Humphry Davy and the Problem of Analogy

Analogy, the comparison of one set of relations to another, was essential to Humphry Davy’s understanding of chemistry. Throughout his career, Davy used analogical reasoning to direct and to interpret his experimental analyses of the chemical reactions between substances. In his writing, he deployed analogies to organise and to explain his theories about the relations between physical processes and between the properties of different chemical elements and compounds. But Davy also regularly expressed two concerns about analogical comparison: first, that it was founded not on the rational interpretation of facts but on imaginative speculation; and second, that it was a kind of rhetoric, the persuasiveness of which depended not on material evidence but on misleading figures of speech. This article discusses the influences that informed Davy’s ambivalent assessment of the value of analogy, and it examines the distinct yet overlapping ways in which this assessment was expressed in his notebooks, his lectures and treatises on chemistry, his philosophical writings, and his poetry.     

One-pot metal templated synthesis for the preparation of 2-quinoxalinol salen metal complexes

Metal complexes of 2-quinoxalinol salen (salqu) ligands can be prepared in a one-pot metal templated synthesis resulting in significantly enhanced yields than if the ligand were prepared and isolated prior to introducing the metal for complexation. Using this method, 12 salqu metal complexes have been prepared and characterized from +2 metal ions.     

Electrochemical screening of biomembrane-active compounds in water

Interactions of biomembrane-active compounds with phospholipid monolayers on microfabricated Pt/Hg electrodes in an on-line high throughput flow system are demonstrated by recording capacitance current peak changes as rapid cyclic voltammograms (RCV). Detection limits of the compounds’ effects on the layer have been estimated from the data. Compounds studied include steroids, polycyclic aromatic hydrocarbons, tricyclic antidepressants and tricyclic phenothiazines. The results show that the extent and type of interaction depends on the—(a) presence and number of aromatic rings and substituents, (b) presence and composition of side chains and, (c) molecular shape. Interaction is only indirectly related to compound hydrophobicity. For a selection of tricyclic antidepressants and tricyclic phenothiazines the detection limit in water is related to their therapeutic normal threshold. The sensing assay has been tested in the presence of humic acid as a potential interferent and in a tap water matrix. The system can be applied to the screening of putative hazardous substances and pharmaceuticals allowing for early detection thereof in the water supply. The measurements are made in real time which means that potentially toxic compounds are detected rapidly within <10 min per assay. This technology will contribute greatly to environment safety and health.     

The center of the 3-dimensional and 4-dimensional Sklyanin algebras

LetA=A(E, ) denote either the 3-dimensional or 4-dimensional Sklyanin algebra associated to an elliptic curveE and a point E. Assume that the base field is algebraically closed, and that its characteristic does not divide the dimension ofA. It is known thatA is a finite module over its center if and only if is of finite order. Generators and defining relations for the centerZ(A) are given. IfS=Proj(Z(A)) andA is the sheaf ofO _S -algebras defined byA(S _(f))=A[f ^–1]₀ then the centerL ofA is described. For example, for the 3-dimensional Sklyanin algebra we obtain a new proof of M. Artin's result thatSpec L². However, for the 4-dimensional Sklyanin algebra there is not such a simple result: althoughSpec L is rational and normal, it is singular. We describe its singular locus, which is also the non-Azumaya locus ofA.     

Virial Expansion Bounds

In the 1960s, the technique of using cluster expansion bounds in order to achieve bounds on the virial expansion was developed by Lebowitz and Penrose (J. Math. Phys. 5:841, 1964) and Ruelle (Statistical Mechanics: Rigorous Results. Benjamin, Elmsford, 1969). This technique is generalised to more recent cluster expansion bounds by Poghosyan and Ueltschi (J. Math. Phys. 50:053509, 2009), which are related to the work of Procacci (J. Stat. Phys. 129:171, 2007) and the tree-graph identity, detailed by Brydges (Phénomènes Critiques, Systèmes Aléatoires, Théories de Jauge. Les Houches 1984, pp. 129–183, 1986). The bounds achieved by Lebowitz and Penrose can also be sharpened by doing the actual optimisation and achieving expressions in terms of the Lambert W-function. The different bound from the cluster expansion shows some improvements for bounds on the convergence of the virial expansion in the case of positive potentials, which are allowed to have a hard core.     

Transient solutions for three-dimensional lid-driven cavity flows by a least-squares finite element method

A time-accurate least-squares finite element method is used to simulate three-dimensional flows in a cubic cavity with a uniform moving top. The time- accurate solutions are obtained by the Crank-Nicolson method for time integration and Newton linearization for the convective terms with extensive linearization steps. A matrix-free algorithm of the Jacobi conjugate gradient method is used to solve the symmetric, positive definite linear system of equations. To show that the least-squares finite element method with the Jacobi conjugate gradient technique has promising potential to provide implicit, fully coupled and time-accurate solutions to large-scale three-dimensional fluid flows, we present results for three-dimensional lid-driven flows in a cubic cavity for Reynolds numbers up to 3200.