Analytical solutions for heat transfer on fractal and pre-fractal domains

Fractals can be used to represent intricate self-similar geometries, but their application to the representation of physical systems is beset with difficulties which stem from an inability to define traditionally derived-physical quantities such as stress, pressure, strain, heat etc. This paper describes a method for the determination of analytical heat-transfer solutions on pre-fractal and fractal domains. The approach requires the construction of maps from pre-fractal domains to the continuum, which facilitate the application of traditional continuum solution methods. Solutions on fractal domains are achievable with this approach, and are defined to be the limit solution of analytical solutions obtained on the pre-fractals approximating the fractal of interest. This approach avoids many of the complications and technical difficulties arising from the use of measure theory and fractional derivatives, but also infers that the governing heat transfer equations are valid on all pre-fractals. The fractals considered are necessarily deterministic and relatively simple in form to demonstrate the solution methodology. The solutions presented are limited to one and two-dimensional domains and, in 1-D, are applied to an idealised composite material consisting of relatively small particles of infinitely low thermal conductivity embedded in a relatively large matrix of infinitely high thermal conductivity. The fractal composite system is thus not truly representative of a realistic physical system, but the methods presented do serve to demonstrate how analytical solutions can be attained on dust-like fractal domains. It is demonstrated that a measurable temperature is possible on a fractal structure along with finite measures of heat flux and energy. Transient and steady state thermal solutions are presented. The solutions on a selection of the pre-fractals are compared against finite element predictions to reinforce the validity of the approach.     

Facile, diversity-orientated one-pot synthesis of ethyl 1,5-disubstituted-1H-1,2,4-triazole-3-carboxylates

Access to the 1,5-disubstituted-1H-1,2,4-triazole-3-carboxamide motif is quite laborious and requires forcing conditions to effect the cyclocondensation step. Herein, we report an efficient and mild one-pot protocol to access this substructure in good chemical yields with high regiocontrol.     

A topological approach to canonical extensions in finitely generated varieties of lattice-based algebras

This paper investigates completions in the context of finitely generated lattice-based varieties of algebras. It is shown that, for such a variety A, the order-theoretic conditions of density and compactness which characterise the canonical extension of (the lattice reduct of) any A∈A have truly topological interpretations. In addition, a particular realisation is presented of the canonical extension of A; this has the structure of a topological algebra nA(A) whose underlying algebra belongs to A. Furthermore, each of the operations of nA(A) coincides with both the σ-extension and the π-extension of the corresponding operation on A, with which a canonical extension is customarily equipped. Thus, in particular, the variety A is canonical, and all its operations are smooth. The methods employed rely solely on elementary order-theoretic and topological arguments, and by-pass the subtle theory of canonical extensions that has been developed for lattice-based algebras in general.     

The isolation of a metastable conglomerate using a combined computational and controlled crystallization approach

While the use of additives to control the crystallization of polymorphs is well known, similar methodology to promote the crystallization of a metastable conglomerate over a stable racemic compound in enantiomeric systems has not been reported. Here we demonstrate this phenomenon in the case of 2-chloromandelic acid.     

Crystallography Aided by Atomic Core-Level Binding Energies: Proton Transfer versus Hydrogen Bonding in Organic Crystal Structures

Ionic bond or hydrogen bridge? Br?nsted proton transfer to nitrogen acceptors in organic crystals causes strong N1s core-level binding energy shifts. A study of 15 organic cocrystal and salt systems shows that standard X-ray photoelectron spectroscopy (XPS) can be used as a complementary method to X-ray crystallography for distinguishing proton transfer from H-bonding in organic condensed matter.     

Computation of Nielsen numbers for maps of closed surfaces

Let be a closed surface, and let be a map. We would like to determine Nielsen fixed point theory provides a lower bound for , called the Nielsen number, which is easy to define geometrically and is difficult to compute.

We improve upon an algebraic method of calculating developed by Fadell and Husseini, so that the method becomes algorithmic for orientable closed surfaces up to the distinguishing of Reidemeister orbits. Our improvement makes tractable calculations of Nielsen numbers for many maps on surfaces of negative Euler characteristic. We apply the improved method to self-maps on the connected sum of two tori including classes of examples for which no other method is known. We also include the application of this algebraic method to maps on the Klein bottle . Nielsen numbers for maps on were first calculated (geometrically) by Halpern. We include a sketch of Halpern's never published proof that for all maps on .

     

New procedure for the preparation of highly sterically hindered alkenes using a hypervalent iodine reagent

New methodology is described to construct the olefinic bond in overcrowded alkenes using a hypervalent iodine reagent, and applied in the synthesis of molecular motors.     

Membrane-introduction mass spectrometry (MIMS)

Membrane-introduction mass spectrometry (MIMS) for chemical analysis involves directly sampling analytes in gaseous, liquid and solid samples through a semi-permeable membrane coupled to a mass spectrometer, yielding selective and sensitive quantitation. Because MIMS is an on-line technique, in which samples can be continuously flowed over a membrane interface, it can yield analytical results in real time without the need for sample clean-up and chromatographic separation. This review highlights trends and developments in MIMS over the past decade and describes recent studies that pertain to its use for on-site, in-situ and in-vivo chemical analysis. We report on advancements in instrumentation, including membrane materials, interface configurations and ionization techniques that have extended the range of analytes amenable to MIMS.We summarize the progress made in the miniaturization of mass spectrometers that have resulted in field-portable systems and review recent applications of continuous mobile monitoring and on-site environmental monitoring to yield both temporally and spatially resolved quantitative and semi-quantitative data. Finally, we describe recent work involving the use of MIMS for in-vivo chemical analysis.     

Discrimination of organic acids using a three molecule array based upon cruciform fluorophores

A small array was obtained from three reactive cruciform fluorophores in six different solvents. The array discerned 10 different aromatic carboxylic acids by protonation-induced fluorescence shifts, which were recorded by digital photography. This simple array can discern acids that have closely spaced pK(a) values.