DUALITY THEORY FOR COMPOSITE GEOMETRIC PROGRAMMING

This research develops an alternative approach to the duality theory of the well-known subject of Geometric Programming (GP), and uses this to then develop a duality theory for Quadratic Geometric Programming (QGP), which is an extension of GP; it then develops a duality theory for (convex) Composite Geometric Programming (CGP), which in turn, is a generalization of QGP. The building block of GP is a special class of functions called posynomials, which are summations of terms, where the logarithm of each term is a linear function of the logarithms of its design variables. Such log-linear relationships often appear as an empirical fit in numerous engineering applications, most notably in engineering design. At other times, these relationships may simply follow the dictates of the laws of nature and/or economics (Varian 1978). Many functions that describe engineering systems are posynomials and hence GP is especially suitable for handling optimization problems involving such functions. For instance, the so-called Machining Economics Problem (MEP) for conventional metals can be handled successfully by GP (Tsai, 1986). The defining relationship of the tool life as a function of machining variables such as cutting speed, depth of cut, feed rate, tool change downtime, etc., is typically log-linear. However, when the logarithm of the tool life for a given alloy is a quadratic (instead of a linear) function of the logarithms of the machining variables, GP is not able to handle this kind of MEP (Hough, 1978; Hough and Goforth, 1981a, b, c). Jefferson and Scott (1985) introduced QGP to successfully handle the quadratic version of the MEP. They also gave primal-dual formulations of the QGP problem, an optimality condition, and three illustrative numerical examples of MEP (Jefferson and Scott 1985, p.144). A strong duality theorem for QGP was later proved by Fang and Rajasekera (1987) using a dual perturbation approach and two simple geometric inequalities. However, more detailed duality theory for QGP and for CGP comparable to the development for GP by Duffin, Peterson, and Zener in chapters IV and VI of their seminal text (1967) are yet to be developed. This theory is rooted in the duality principle for ‘conjugate’ pairs of convex functions, which translates the analysis of one optimization problem into an equivalent, yet very different optimization problem. It allows us to view the problem from two different angles, often with new insights and with other remarkable consequences such as suggesting an easier solution approach. In this thesis, we extend QGP problems to the more general CGP problems to account for the even more general log-convex (as opposed to log-linear) relationships. The aim of this dissertation is to develop a comprehensive duality theory for both QGP and CGP

A magnetohydrodynamic model for multi-wavelength flares from Sagittarius~A⋆^\star (I): model and the near-infrared and X-ray flares

Flares from the supermassive black hole in our Galaxy, Sagittarius~A$^\star$ (Sgr A$^\star$), are routinely observed over the last decade or so. Despite numerous observational and theoretical efforts, the nature of such flares still remains poorly understood, although a few phenomenological scenarios have been proposed. In this work, we develop the Yuan et al. (2009) scenario into a magnetohydrodynamic (MHD) model for Sgr A$^\star$ flares. This model is analogous with the theory of solar flares and coronal mass ejection in solar physics. In the model, magnetic field loops emerge from the accretion flow onto Sgr A$^\star$ and are twisted to form flux ropes because of shear and turbulence. The magnetic energy is also accumulated in this process until a threshold is reached. This then results in a catastrophic evolution of a flux rope with the help of magnetic reconnection in the current sheet. In this catastrophic process, the magnetic energy is partially converted into the energy of non-thermal electrons. We have quantitatively calculated the dynamical evolution of the height, size, and velocity of the flux rope, as well as the magnetic field in the flare regions, and the energy distribution of relativistic electrons in this process. We further calculate the synchrotron radiation from these electrons and compare the obtained light curves with the observed ones. We find that the model can reasonably explain the main observations of near-infrared (NIR) and X-ray flares including their light curves and spectra. It can also potentially explain the frequency-dependent time delay seen in radio flare light curves.Comment: 17 pages, 13 figures, accepted by MNRA

(De-)activating the growth machine for redevelopment: the case of Liede urban village in Guangzhou

This research investigates the mechanism of urban village redevelopment in south China. Through a revised typology of place entrepreneurs based on the growth machine thesis and a case study of Liede village in central Guangzhou, it illustrates how land-based interests embedded in an imbalanced power relationship can (de-)activate urban village redevelopment. The study reveals that while urban villagers, as represented by the village collective, have entrenched interests in the redevelopment process, the city government – as monopolistic land manager and place entrepreneur – plays the deciding role in forging and halting a growth machine geared towards urban village redevelopment. Although developers are also part of the process, the (de-)activation of redevelopment growth machine/coalition in Guangzhou has largely been dominated by the city government. With a comparative view on the original growth machine model, it is hoped that this study would furnish both theoretical and practical thoughts for future research

The (re)making of polycentricity in China’s planning discourse: the case of Tianjin

Polycentricity is promoted as an ideal urban form to achieve sustainable and balanced development, and it has been widely adopted by planners in China, especially in large cities. However, the rhetoric about polycentricity has rarely been interrogated in planning research in terms of scales, contextuality, power and rationality. To fill this gap, we carried out a Foucauldian discourse analysis in our research to interpret the nature of polycentric practice in City Master Plans, using Tianjin as a case study. Through an analysis of how the discourse of polycentricity is being deployed in planning documents, we develop two principal arguments in this article. First, the conceptual substance of polycentricity evolved alongside the urban transition process in China, and its discursive practice involved multiple scales and spatial elements. Secondly, rather than being mere technocratic practice, the production and legitimation of distinct discourses of polycentricity is an articulation of multi‐scalar power involving various stakeholders, which is disguised and justified by the planning profession

Urban villages, their redevelopment and implications for inequality and integration

Urban villages are a unique product of China’s rapid urban expansion. They provide a new way of life sustained by property rental income for local villagers. More importantly, urban villages provide cheap accommodation for millions of rural migrant workers in most large cities. Recently, with the increasing demand for land by commercial developers and public projects, urban villages have become the targets for redevelopment. This chapter uses a case study village in Beijing as an example to assess the social and economic impacts of urban village redevelopment on both the original local inhabitants and migrants in rented accommodation. The case study village went through a very long and complicated redevelopment process from 2004 to 2017 involving different stages of demolition and relocation. It provided a rare opportunity to evaluate the effects on the local population, both pre- and post-redevelopment. The study involved several field visits, observation and interviews with village residents. It shows that urban village redevelopment offered no positive benefits for migrant workers who often lost their homes to demolition. For local villagers, redevelopment and relocation into new flats may improve their living conditions. However, most suffer from the loss of long-term economic and income generation opportunities. Moreover, the new property rights for the replacement flats confer no additional rights of citizenship for the relocated villagers who remain ‘second-class citizens’ within Chinese cities