The phase diagram of the mercury-indium alloy system

The mercury-indium phase diagram has been investigated over the whole composition range from -78°C to the melting point of indium, using thermal analysis, X-ray and superconductivity techniques. This is believed to be the first application of superconductivity measurements to phase diagram investigations. A compound, HgIn, of very limited range of composition, melts congruently at -19.3°C; and gives rise to eutectics at 61.5 at. % indium and -31°C, and at 34.7% indium and -37.2°C. The β phase extends from 2.5 to 19.1 % indium and has a maximum melting point of -14.2°C at 14.2% indium. It forms a peritectic or eutectic at a temperature indistinguishable from the melting point of pure mercury with a solid solution in mercury containing some, but less than 0.3%, indium. A transition from face-centred tetragonal to face-centred cubic in the indium-rich solid solutions at about 93% indium gives rise to a peritectic at 108°C. The solubility of mercury in this face-centred cubic phase falls from about 22% at-31°C to 13% at -78°C. © 1963.

Controller system design using the coefficient diagram method

Coefficient diagram method is a controller design technique for linear time-invariant systems. This design procedure occurs into two different domains: an algebraic and a graphical. The former is closely paired to a conventional pole placement method and the latter consists on a diagram whose reading from the plotted curves leads to insights regarding closed-loop control system time response, stability and robustness. The controller structure has two degrees of freedom and the design process leads to both low overshoot closed-loop time response and good robustness performance regarding mismatches between the real system and the design model. This article presents an overview on this design method. In order to make more transparent the presented theoretical concepts, examples in Matlab®code are provided. The included code illustrates both the algebraic and the graphical nature of the coefficient diagram design method. © 2016, King Fahd University of Petroleum & Minerals.

Radiation from a D-dimensional collision of shock waves: two-dimensional reduction and Carter–Penrose diagram

We analyze the causal structure of the two-dimensional (2D) reduced background used in the perturbative treatment of a head-on collision of two D-dimensional Aichelburg–Sexl gravitational shock waves. After defining all causal boundaries, namely the future light-cone of the collision and the past light-cone of a future observer, we obtain characteristic coordinates using two independent methods. The first is a geometrical construction of the null rays which define the various light cones, using a parametric representation. The second is a transformation of the 2D reduced wave operator for the problem into a hyperbolic form. The characteristic coordinates are then compactified allowing us to represent all causal light rays in a conformal Carter–Penrose diagram. Our construction holds to all orders in perturbation theory. In particular, we can easily identify the singularities of the source functions and of the Green’s functions appearing in the perturbative expansion, at each order, which is crucial for a successful numerical evaluation of any higher order corrections using this method.

Adaptivity and a posteriori error control for bifurcation problems I: the Bratu problem

This article is concerned with the numerical detection of bifurcation points of nonlinear partial differential equations as some parameter of interest is varied. In particular, we study in detail the numerical approximation of the Bratu problem, based on exploiting the symmetric version of the interior penalty discontinuous Galerkin finite element method. A framework for a posteriori control of the discretization error in the computed critical parameter value is developed based upon the application of the dual weighted residual (DWR) approach. Numerical experiments are presented to highlight the practical performance of the proposed a posteriori error estimator.

Adaptivity and a posteriori error control for bifurcation problems II: Incompressible fluid flow in open systems with Z_2 symmetry

In this article we consider the a posteriori error estimation and adaptive mesh refinement of discontinuous Galerkin finite element approximations of the bifurcation problem associated with the steady incompressible Navier-Stokes equations. Particular attention is given to the reliable error estimation of the critical Reynolds number at which a steady pitchfork or Hopf bifurcation occurs when the underlying physical system possesses reflectional or Z_2 symmetry. Here, computable a posteriori error bounds are derived based on employing the generalization of the standard Dual-Weighted-Residual approach, originally developed for the estimation of target functionals of the solution, to bifurcation problems. Numerical experiments highlighting the practical performance of the proposed a posteriori error indicator on adaptively refined computational meshes are presented.

On the zeros of the Abelian integrals for a class of Liénard systems

A planar polynomial differential system has a finite number of limit cycles. However, finding the upper bound of the number of limit cycles is an open problem for the general nonlinear dynamical systems. In this paper, we investigated a class of Liénard systems of the form x'=y, y'=f(x)+y g(x) with deg f=5 and deg g=4. We proved that the related elliptic integrals of the Liénard systems have at most three zeros including multiple zeros, which implies that the number of limit cycles bifurcated from the periodic orbits of the unperturbed system is less than or equal to 3.

Implications of precursor chemistry on the alkaline hydrothermal synthesis of titania/titanate nanostructures

A systematic study of four parameters within the alkaline hydrothermal treatment of three commercial titania powders—anatase, rutile, and Degussa P25—was made. These powders were treated with 5, 7.5, 9, and 10 M NaOH between 100 and 220 °C for 20 h. The effects of alkaline concentration, hydrothermal temperature, and precursor phase and crystallite size on the resultant nanostructure formation have been studied through X-ray diffraction, Raman spectroscopy, transmission electron microscopy, and nitrogen adsorption. Through the correlation of these data, morphological phase diagrams were constructed for each commercial powder. Interpretation of the resultant morphological phase diagrams indicates that alkaline concentration and hydrothermal temperature affect nanostructure formation independently, where nanoribbon formation is significantly influenced by temperature for initial formation. The phase and crystallite size of the precursor also significantly influenced nanostructure formation, with rutile displaying a slower rate of precursor consumption compared with anatase. Small crystallite titania precursors formed nanostructures at reduced hydrothermal temperatures.

Diagramming the interior

Mark Taylor's new essay assesses the impact of the diagram on interior design from the late 19th century to the present. Taylor identifies the pop-cultural discourse of advice writing in both books and magazines as a starting point for his analysis. Drawing on diverse sources, his analysis focuses on texts relating to the dynamics of use and flexibility by Catherine Beecher, Harriet Beecher Stowe, Melusina Fay Peirce, Mary Haweis and Christine Frederick among others. The examples in these texts use the home, domestic housekeeping and kitchens as the sites and practices of intervention through which interior design innovations can be enacted. Taylor's analysis identified the innovations in both the social and the political aspects of space and the critique of static space behind these seemingly amateurish and innocuous texts. Identifying these contributions as early precursors of Modernism's open-plan and flexible, dynamic spaces, Taylor also interprets them with a critical concern for the oppositions and hierarchies that can exist in spatial design, and which are the hallmarks of recent Postmodern, phenomenological approaches to interior design and its theorisations. The progressive and subversive "paradigms for living" implicit in these diagrams can be argued to present a model of greater economic, social and political equality as well as representing a more balanced set of power relations in the home. Progressing through the 20th century to the present, Taylor's analysis shifts byond the dressed body and on to the more intimate rituals of the revealed body to further examine how diagrams of the interior, and the interior as a set of diagrams, are also mediators, sites and grounds for the design of social and sexual intimacy. Through a consideration of the link between design, indentity and intimacy (whether of the invisible, fashioned or sexualised body), the diagrms of interiors are reconfigured as radical and critical tools for an animate, material and emancipatory "redressing" of the balance between the body, identity, sexuality, gender, function, mis(use), aesthetics and the interior.

A process for the management of physical infrastructure

Physical infrastructure assets are important components of our society and our economy. They are usually designed to last for many years, are expected to be heavily used during their lifetime, carry considerable load, and are exposed to the natural environment. They are also normally major structures, and therefore present a heavy investment, requiring constant management over their life cycle to ensure that they perform as required by their owners and users. Given a complex and varied infrastructure life cycle, constraints on available resources, and continuing requirements for effectiveness and efficiency, good management of infrastructure is important. While there is often no one best management approach, the choice of options is improved by better identification and analysis of the issues, by the ability to prioritise objectives, and by a scientific approach to the analysis process. The abilities to better understand the effect of inputs in the infrastructure life cycle on results, to minimise uncertainty, and to better evaluate the effect of decisions in a complex environment, are important in allocating scarce resources and making sound decisions. Through the development of an infrastructure management modelling and analysis methodology, this thesis provides a process that assists the infrastructure manager in the analysis, prioritisation and decision making process. This is achieved through the use of practical, relatively simple tools, integrated in a modular flexible framework that aims to provide an understanding of the interactions and issues in the infrastructure management process. The methodology uses a combination of flowcharting and analysis techniques. It first charts the infrastructure management process and its underlying infrastructure life cycle through the time interaction diagram, a graphical flowcharting methodology that is an extension of methodologies for modelling data flows in information systems. This process divides the infrastructure management process over time into self contained modules that are based on a particular set of activities, the information flows between which are defined by the interfaces and relationships between them. The modular approach also permits more detailed analysis, or aggregation, as the case may be. It also forms the basis of ext~nding the infrastructure modelling and analysis process to infrastructure networks, through using individual infrastructure assets and their related projects as the basis of the network analysis process. It is recognised that the infrastructure manager is required to meet, and balance, a number of different objectives, and therefore a number of high level outcome goals for the infrastructure management process have been developed, based on common purpose or measurement scales. These goals form the basis of classifYing the larger set of multiple objectives for analysis purposes. A two stage approach that rationalises then weights objectives, using a paired comparison process, ensures that the objectives required to be met are both kept to the minimum number required and are fairly weighted. Qualitative variables are incorporated into the weighting and scoring process, utility functions being proposed where there is risk, or a trade-off situation applies. Variability is considered important in the infrastructure life cycle, the approach used being based on analytical principles but incorporating randomness in variables where required. The modular design of the process permits alternative processes to be used within particular modules, if this is considered a more appropriate way of analysis, provided boundary conditions and requirements for linkages to other modules, are met. Development and use of the methodology has highlighted a number of infrastructure life cycle issues, including data and information aspects, and consequences of change over the life cycle, as well as variability and the other matters discussed above. It has also highlighted the requirement to use judgment where required, and for organisations that own and manage infrastructure to retain intellectual knowledge regarding that infrastructure. It is considered that the methodology discussed in this thesis, which to the author's knowledge has not been developed elsewhere, may be used for the analysis of alternatives, planning, prioritisation of a number of projects, and identification of the principal issues in the infrastructure life cycle.

Eucharistic rituals in Catholic primary schools in the Archdiocese of Brisbane : a study of administrators' conceptions

The focus of this study is the celebration of Eucharist in Catholic primary schools within the Archdiocese of Brisbane. The context of the contemporary Australian Catholic primary school embodies certain 'problematical realities' in relation to the time-honoured way in which school Eucharistic rituals have been celebrated. These contemporary realities raise a number of issues that impact on school celebrations of Eucharist. The purpose of this study is to explore administrators' differing conceptions of school Eucharistic rituals in an attempt to investigate some of these issues and assist members of individual school communities as they strive to make celebrations of Eucharist appropriate and meaningful for the group gathered. The phenomenographic research approach was adopted, as it is well suited to the purpose of this study and the nature of the research question. Phenomenography is essentially a study of variation. It attempts to map the 'whole' phenomenon under investigation by describing on equal terms all conceptions of the phenomenon and establishing an ordered relationship among them. The purpose of this study and the nature of the research question necessitate an approach that allows the identification and description of the different ways in which administrators' experience school Eucharistic rituals. Accordingly, phenomenography was selected. Members of the Administration Team, namely the principal, the APRE (Assistant to the Principal Religious Education) and, in larger primary schools, the AP A (Assistant to the Principal Administration) share responsibility for leading change in Catholic primary schools in the Archdiocese of Brisbane. In practice, however, principals delegate the role of leading the development of the school's religion program and providing leadership in the religious life of the school community to the APRE (Brisbane Catholic Education, 1997). Informants in this study are nineteen APREs from a variety of Catholic primary schools in the Archdiocese of Brisbane. These APREs come from schools across the archdiocese, rather than from within one particular region. Several significant findings resulted from this study. Firstly, the data show that there are significant differences in how APREs' experience school Eucharistic rituals, although the number of these qualitatively different conceptions is quite limited. The study identifies and describes six distinct yet related conceptions of school Eucharistic rituals. The logical relationship among these conceptions (the outcome space) is presented in the form of a diagram with accompanying explication. The variation among the conceptions is best understood and described in terms of three dimensions of the role of Eucharist in the Catholic primary school and is represented on the model of the outcome space. Individual transcripts suggest that individual APREs tend to emphasise some conceptions more than others. It is the contention of the present study that change in the practice of school Eucharistic rituals is unlikely to occur until all of a school community's conceptions are brought out into the open and articulated. As leaders of change, APREs need to be alerted to their own biases and become aware of alternative ways of conceiving school Eucharistic ritual. It is proposed that the different categories of description and dimensions, represented by the model of the outcome space, can be used to help in the process of articulating a school community's conceptions of Eucharist, with the APRE as facilitator of this process. As a result, the school community develops a better understanding of why their particular school does what it does in relation to school Eucharistic rituals.

Frequency Domain Characterization Of Sliding Mode Control Of An Inverter Used In DSTATCOM Application

In this paper, the commonly used switching schemes for sliding mode control of power converters is analyzed and designed in the frequency domain. Particular application of a distribution static compensator (DSTATCOM) in voltage control mode is investigated in a power distribution system. Tsypkin's method and describing function is used to obtain the switching conditions for the two-level and three-level voltage source inverters. Magnitude conditions of carrier signals are developed for robust switching of the inverter under carrier-based modulation scheme of sliding mode control. The existence of border collision bifurcation is identified to avoid the complex switching states of the inverter. The load bus voltage of an unbalanced three-phase nonstiff radial distribution system is controlled using the proposed carrier-based design. The results are validated using PSCAD/EMTDC simulation studies and through a scaled laboratory model of DSTATCOM that is developed for experimental verification

Stability analysis based on birfurcation theory of the DSTATCOM operating in current control mode

This paper presents the stability analysis for a distribution static compensator (DSTATCOM) that operates in current control mode based on bifurcation theory. Bifurcations delimit the operating zones of nonlinear circuits and, hence, the capability to compute these bifurcations is of important interest for practical design. A control design for the DSTATCOM is proposed. Along with this control, a suitable mathematical representation of the DSTATCOM is proposed to carry out the bifurcation analysis efficiently. The stability regions in the Thevenin equivalent plane are computed for different power factors at the point of common coupling. In addition, the stability regions in the control gain space, as well as the contour lines for different Floquet multipliers are computed. It is demonstrated through bifurcation analysis that the loss of stability in the DSTATCOM is due to the emergence of a Neimark bifurcation. The observations are verified through simulation studies.