On the adjacent equilibrium method in the stability theory of conservative elastic continua

The relationship of the adjacent equilibrium method, the regular perturbation method and the energy method for neutral equilibrium is studied. It is shown that unlike the adjacent equilibrium method, the regular perturbation method yields, for the problems under consideration, non-homogeneous perturbation equations and that adjacent states of equilibrium do not exist at the bifurcation point. These results are then compared with the result of the energy criterion for neutral equilibrium V₂[u] = 0. It is found that although the physical arguments are different in the three methods, the resulting stability equations are identical; thus showing why the adjacent equilibrium argument, even for cases when it is incorrect, yields correct critical loads. This is followed by a discussion of an incorrect derivation of a stability condition and a notion about a load type introduced in the stability literature, which are consequences of the assumption of the general existence of adjacent equilibrium states at bifurcation points.     

Stability of a water tower

Summary The stability of a water tower, consisting of a spherical shell rigidly attached to the top of a vertical column, is analyzed. At first, it is shown on a simple conceptual model that problems of this type are imperfection insensitive; thus, the first bifurcation load from the straight state of equilibrium could be considered the buckling load. This is followed by the analysis of the water tower problem taking into consideration the flexibility of the column, the own weight of the structure, the weight of the liquid, and the rotational stiffness of the soil base. Although the differential equation of the resulting eigenvalue problem has a variable coefficient, the problem is solved exactly in closed form. To simplify the utilization of the obtained results, they are presented graphically for a range of water tower and soil stiffness parameters. Model tests were conducted that confirmed the analytical findings. However, nearP _cr , at the smallest disturbance the model underwent large oscillatory motions. This finding suggests that, for water tower design, only a fraction ofP _cr should be used.

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Stabilität eines Wasserturms

Übersicht Untersucht wird die Stabilität eines Wasserturms aus einer senkrechten Säule mit kugelförmigem Behälter an der Spitze. Zunächst wird anhand einer einfachen Modellabstraktion nachgewiesen, daß Probleme dieser Art unempfindlich sind gegen Imperfektionen; deshalb kann die erste aus dem geraden Gleichgewichtszustand führende Verzweigungslast als Knicklast angesehen werden. Es schließt sich die Untersuchung des Wasserturms mit Nachgiebigkeit und Eigengewicht der Säule, mit Gewicht von Behälter und Inhalt sowie Drehsteifigkeit des Fundaments an. Die Lösung des Eigenwertproblems, dessen Differentialgleichung einen variablen Koeffizienten besitzt, läßt sich geschlossen angeben. Zur bequemen Anwendung werden die Ergebnisse für weite Parameterberciche von Turm und Fundament graphisch dargestellt. Durchgeführte Modellversuche unterstützen die analytischen Ergebnisse. Allerdings vollführte das Modell in der Nähe der kritischen LastP _cr selbst bei kleinsten Störungen große Schwingbewegungen. Deshalb sollte bei einer Auslegung nur ein Bruchteil vonP _cr zugrunde gelegt werden.

     

Development of chiral heteroleptic magnesium amides; asymmetric deprotonations mediated by six-membered metallocyclic amidomagnesium naphtholates

A series of enantioenriched six-membered metallocyclic amidomagnesium naphtholates were prepared and used to probe the structure–reactivity/selectivity relationships of heteroleptic magnesium base complexes within asymmetric deprotonation reactions. An effective complex was identified and applied within enantioselective enolisation processes, delivering good levels of enantioselectivity and also revealing key structural requirements for achieving such selectivity.     

Influence of precursor solvent extraction on stable isotope signatures of methylamphetamine prepared from over-the-counter medicines using the Moscow and Hypophosphorous routes

A number of methods of clandestine manufacture of methylamphetamine involve the extraction and subsequent reaction of pseudoephedrine hydrochloride with other essential chemicals. The precursor can be easily extracted from over-the-counter medication widely available in the UK and elsewhere. Essential chemicals such as iodine and red phosphorous are also readily available and can be extracted from iodine tinctures and matchboxes, respectively. This work reports the repetitive preparation of methylamphetamine using two popular routes (the Moscow and Hypophosphorous synthesis). The focus was on the extraction solvent used for isolation of the precursor chemical and any consequential isotopic variation which may arise in the final product. Six batches of methylamphetamine were prepared under precisely controlled conditions for each synthetic route and for each of three different precursor extraction solvents. Synthesis of the final product from laboratory grade precursor using the synthetic methods described was used as a template for comparison. The resultant IRMS data from all 48 prepared samples suggests some underlying trends in the identification of the synthetic route which may aid in the interpretation of IRMS data derived from clandestine samples.     

Controlled Synthesis of Large Single Crystals of Metal-Organic Framework CPO-27-Ni Prepared by a Modulation Approach: In situ Single-Crystal X-ray Diffraction Studies

The size of single crystals of the metal-organic framework CPO-27-Ni was incrementally increased through a series of modulated syntheses. A novel linker modulated synthesis using 2,5-dihydroxyterephthalic acid and the isomeric ligand 4,6-dihydroxyisophthalic acid yielded large single crystals of CPO-27-Ni (∼70 μm). All materials were shown to have high crystallinity and phase purity through powder X-ray diffraction, electron microscopy methods, thermogravimetry, and compositional analysis. For the first time single-crystal structure analyses were carried out on CPO-27-Ni. High BET surface areas and nitric oxide (NO) release efficiencies were recorded for all materials. Large single crystals of CPO-27-Ni showed a prolonged NO release and proved suitable for in situ single-crystal diffraction experiments to follow the NO adsorption. An efficient activation protocol was developed, leading to a dehydrated structure after just 4 h, which subsequently was NO-loaded, leading to a first NO loaded single-crystal structural model of CPO-27-Ni.     

Iridium(I)‐Catalyzed Regioselective CH Activation and Hydrogen‐Isotope Exchange of Non‐aromatic Unsaturated Functionality

Isotopic labelling is a key technology of increasing importance for the investigation of new C?H activation and functionalization techniques, as well as in the construction of labelled molecules for use within both organic synthesis and drug discovery. Herein, we report for the first time selective iridium‐catalyzed C?H activation and hydrogen‐isotope exchange at the β‐position of unsaturated organic compounds. The use of our highly active [Ir(cod)(IMes)(PPh₃)][PF₆] (cod=1,5‐cyclooctadiene) catalyst, under mild reaction conditions, allows the regioselective β‐activation and labelling of a range of α,β‐unsaturated compounds with differing steric and electronic properties. This new process delivers high levels of isotope incorporation over short reaction times by using low levels of catalyst loading.     

Iridium-Catalyzed Formyl-Selective Deuteration of Aldehydes

We report the first direct catalytic method for formyl-selective deuterium labeling of aromatic aldehydes under mild conditions, using an iridium-based catalyst designed to favor formyl over aromatic C−H activation. A good range of aromatic aldehydes is selectively labeled, and a one-pot labeling/olefination method is also described. Computational studies support kinetic product control over competing aromatic labeling and decarbonylation pathways.     

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