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Thesis advisor: Ying Ran / In this thesis, I investigated and implemented various numerical and simulation methods, including mean field theory, functional renormalization group method (fRG), density matrix renormalization group (DMRG) method etc., to find different quantum phases and quantum phase diagrams on models of correlated electronic systems. I found different phase diagrams with phases such as magnetism, superconductivity. By summarizing the strength and limitations of these methods, I investigated the projected entangled paired states (PEPS) with symmetry quantum number to sharply distinguish phases into crude classes and applied a variation of fast full update (FFU) prototype[58] to simulate different phases numerically. This method provides a promising, powerful and efficient way to simulate unconventional quantum phases and quantum phase diagrams in correlated electronic systems. / Thesis (PhD) — Boston College, 2016. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Physics.

The thesis describes research into graphical notations for software engineering, with a principal interest in ways of formalizing them. The research seeks to provide a theoretical basis that will help in designing both notations and the software tools that process them. The work starts from a survey of literature on notation, followed by a review of techniques for formal description and for computational handling of notations. The survey concentrates on collecting views of the benefits and the problems attending notation use in software development; the review covers picture description languages, grammars and tools such as generic editors and visual programming environments. The main problem of notation is found to be a lack of any coherent, rigorous description methods. The current approaches to this problem are analysed as lacking in consensus on syntax specification and also lacking a clear focus on a defined concept of notated expression. To address these deficiencies, the thesis embarks upon an exploration of serniotic, linguistic and logical theory; this culminates in a proposed formalization of serniosis in notations, using categorial model theory as a mathematical foundation. An argument about the structure of sign systems leads to an analysis of notation into a layered system of tractable theories, spanning the gap between expressive pictorial medium and subject domain. This notion of 'tectonic' theory aims to treat both diagrams and formulae together. The research gives details of how syntactic structure can be sketched in a mathematical sense, with examples applying to software development diagrams, offering a new solution to the problem of notation specification. Based on these methods, the thesis discusses directions for resolving the harder problems of supporting notation design, processing and computer-aided generic editing. A number of future research areas are thereby opened up. For practical trial of the ideas, the work proceeds to the development and partial implementation of a system to aid the design of notations and editors. Finally the thesis is evaluated as a contribution to theory in an area which has not attracted a standard approach.

In Chapter 1, we briefly review the thermodynamics of polymer solutions, including the ideal solution based on the Flory-Huggins lattice chain model. The entropy change in the mixing of macromolecules with small solvent molecules is much smaller than that in the mixing of two kinds of small molecules. Therefore, the effect of the solution temperature is also smaller. / In Chapter 2, we describe the basic difference between the complicate polymeric and simple Newtonian fluid and list some dimensionless numbers relevant to various physical phenomena, including the Reynolds number (Re) and the capillary number (Ca), respectively related to the inertial effect and the interfacial tension. As a fluid goes down to the micro scale, the inertial effect is usually negligible so that the flow becomes laminar. However, the interfacial tension starts to play a significant role, which leads to the development of some droplet-based (or digital) microfluidic systems. Using small droplets leads to the following advantages: (1) the reagents are limited within a small boundary of each droplet; and (2) no complex microfluidic device is required. / In Chapter 3, we use PNIPAM in water as a model system to detail how to construct a polymer phase diagram by using a microfluidic device, including the choice of the carrier fluid, the principle and experimental procedure of forming concentration-controllable PNIPAM droplets, the determination of PNIPAM concentration in each droplet by using a fluorescein probe, the effect of fluorescein on the phase transition, and the detection of the phase transition by dark field viewing. For comparison, we also did the normal LLS measurement of the phase transition of PNIPAM in water. / In Chapter 4, PS in cyclohexane is used as a model system to illustrate how to handle organic solvents because cyclohexane swells the PDMS channels. The swelling is much eliminated by directly loading the PS solution into the junction via glass capillaries. Since the addition of a fluorescence concentration probe dramatically influences the PS phase transition, we have to use a so-called parallel experimental method to produce concentration-controllable PS droplets. In this method, several PDMS chips from the same batch are used in the formation of small PS droplets. When the numbers of small PS droplets produced in the same procedure are similar to each other, the PS concentrations in different corresponding droplets are comparable. Therefore we are able to index the PS concentration in each droplet by comparing it with the droplets prepared by the same procedure, but with some added fluorescence probes. / In Chapter 5, on the basis of numerous experiments, we find inorganic salts play a significant role on the droplet forming. Thus we propose that droplet formation is a kinetics governed process when two immiscible liquids meet each other in microchannels. / In this thesis we have proposed and established a new method of constructing polymer phase diagrams. By employing the droplets-based microfluidic system, we are able to form an array of droplets of polymer solutions with several nanoliters in size. Each droplet has a controllable composition. The array of polymer droplets can be transferred and stored in a glass capillary; there the turbidity of each droplet due to the difference of scatted light immediately after the phase transition can be monitored under a microscope via dark field viewing, when the solution temperature changes. Therefore, we are able to construct a polymer phase diagram by simply combing each phase transition temperature with its corresponding compositions of polymer solution droplets. / This method has two distinguished advantages; namely, minimal sample consumption and much reduced experimental time required for the phase transition to reach its equilibrium at each given temperature. This is because the greatly increased surface-to-volume ratio allows rapid diffusion and fast heat transfer. To demonstrate the principle, we have chosen PS in cyclohexane with an upper critical solution temperature (UCST) and Poly(N-isopropylacrylamide) (PNIPAM) in water with a lower critical solution temperature (LCST) as two model systems. Primarily established phase diagrams of these two polymer solutions have demonstrated the feasibility of using droplets-based microfluidic system to construct polymer phase diagrams. / Shi, Feng. / Advisers: Chi Wu; Bo Zheng. / Source: Dissertation Abstracts International, Volume: 70-06, Section: B, page: 3532. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references. / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.

Thesis (Ph. D.)--University of Missouri-Columbia, 1998. / Typescript. Vita. Includes bibliographical references (leaf 93). Also available on the Internet.

Includes bibliographical references (p. 107-121).

Thesis (M. Phil.)--Hong Kong University of Science and Technology, 2004. / Includes bibliographical references (leaves 114-120). Also available in electronic version. Access restricted to campus users.

Thesis (Ph. D.)--University of Missouri-Columbia, 1998. / Typescript. Vita. Includes bibliographical references (leaf 93). Also available on the Internet.

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