A study of eddy-current couplings with and without endrings

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Fundamental Pd0/PdII redox steps in cross-coupling reactions:homogeneous, hybrid homogeneous-heterogeneous to heterogeneous mechanistic pathways for C-C couplings

C–C bond-forming, cross-coupling reactions of organohalides with nucleophilic compounds, catalysed by palladium, are amongst the most important chemical reactions available to the synthetic chemist. The intimate mechanisms of these reactions, involving Pd0/PdII redox steps, have been of great historical interest and continue to be so. The myriad of possible mechanisms is reviewed in this chapter. The interplay of mononuclear Pd species with higher order Pd species, e.g. nanoclusters/nanoparticles are considered as being equally important in cross-coupling reaction mechanisms. A focus is placed on trichotomic behaviour of cross-coupling catalytic manifolds, from homogeneous to hybrid homogeneous–heterogeneous to truly heterogeneous behaviour. For the latter, surface chemistry and metal atom leaching (and various experimental techniques) are broadly discussed. It is now clear that mechanism for general cross‐coupling reactions, that is as presented to undergraduate students studying Chemistry degrees across the world, is undoubtedly more complex than first thought. New opportunities for catalyst design have therefore emerged in the area of Pd nanoparticles and nanocatalysis, with some wonderful applications especially in chemical biology, providing a snapshot of what the future might hold.

The TAP approach to intensive and extensive connectivity systems

The Thouless-Anderson-Palmer (TAP) approach was originally developed for analysing the Sherrington-Kirkpatrick model in the study of spin glass models and has been employed since then mainly in the context of extensively connected systems whereby each dynamical variable interacts weakly with the others. Recently, we extended this method for handling general intensively connected systems where each variable has only O(1) connections characterised by strong couplings. However, the new formulation looks quite different with respect to existing analyses and it is only natural to question whether it actually reproduces known results for systems of extensive connectivity. In this chapter, we apply our formulation of the TAP approach to an extensively connected system, the Hopfield associative memory model, showing that it produces identical results to those obtained by the conventional formulation.

Evaluation of the sonically induced narrowing of nuclear magnetic resonance spectra of solids

The Nuclear Magnetic Resonance (NMR) spectra of liquids contain a wealth of quantitative information that may be derived, for instance, from chemical shifts and spin-spin couplings. The available information depends on the incoherent rapid molecular motion that causes complicating effects present in the solid state to average to zero. Whereas liquid state NMR spectra show narrow lines, the corresponding NMR spectra from the solid state are normally composed of exceedingly broad resonance lines due to highly restricted molecular motion. It is, therefore, difficult to obtain directly as detailed information from the spectra of solids as from those derived from the liquid state. Studies on a new technique (SINNMR, the sonically induced narrowing of the NMR spectra of solids) to remove line broadening effects in the NMR spectra of the solid state are reported within this thesis. SINNMR involves narrowing the NMR absorptions from solid particles by irradiating them with ultrasound when they are suspended in a support liquid. It is proposed that ultrasound induces incoherent motion of the suspended particles, producing motional characteristics of the particles similar to those of rather large molecules. The first report of apparently successful experiments involving SINNMR[1] emphasised both the irreproducibility of the technique and the uncertainty regarding its true origin. If SINNMR can be made reproducible and the effect definitively attributed to the sonically induced incoherent motional averaging of particles, the technique could offer a simple alternative to the now classical magic-angle spinning (MAS) NMR[2] and the recently reported dynamic angle spinning (DAS)[3] and double rotation (DOR)[4] techniques. Evidence is presented in this thesis to support the proposal that ultrasound may be used to narrow the NMR spectral resonances from solids by inducing incoherent motion of particles suspended in support liquids and, additionally, for some solids, by inducing rotational motion of molecular constituents in the lattices of solids. Successful SINNMR line narrowing using 20 kHz ultrasound is reported for a variety of samples: including trisodium orthophosphate, polytetrafluoroethylene and aluminium alloys. Investigations of SINNMR line narrowing in trisodium phosphate have revealed the relationship between ultrasonic power, particle size and support liquid density for the production of optimum SINNMR conditions. It is also proposed that the incoherent motion of particles induced by 20 kHz ultrasound can originate from interactions between acoustically induced cavitation microjets and particles.

Development of novel NMR pulse sequences

To elucidate the structures of orgamc molecules in solution using pulse FT NMR, heteronuclear pulse sequence experiments to probe carbon-13 (13C) and proton (1H) spin systems are invaluable. The one-dimensional insensitive nucleus detected PENDANT experiment finds popular use for structure determination via one-bond 13C-1H scalar couplings. PENDANT facilitates the desired increase in 13C signal-to-noise ratio, and unlike many other pulse sequence experiments (e.g., refocused INEPT and DEPT), allows the simultaneous detection of 13C quaternary nuclei. The tlrst chapter herein details the characterisation of PENDANT and the successful rectification of spectral anomalies that occur when it is used without proton broadband decoupling. Multiple-bond (long-range) l3C-1H scalar coupling correlations can yield important bonding information. When the molecule under scrutiny is devoid of proton spectral crowding, and more sensitive 'inverse' pulse sequence experiments are not available, one may use insensitive nucleus detected long-range selective one-dimensional correlation methods, rather than more time consuming and insensitive multidimensional analogues. To this end a novel long-range selective one-dimensional correlation pulse sequence experiment has been invented. Based on PENDANT, the new experiment is shown to rival the popular selective INEPT technique because it can determine the same correlations while simultaneously detecting isolated 13C quaternary nuclei. INEPT cannot facilitate this, potentially leaving other important quaternary nuclei undetected. The novel sequence has been modified further to yield a second novel experiment that simultaneously yields selective 13C transient nOe data. Consequently, the need to perform the two experiments back-to-back is conveniently removed, and the experimental time reduced. Finally, the SNARE pulse sequence was further developed. SNARE facilitates the reduction of experimental time by accelerating the relaxation of protons upon which pulse sequences, to which SNARE is appended, relies. It is shown, contrary to the original publication, that reiaxation time savings can be derived from negative nOes.

Applications of differential geometry to high spin field theories

The main aim of this thesis is to investigate the application of methods of differential geometry to the constraint analysis of relativistic high spin field theories. As a starting point the coordinate dependent descriptions of the Lagrangian and Dirac-Bergmann constraint algorithms are reviewed for general second order systems. These two algorithms are then respectively employed to analyse the constraint structure of the massive spin-1 Proca field from the Lagrangian and Hamiltonian viewpoints. As an example of a coupled field theoretic system the constraint analysis of the massive Rarita-Schwinger spin-3/2 field coupled to an external electromagnetic field is then reviewed in terms of the coordinate dependent Dirac-Bergmann algorithm for first order systems. The standard Velo-Zwanziger and Johnson-Sudarshan inconsistencies that this coupled system seemingly suffers from are then discussed in light of this full constraint analysis and it is found that both these pathologies degenerate to a field-induced loss of degrees of freedom. A description of the geometrical version of the Dirac-Bergmann algorithm developed by Gotay, Nester and Hinds begins the geometrical examination of high spin field theories. This geometric constraint algorithm is then applied to the free Proca field and to two Proca field couplings; the first of which is the minimal coupling to an external electromagnetic field whilst the second is the coupling to an external symmetric tensor field. The onset of acausality in this latter coupled case is then considered in relation to the geometric constraint algorithm.

Design methodology for the servo control of high speed multi-axis machinery (BL): decoupling and synchronisation of a generic machine by blockwise decentralised MIMO control

Traditional machinery for manufacturing processes are characterised by actuators powered and co-ordinated by mechanical linkages driven from a central drive. Increasingly, these linkages are replaced by independent electrical drives, each performs a different task and follows a different motion profile, co-ordinated by computers. A design methodology for the servo control of high speed multi-axis machinery is proposed, based on the concept of a highly adaptable generic machine model. In addition to the dynamics of the drives and the loads, the model includes the inherent interactions between the motion axes and thus provides a Multi-Input Multi-Output (MIMO) description. In general, inherent interactions such as structural couplings between groups of motion axes are undesirable and needed to be compensated. On the other hand, imposed interactions such as the synchronisation of different groups of axes are often required. It is recognised that a suitable MIMO controller can simultaneously achieve these objectives and reconciles their potential conflicts. Both analytical and numerical methods for the design of MIMO controllers are investigated. At present, it is not possible to implement high order MIMO controllers for practical reasons. Based on simulations of the generic machine model under full MIMO control, however, it is possible to determine a suitable topology for a blockwise decentralised control scheme. The Block Relative Gain array (BRG) is used to compare the relative strength of closed loop interactions between sub-systems. A number of approaches to the design of the smaller decentralised MIMO controllers for these sub-systems has been investigated. For the purpose of illustration, a benchmark problem based on a 3 axes test rig has been carried through the design cycle to demonstrate the working of the design methodology.

Typical case behaviour of spin systems in random graph and composite ensembles

This thesis includes analysis of disordered spin ensembles corresponding to Exact Cover, a multi-access channel problem, and composite models combining sparse and dense interactions. The satisfiability problem in Exact Cover is addressed using a statistical analysis of a simple branch and bound algorithm. The algorithm can be formulated in the large system limit as a branching process, for which critical properties can be analysed. Far from the critical point a set of differential equations may be used to model the process, and these are solved by numerical integration and exact bounding methods. The multi-access channel problem is formulated as an equilibrium statistical physics problem for the case of bit transmission on a channel with power control and synchronisation. A sparse code division multiple access method is considered and the optimal detection properties are examined in typical case by use of the replica method, and compared to detection performance achieved by interactive decoding methods. These codes are found to have phenomena closely resembling the well-understood dense codes. The composite model is introduced as an abstraction of canonical sparse and dense disordered spin models. The model includes couplings due to both dense and sparse topologies simultaneously. The new type of codes are shown to outperform sparse and dense codes in some regimes both in optimal performance, and in performance achieved by iterative detection methods in finite systems.

Reactive processing of polymers: structural characterization of products by 1H and 13C NMR spectroscopy for glycidyl methacrylate grafting onto EPR in the absence and presence of a reactive comonomer

Grafted GMA on EPR samples were prepared in a Thermo-Haake internal mixer by free radical melt grafting reactions in the absence (conventional system; EPR-g-GMA(CONV)) and presence of the reactive comonomer divinyl benzene, DVB (EPR-g-GMA(DVB)). The GMA-homopolymer (poly-GMA), a major side reaction product in the conventional system, was almost completely absent in the DVB-containing system, the latter also resulted in a much higher level of GMA grafting. A comprehensive microstructure analysis of the formed poly-GMA was performed based on one-dimensional H-1 and C-13 NMR spectroscopy and the complete spectral assignments were supported by two-dimensional NMR techniques based on long range two and three bond order carbon-proton couplings from HMBC (Heteronuclear Multiple Bond Coherence) and that of one bond carbon-proton couplings from HSQC (Heteronuclear Single Quantum Coherence), as well as the use of Distortionless Enhancement by Polarization Transfer (DEPT) NMR spectroscopy. The unambiguous analysis of the stereochemical configuration of poly-GMA was further used to help understand the microstructures of the GMA-grafts obtained in the two different free radical melt grafting reactions, the conventional and comonomer-containing systems. In the grafted GMA, in the conventional system (EPR-g-GMA(CONV)), the methylene protons of the GMA were found to be sensitive to tetrad configurational sequences and the results showed that 56% of the GMA sequence in the graft is in atactic configuration and 42% is in syndiotactic configuration whereas the poly-GMA was predominantly syndiotactic. The differences in the microstructures of the graft in the conventional EPR-g-GMA(CONV) and the DVB-containing (EPR-g-GMA(DVB)) systems is also reported (C) 2009 Elsevier Ltd. All rights reserved.

True chemical shift correlation maps:a TOCSY experiment with pure shifts in both dimensions

Signal resolution in H NMR is limited primarily by multiplet structure. Recent advances in pure shift NMR, in which the effects of homonuclear couplings are suppressed, have allowed this limitation to be circumvented in 1D NMR, gaining almost an order of magnitude in spectral resolution. Here for the first time an experiment is demonstrated that suppresses multiplet structure in both domains of a homonuclear two-dimensional spectrum. The principle is demonstrated for the TOCSY experiment, generating a chemical shift correlation map in which a single peak is seen for each coupled relationship, but the principle is general and readily extensible to other homonuclear correlation experiments. Such spectra greatly simplify manual spectral analysis and should be well-suited to automated methods for structure elucidation. © 2010 American Chemical Society.

Generalized mean field approximation for parallel dynamics of the Ising model

The dynamics of the non-equilibrium Ising model with parallel updates is investigated using a generalized mean field approximation that incorporates multiple two-site correlations at any two time steps, which can be obtained recursively. The proposed method shows significant improvement in predicting local system properties compared to other mean field approximation techniques, particularly in systems with symmetric interactions. Results are also evaluated against those obtained from Monte Carlo simulations. The method is also employed to obtain parameter values for the kinetic inverse Ising modeling problem, where couplings and local field values of a fully connected spin system are inferred from data. © 2014 IOP Publishing Ltd and SISSA Medialab srl.

Surface catalysed Suzuki-Miyaura cross-coupling by Pd nanoparticles:an operando XAS study

Size-controlled, catalytically active PVP-stabilised Pd nanoparticles have been studied by operando liquid phase XAS during the Suzuki cross-coupling of iodonanisole and phenylboronic acid in MeOH-toluene using KOMe base. XAS reveals nanoparticles are stable to metal leaching throughout the reaction, with surface density Pd defect sites directly implicated in the catalytic cycle. The efficacy of popular selective chemical and structural poisons for distinguishing heterogeneous and homogeneous contributions in Pd catalysed cross-couplings is also explored. © 2010 The Royal Society of Chemistry.

Investigating the role of capacitive coupling between the operating table and the return electrode of an electrosurgery unit in the modification of the current density distribution within the patients’ body

Background: Electrosurgery units are widely employed in modern surgery. Advances in technology have enhanced the safety of these devices, nevertheless, accidental burns are still regularly reported. This study focuses on possible causes of sacral burns as complication of the use of electrosurgery. Burns are caused by local densifications of the current, but the actual pathway of current within patient's body is unknown. Numerical electromagnetic analysis can help in understanding the issue. Methods: To this aim, an accurate heterogeneous model of human body (including seventy-seven different tissues), electrosurgery electrodes, operating table and mattress was build to resemble a typical surgery condition. The patient lays supine on the mattress with the active electrode placed onto the thorax and the return electrode on his back. Common operating frequencies of electrosurgery units were considered. Finite Difference Time Domain electromagnetic analysis was carried out to compute the spatial distribution of current density within the patient's body. A differential analysis by changing the electrical properties of the operating table from a conductor to an insulator was also performed. Results: Results revealed that distributed capacitive coupling between patient body and the conductive operating table offers an alternative path to the electrosurgery current. The patient's anatomy, the positioning and the different electromagnetic properties of tissues promote a densification of the current at the head and sacral region. In particular, high values of current density were located behind the sacral bone and beneath the skin. This did not occur in the case of non-conductive operating table. Conclusion: Results of the simulation highlight the role played from capacitive couplings between the return electrode and the conductive operating table. The concentration of current density may result in an undesired rise in temperature, originating burns in body region far from the electrodes. This outcome is concordant with the type of surgery-related sacral burns reported in literature. Such burns cannot be immediately detected after surgery, but appear later and can be confused with bedsores. In addition, the dosimetric analysis suggests that reducing the capacity coupling between the return electrode and the operating table can decrease or avoid this problem. © 2013 Bifulco et al.; licensee BioMed Central Ltd.