Thesis (Doctor of Science)--University of Michigan, 1937. / eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Thesis (Sc. D.)--University of Michigan, 1934. / "This paper was presented at the 26th semi-annual meeting of the American institute of chemical engineers, New York, N.Y., May, 1934, and is reprinted from volume no. 30 of the Transactions." "References dealing with distillation and vapor-liquid equilibria": p. 26-27.

Thesis (Ph. D.)--University of Michigan, 1934. / Cover title. Caption title: Design of fractionating columns. III. Plate efficiency and number of plates for petroleum columns [by] Sidney Charles Singer, jr., Roy Russell Wilson, and George Granger Brown. "Reprinted from Industrial and engineering chemistry, vol. 28 ... July, 1936." Bibliography: p. 835.

Thesis (Ph. D.)--Colorado State University, 2004. / Includes bibliographical references.

The paper deals with a three variable analogues of certain fractional integral operators introduced by M. Saigo. Resides giving three variable analogues of earlier known fractional integral operators of one variable as a special cases of newly defined operators, the paper establishes certain results in the form of theorems including integration by parts.

Fractional calculus, which is a generalization of classical calculus, has been the subject of numerous applications in physics and engineering during the last decade. In this thesis, fractional calculus has been implemented for chemical engineering applications, namely in process control and in the modeling mass transfer in adsorption. With respect to process control, some researchers have proposed fractional PIλDμ controllers based on fractional calculus to replace classical PI and PID controllers. The closed-loop control of different benchmark dynamic systems using optimally-tuned fractional PIλDμ controllers were investigated to determine for which dynamic systems this more computationally-intensive controller would be beneficial. Four benchmark systems were used: first order plus dead time system, high order system, nonlinear system, and first order plus integrator system. The optimal tuning of the fractional PIλDμ controller for each system was performed using multi-objective optimization minimizing three performance criteria, namely the ITAE, OZ, and ISDU. Conspicuous advantages of using PIλDμ controllers were confirmed and compared with other types of controllers for these systems. In some cases, a PIλ controller was also a good alternative to the PIλDμ controller with the advantage of being less computationally intensive. For the optimal tuning of fractional controllers for each benchmark dynamic system, a new version of the non-dominated sorting genetic algorithm (NSGA-III) was used to circumscribe the Pareto domain. However, it was found that for the tuning of PIλDμ controllers, it was difficult to circumscribe the complete Pareto domain using NSGA-III. Indeed, the Pareto domain obtained was sometimes fragmentary, unstable and/or susceptible to user-defined parameters and operators of NSGA-III. To properly use NSGA-III and determine a reliable Pareto domain, an investigation on the effect of these user-defined operators and parameters of this algorithm was performed. It was determined that a reliable Pareto domain was obtained with a crossover operator with a significant extrapolation component, a Gaussian mutation operator, and a large population. The findings on the proper use of NSGA-III can also be used for the optimization of other systems. Fractional calculus was also implemented in the modeling of breakthrough curves in packed adsorption columns using finite differences. In this investigation, five models based on different assumptions were proposed for the adsorption of butanol on activated carbon. The first four models are based on integer order partial differential equations accounting for the convective mass transfer through the packed bed and the diffusion and adsorption of an adsorbate within adsorbent particles. The fifth model assumes that the diffusion inside adsorbent particles is potentially anomalous diffusion and expressed by a fractional partial differential equation. For all these models, the best model parameters were determined by nonlinear regression for different sets of experimental data for the adsorption of butanol on activated carbon. The recommended model to represent the breakthrough curves for the two different adsorbents is the model that includes diffusion within the adsorbent particles. For the breakthrough experiments for the adsorption of butanol on activated carbon F-400, it is recommended using a model which accounts for the inner diffusion within the adsorbent particles. It was found that instantaneous or non-instantaneous adsorption models can be used. Best predictions were obtained with fractional order diffusion with instantaneous adsorption. For the adsorption of butanol on activated carbon Norit ROW 0.8, it is recommended using an integer diffusion model with instantaneous adsorption. The gain of using fractional order diffusion equation, given the intensity in computation, was not sufficient to recommend its use.

University of Macau / Faculty of Science and Technology / Department of Mathematics

The production of uniform-sized drops without small follower drops or "trailers" in liquid-liquid systems was studied using a periodic injection technique for dispersing one liquid through a sharp edged nozzle into the other. Previous investigators using a continuous flow technique found that uniform sized drops without trailers were limited to systems of higher interfacial tension. The effects of nozzle inside diameter, nozzle material, and of velocity-time profile of the dispersed fluid through a nozzle at drop formation were examined using two systems; n-butanol and water of very low interfacial tension, and methyl isobutyl ketone and water of low interfacial tension. These two systems were chosen so that the results of this study could be integrated with other work. The velocity-time profiles were obtained by using a positive displacement bellows pump, the stroke of which was controlled by a cam follower through a variable ratio linkage using three different cam profiles. The conditions under which uniform sized drops without trailers were formed, were located for both systems. The effects of surface active contaminants and the wetting of the nozzle tip by the dispersed phase were considered. / Applied Science, Faculty of / Chemical and Biological Engineering, Department of / Graduate

In this dissertation, a new numerical method for solving fractional calculus problems is presented. The method is based upon the fractional Taylor vector approximations. The operational matrix of the fractional integration for the fractional Taylor vector is introduced. This matrix is then utilized to reduce the solution of the fractional calculus problems to the solution of a system of algebraic equations. This method is used to solve fractional differential equations, Bagley-Torvik equations, fractional integro-differential equations, and fractional duffing problems. Illustrative examples are included to demonstrate the validity and applicability of this technique.

Thesis (Ph.D.)--Boston University / PLEASE NOTE: Boston University Libraries did not receive an Authorization To Manage form for this thesis or dissertation. It is therefore not openly accessible, though it may be available by request. If you are the author or principal advisor of this work and would like to request open access for it, please contact us at open-help@bu.edu. Thank you. / In the first part of this thesis, I describe how to obtain a consistent high-temperature approximation for the effective potential which is used to investigate temperature induced phase transitions in quantum field theories. In order to obtain meaningful results, at high temperature, it is necessary to include multi-loop contributions even when the coupling constants of the theory are very small. I show that the dominant multi-loop contributions can be resummed in the formalism of the effective action for composite operators. I then use the resummed effective potential to study the phase transitions of the lambda theta 4 model, a theory describing self-interacting scalar fields, and of the Abelian Higgs Model, a gauge theory describing scalar electrodynamics. I conclude that, within this approximation, the phase transition in the lambda theta 4 model is second order or very weakly first order, whereas it is first order in the Abelian Higgs Model, with strength dependent on the magnitude of the couplings. The second part of the thesis is devoted to the investigation of systems of anyons, which are particles with fractional spin and anomalous (fractional) quantum statistics in two spatial dimensions. As a consequence of the difficulties introduced by the anomalous statistics, the complete energy spectrum is not known even for very simple anyonic systems. In order to gain information on these spectra, I use a perturbative approach in which the small parameter is the deviation of the statistics from the bosonic limit. In the case of anyons in an harmonic potential, I find a class of eigenstates whose energies can be evaluated perturbatively up to second order. The results of my analysis indicate a series of properties which might characterize general many-anyon systems, and could be used in attempts to understand the Fractional Quantum Hall Effect. / 2999-01-01