. If the second normal stress difference is positive, then the flow is more stable and there is no torque reduction. Experimental data related to the present work are discussed.Nomenclature a amplitude of the fundamentals - A _ij ⁽¹⁾ , A _ij ⁽²⁾ first and second Rivlin-Ericksen tensors - d r ₂–r ₁ - D d/dx - E - F - g _ij metric tensor - G torque on the inner cylinder in the supercritical regime - h height of the cylinders - k ₀ /d ² - k ₁ /d ² - I ₁ - I ₂ - I ₃ - I ₄ - r ₁, r ₂ radii of inner and outer cylinders respectively - r ₀ 1/2(r ₁+r ₂) - R Reynolds number ₁ r ₁ d/ ₀ - R _c critical Reynolds number - T Taylor number r _{1 1} ² d ^{3 2}/ ₀ ² *) - T _c critical Taylor number - u ₁, v ₁, w ₁ Fundamentals of the disturbance - u _i , v _i , w _i , (i>1) harmonics - mean velocity (not laminar velocity) - u –u ₁/ar _{1 1} - v v ₁/Rar _{1 1} - x (r–r ₀)/d - , material constants - 0 viscosity - wave number d - density - ₁ angular velocity of inner cylinder - tilde denotes complex conjugate     

Studies on Immobilization and Partial Characterization of Lipases from Wheat Seeds (<Emphasis Type="Italic">Triticum aestivum</Emphasis>)

The objective of this study was to provide some features on immobilization and partial characterization of lipases from wheat seeds. The optimum pH and temperature were found to be 5.5 and 32–37 °C, respectively. The stability of the concentrated enzymatic extract to high temperatures (25, 35, 45, and 55 °C) showed that the incubation of the extract at 55 °C led to its complete inactivation. The concentrated enzymatic extract kept 90% of its hydrolytic and esterification activities until 70 and 40 days of storage at 4 °C, respectively. The extract presented higher hydrolytic specificity to substrates of medium and long chains and higher esterification affinity to fatty acids of short and medium chains and alcohols with two and three carbon atoms. After the immobilization process using activated coal and sodium alginate as supports, an enhancement of about threefold in lipase activity was observed. The development of the present work permitted us to point out some characteristics of lipases from wheat seeds necessary for the proposition of new future industrial applications for this important biocatalyst.     

Aryl-aryl bond formation by the fluoride-free cross-coupling of aryldisiloxanes with aryl bromides

The prevalence of the biaryl structural motif in biologically interesting and synthetically important molecules has inspired considerable interest in the development of methods for aryl-aryl bond formation. Herein we describe a novel strategy for this process involving the fluoride-free, palladium-catalysed cross-coupling of readily accessible aryldisiloxanes and aryl bromides. Using a statistical-based optimisation process, preparatively useful reaction conditions were formulated to allow the cross-coupling of a wide range of different substrates. This methodology represents an attractive, cost-efficient, flexible and robust alternative to the traditional transition-metal-catalysed routes typically used to generate molecules containing the privileged biaryl scaffold.     

Investigating the provenance of un-dyed spun cotton fibre using multi-isotope profiles and chemometric analysis

The analysis of un-dyed spun cotton fibres can be challenging within a forensic science context where discrimination of one fibre from another is of importance. Conventional microscopic and chemical analysis of these fibres is generally unsuccessful because of their similar morphology. In this work we have explored the potential of isotope ratio mass spectrometry (IRMS) as a tool for spun cotton fibre analysis in an attempt to reveal any discriminatory information available. Seven different batches of un-dyed spun cotton fibre from four different countries were analysed. A combination of the hydrogen and oxygen isotopic data facilitated the correct association of the samples, demonstrating, for the first time, the applicability of IRMS to fibre analysis in this way.     

Dissociation techniques in mass spectrometry-based proteomics

The field of proteomics, the large-scale analysis of proteins, has undergone a huge expansion over the past decade. Mass spectrometry-based proteomics relies on the dissociation of peptide and/or protein ions to provide information on primary sequence and sites of post-translational modifications. Fragmentation techniques include collision-induced dissociation, electron capture dissociation and electron transfer dissociation. Here, we describe each of these techniques and their use in proteomics. The principles, advantages, limitations, and applications are discussed.     

Synthesis and Characterization of Antimony(III) Complexes of Thioamides,and Crystal Structure of {[Sb(Imt)2Cl2]2((2‐Imt)}Cl2(Imt=Imidazolidine‐2‐thione)

Antimony(III) complexes of thioamides [thioamides=thiourea (Tu), N,N′‐dimethylthiourea (Dmtu), tetramethylthiourea (Tmtu), imidazolidine‐2‐thione (Imt) and diazinane‐2‐thione (Diaz)] with the general formulae, Sb(thione)_nCl₃ (n=1, 2, 2.5, 3) were prepared and characterized by elemental analysis, IR and NMR (¹H, ¹³C) spectroscopic methods. The spectral data of the complexes are consistent with the coordination of the thiones to antimony(III). The crystal structure of one of them, {[Sb(Imt)₂Cl₂]₂(μ₂‐Imt)}Cl₂ ( 1 ), was determined by X‐ray crystallography, which shows that the complex is dinuclear consisting of two [Sb(Imt)₂Cl₂] units bridged by an Imt molecule. In 1 , the antimony atom is bonded to two chlorine atoms, two sulfur atoms of coordinated Imt molecules and one sulfur atom of a bridging Imt molecule. The antimony environment can be considered to be distorted octahedral with one Cl^? ion weakly bound to antimony.     

Formation of gallaoxetanes: C-O activation of 1,2-epoxybutane by ground-state Ga atoms

(69/71)Ga atoms were reacted with 1,2-epoxybutane and its isotopomers, 1,2-epoxybutane-1,1-d(2) (CH(3)CH(2)CHOCD(2)) and 1,2-epoxybutane-2-d(1) (CH(3)CH(2)CDOCH(2)), under matrix-isolation conditions. The novel gallaoxetanes CH(3)CH(2)CHCH(2)GaO and CH(3)CH(2)CHCH(2)OGa, resulting from the insertion of the metal atom in the C(1)-O and C(2)-O bonds, respectively, of the 1,2-epoxybutane, were detected by EPR spectroscopy. The Ga and H hyperfine interaction (hfi) values of the gallaoxetanes, calculated using a DFT method, were used to help assign the EPR spectra. A third Ga-centered species, detected at 190 K, underwent spectral changes similar to those of the C(2)-O insertion product upon isotopic substitution of the 1,2-epoxybutane. Although the Ga hfi for this species was 36% smaller than that of the C(2)-O insertion product, the values for the H hfi were similar, suggesting that the carrier of the spectrum was the C(2)-O insertion product where Ga was perturbed by the matrix constraints. The alkyl radical CH(3)CH(2)(?CH)CH(2)OGa, resulting from ring-opening at the C(2)-O bond of 1,2-epoxybutane, was observed at temperatures below 150 K. This radical has been implicated in the formation of the C(2)-O insertion product. The unusually small value found for two of the β-hydrogens of the alkyl radical is discussed.     

An efficient approach to azirino and pyrrolo-fused dibenzazepines. Conformations of substituted dibenzo[c,f]pyrrolo[1,2-a]azepines

An effective approach to azepino-fused heterocycles is described. trans-1-Aryl-7,11b-dihydro-1H-azirino[1,2-a]dibenzo[c,f]azepines were synthesised via a domino sequence: isomerization of gem-dichloroaziridine-intramolecular Friedel-Crafts acylation of the tethered benzene ring catalysed by SnCl(4) and subsequent hydride induced intramolecular cyclization. Cycloaddition of dibenzazepinium ylides, generated by heating these aziridines, to activated C[double bond]C, C[triple bond]C dipolarophiles and fullerene C(60), leads to derivatives of dibenzo[c,f]pyrrolo[1,2-a]azepine. The reaction proceeds with complete stereoselectivity via cycloaddition of only W-ylide, which due to the high barrier does not undergo E,Z-isomerization under the reaction conditions. It was found that 2,3,9,13b-tetrahydro-1H-dibenzo[c,f]pyrrolo[1,2-a]azepine systems can exist in conformations of two types depending on the substituents at the pyrrolidine carbons in β-position with respect to nitrogen. Details of cycloaddition reactions and the conformational behavior of cycloadducts were studied by DFT calculations at the B3LYP/6-31G(d) level.     

Inorganic approaches for radiolabelling biomolecules with fluorine-18 for imaging with positron emission tomography

Conventional methods for radiolabelling biomolecules such as proteins and peptides with fluorine-18 for PET imaging rely on carbon-fluorine bond formation and are complex and inefficient. Several non-carbon elements form strong bonds (i.e. with high bond enthalpy) with fluorine, but with lower activation energy for their formation compared to carbon-fluorine bonds, whilst preserving a relatively high kinetic stability. In particular, by incorporating boron-, aluminium- and silicon-containing prosthetic groups into biomolecules, promising results have recently been achieved in the radiolabelling with F-18-fluoride under mild aqueous conditions, affording a level of convenience, efficiency and specific activity potentially superior to those offered by conventional C-F bond formation methods. The promise already shown by these early studies heralds a new branch of bioconjugate radiochemistry involving a wider range of "fluoridephilic" elements for synthesis of PET molecular imaging agents.