Some bounds for quantities associated with two-dimensional anisotropic media

Zusammenfassung Es werden Ungleichheiten für einige mit gewissen anisotropen Stoffen assoziierte Grössen hergeleitet, analog denen, die in früheren Mitteilungen für die Torsionsfestigkeit orthotroper Zylinder gewonnen wurden.     

Pointwise and Other Decay Estimates for an Isotropic Elastic Strip

This paper is concerned with an homogeneous isotropic linear elastic strip, in plane strain. It is supposed that its lateral boundaries are displacement-free and that the deformation is generated by actions on the ends. A cross-sectional measure of deformation, complementing that of a previous paper, is defined and shown to satisfy a generalised convexity condition in the axial variable x ₁, for materials with negative Poisson's ratio σ. An enhanced measure is subsequently defined, and, in the case of a semi-infinite strip, is shown to yield pointwise exponential decay estimates for both the axial and the transverse displacement components for materials with positive Poisson's ratio. This revised version was published online in July 2006 with corrections to the Cover Date.     

The development of a novel smart mid-infrared sensing methodology for residual solvents

The potential of a novel polymer modified mid-infrared technique as a ‘smart’ sensing methodology is demonstrated. Diffusion of a penetrant (analyte molecule) was monitored into a Teflon® AF2400 membrane through observation of one of its infrared absorption bands. During the diffusion of select analytes, mid-IR polymer bands were observed to experience a red shift (reduction in absorption frequency). The rate of appearance of these bands matched that of analyte diffusion. As these bands are specific to certain analytes, and their intensity is analyte-dependent, monitoring of these shifted bands forms the basis of a ‘smart’ sensing regime. The suitability of this smart sensing methodology for the enhanced detection of several residual solvents is presented. A fivefold increase in sensitivity through the monitoring of these bands was realized for the detection of ethylbenzene. One of the aims of this work was to determine whether the cause of the polymer band shifting is chemical or optical in nature. Result data presented support the hypothesis that polymer/diffusant interactions cause this band shifting. This is demonstrated by the fact that a penetrant (tetrahydrofuran), which affected a band shift in the polymer, displayed a blue shift (increase in absorption frequency) in its own spectrum. Ethanol did not cause a polymer band shift and displayed no band shifts in its absorbance spectrum. The relative absorbance of the shifted polymer bands is compared between analytes and does not demonstrate a correlation to analyte refractive indices supporting a polymer/diffusant interaction hypothesis.     

The first example of molecularly imprinted nanogels with aldolase type I activity

The molecular-imprinting approach was used to obtain a nanogel preparation capable of catalysing the cross-aldol reaction between 4-nitrobenzaldehyde and acetone. A polymerisable proline derivative was used as the functional monomer to mimic the enamine-based mechanism of aldolase type I enzymes. The diketone template used to create the cavity was designed to imitate the intermediate of the aldol reaction and was bound to the functional monomer using a reversible covalent interaction prior to polymerisation. By using a high-dilution polymerisation method, soluble imprinted nanogels were prepared with dimensions similar to those of an enzyme and with the advantage of solubility and flexibility previously unattainable with monolithic polymers. Following template removal and estimation of active-site concentrations, the kinetic characterisation of both imprinted and non-imprinted nanogels was carried out with catalyst concentrations between 0.7 and 3.5 mol %. Imprinted nanogel AS147 was found to have a k(cat) value of 0.25 x 10(-2) min(-1), the highest value ever achieved with imprinted polymers catalysing C--C bond formation. Comparison of the catalytic constants for both imprinted nanogel AS147 and non-imprinted nanogel AS133 gave a ratio of k(cat 147)/k(cat 133)=18.8, which is indicative of good imprinting efficiency and highlights the significance of the template during the imprinting process. This work represents a significant demonstration of the superiority of nanogels, when the molecular-imprinting approach is used, over "bulk" polymers for the generation of catalysts.     

A nonlinear fourth order diffusion problem: Convergence to the steady state and non-negativity of solutions

The paper deals with nonlinear diffusion, both time-dependent and time-independent. The spatial terms in the partial differential equation (p.d.e.) contain a second order nonlinear part (where the non-negative diffusivity depends on the dependent variable) and a fourth order linear part. In the context of non-null, time-independent boundary conditions, convergence of the unsteady to the steady state is established. The second part of the paper discusses criteria on data ensuring non-negativity of the solutions. This is done for the steady state irrespective of the spatial dimension; and it is done for the unsteady state for the one-dimensional rectilinear case only, using a result from the first part of the paper.     

A comparison of polymeric materials as pre-concentrating media for use with ATR/FTIR sensing

Polymer-modified ATR-FTIR spectroscopy was investigated to determine its potential suitability for use as an analytical methodology for process stream analysis. The process stream under investigation contains toluene, tetrahydrofuran, ethanol, and acetonitrile in an aqueous matrix. Four polymers, Teflon® AF2400, poly(acrylonitrile-co-butadiene) (PAB), polydimethylsiloxane (PDMS), and poly(styrene-co-butadiene) (PSB), were chosen for study based on partition coefficients measured using a novel automated GC technique. Polymer suitability as pre-concentration media was assessed utilizing analyte/polymer diffusion coefficient data, equilibrium absorbance values, water ingress, and polymer plasticization. PAB displayed the fastest sensing times and enhanced sensitivities. Teflon® AF2400 demonstrated a low water absorption and a low degree of plasticization. Other factors affecting the diffusion rate of analytes were also investigated including molecular size, shape and analyte concentration. This research demonstrated that the choice of pre-concentrating medium is not a trivial issue, being dictated by a combination of sensitivity constraints as well as polymer robustness in real sample matrices.     

Cross-diffusion influence on the non-linear L2-stability analysis for a Lotka Volterra reaction diffusion system of PDEs

The paper considers non-linear stability and instability ofthe zero solutions of a pair of reaction–diffusion partialdifferential equations, which incorporate both self-diffusionand cross-diffusion, and non-linear source/forcing terms dependingon the dependent variables. Both Dirichlet and Neumann boundaryconditions are considered. Lyapunov functionals are used toobtain the stability and instability criteria.     

A Versatile Approach for Synthesis of 2,3-Dimethyl Chroman-4-ones,Intermediate for Calanolide Anti-HIV Agents,VIA Aldol/Mitsunobu Reactions

Combined aldol/Mitsunobu reactions have been employed for the first time for synthesis of 2,3-dimethyl chroman-4-ones, intermediates for calanolide anti-HIV agents. Thus, the lithium enolate of chromene 1 reacted with acetaldehyde at -78°C to afford the aldol products 4 and 5. Under Mitsunobu conditions (Ph₃P/DEAD), the syn aldol product 4 led to the formation of trans-2,3-dimethyl chroman-4-one 2 while the anti aldol product 5 yielded both trans and cis derivatives (2 and 3). The use of other phosphorous and azo compounds in this reaction has also been investigated.