Simultaneous chemical reaction and distillation of formaldehyde

The thesis is concerned with the development and testing of a mathematical model of a distillation process in which the components react chemically. The formaldehyde-methanol-water system was selected and only the reversible reactions between formaldehyde and water giving methylene glycol and between formaldehyde and methanol producing hemiformal were assumed to occur under the distillation conditions. Accordingly the system has been treated as a five component system. The vapour-liquid equilibrium calculations were performed by solving iteratively the thermodynamic relationships expressing the phase equilibria with the stoichiometric equations expressing the chemical equilibria. Using optimisation techniques, the Wilson single parameters and Henry's constants were calculated for binary systems containing formaldehyde which was assumed to be a supercritical component whilst Wilson binary parameters were calculated for the remaining binary systems. Thus the phase equilibria for the formaldehyde system could be calculated using these parameters and good accuracy was obtained when calculated values were compared with experimental values. The distillation process was modelled using the mass and energy balance equations together with the phase equilibria calculations. The plate efficiencies were obtained from a modified A.I.Ch.E. Bubble Tray method. The resulting equations were solved by an iterative plate to plate calculation based on the Newton Raphson method. Experiments were carried out in a 76mm I.D., eight sieve plate distillation column and the results were compared with the mathematical model calculations. Overall, good agreement was obtained but some discrepancies were observed in the concentration profiles and these may have been caused by the effect of limited physical property data and a limited understanding of the reactions mechanism. The model equations were solved in the form of modular computer programs. Although they were written to describe the steady state distillation with simultaneous chemical reaction of the formaldehyde system, the approach used may be of wider application.

A combinatorial approach to the chemical synthesis and biological evaluation of 3,4,5-trisubstiituted furan-2(5H)-ones

Many important natural products contain the furan-2(5H)-one structure. The structure of this molecule lends itself to manipulation using combinatorial techniques due to the presence of more than one site for the attachment of different suhstituents. By developing different reaction schemes at the three sites available for attachment on the furan-2(5H)-one scaffold, combinatorial chemistry techniques can be employed to assemble libraries of novel furan 2(5H)-ones. These libraries can then be entered into various biological screening programmes. This approach will enable a vast diversity or compounds to be examined, in the hope or finding new biologically active Iead structures. The work in this thesis has investigated the potential that combinatorial chemistry has in the quest for new biologically active lead structures based on the furan-2(5H)-one structure. Different reactions were investigated with respect to their suitability for inclusion in a library. Once sets of reactions at the various sites had been established, the viability of these reactions in the assembly of combinatorial libraries was investigated. Purification methods were developed, and the purified products entered into suitable biological screening tests. Results from some of these tests were optimised using structure activity relationships, and the resulting products re-screened. The screening tests performed were for anticancer and antimicrobial activity, cholecystokinin (CCK-B) antagonism and anti-inflammatory activity (in the quest for novel cyclo-oxygenase (COX-2) selective non-steroidal anti-inflammatory drugs). It has been shown that many reactions undergone by the furan-2(5H)-one structure are suitable for the assembly of a combinatorial library. Investigation into the assembly of different libraries has been carried out with initial screening results included. From this work, further investigation into combinatorial library assembly and structure activity relationships of screened reaction products can be undertaken.

Seminar 1 impurity in the tomonaga-luttinger model:a functional integral approach

This chapter explains a functional integral approach about impurity in the Tomonaga–Luttinger model. The Tomonaga–Luttinger model of one-dimensional (1D) strongly correlates electrons gives a striking example of non-Fermi-liquid behavior. For simplicity, the chapter considers only a single-mode Tomonaga–Luttinger model, with one species of right- and left-moving electrons, thus, omitting spin indices and considering eventually the simplest linearized model of a single-valley parabolic electron band. The standard operator bosonization is one of the most elegant methods developed in theoretical physics. The main advantage of the bosonization, either in standard or functional form, is that including the quadric electron–electron interaction does not substantially change the free action. The chapter demonstrates the way to develop the formalism of bosonization based on the functional integral representation of observable quantities within the Keldysh formalism.

Source localization of reaction-diffusion models for brain tumors

We propose a mathematically well-founded approach for locating the source (initial state) of density functions evolved within a nonlinear reaction-diffusion model. The reconstruction of the initial source is an ill-posed inverse problem since the solution is highly unstable with respect to measurement noise. To address this instability problem, we introduce a regularization procedure based on the nonlinear Landweber method for the stable determination of the source location. This amounts to solving a sequence of well-posed forward reaction-diffusion problems. The developed framework is general, and as a special instance we consider the problem of source localization of brain tumors. We show numerically that the source of the initial densities of tumor cells are reconstructed well on both imaging data consisting of simple and complex geometric structures.