Numerical solution to the Saffman-Taylor finger problem with kinetic undercooling regularisation

The Saffman-Taylor finger problem is to predict the shape and,in particular, width of a finger of fluid travelling in a Hele-Shaw cell filled with a different, more viscous fluid. In experiments the width is dependent on the speed of propagation of the finger, tending to half the total cell width as the speed increases. To predict this result mathematically, nonlinear effects on the fluid interface must be considered; usually surface tension is included for this purpose. This makes the mathematical problem suffciently diffcult that asymptotic or numerical methods must be used. In this paper we adapt numerical methods used to solve the Saffman-Taylor finger problem with surface tension to instead include the effect of kinetic undercooling, a regularisation effect important in Stefan melting-freezing problems, for which Hele-Shaw flow serves as a leading order approximation when the specific heat of a substance is much smaller than its latent heat. We find the existence of a solution branch where the finger width tends to zero as the propagation speed increases, disagreeing with some aspects of the asymptotic analysis of the same problem. We also find a second solution branch, supporting the idea of a countably infinite number of branches as with the surface tension problem.

Mechanism of p-nitrophenol adsorption from aqueous solution by HDTMA+-pillared montmorillonite : implications for water purification

HDTMA+ pillared montmorillonites were obtained by pillaring different amounts of the surfactant hexadecyltrimethylammonium bromide (HDTMAB) into sodium montmorillonite (Na-Mt) in an aqueous solution. The optimum conditions and batch kinetics of sorption of p-nitrophenol from aqueous solutions were reported. The solu-tion pH had a very important effect on the sorption of p-nitrophenol. The maximum p-nitrophenol absorption/adsorption occurs when solution pH (7.15~7.35) is approx-imately equal to the pKa (7.16) of the p-nitrophenol ion deprotonation reaction. X-ray diffraction analysis showed that surfactant cations had been pillared into the interlayer and the p-nitrophenol affected the arrangement of surfactant. With the increased con-centration of surfactant cations, the arrangement of HDTMA+ within the clay inter-layer changes and the sorption of p-nitrophenol increases. HDTMA+ pillared mont-morillonites are more effective than Na-Mt for the adsorption of p-nitrophenol from aqueous solutions. The Langmuir, Freundlich and dual-mode sorption were tested to fit the sorption isotherms.

The coming of post-reflexive society : a critique of the political economy of digital capitalism

Language is a unique aspect of human communication because it can be used to discuss itself in its own terms. For this reason, human societies potentially have superior capacities of co-ordination, reflexive self-correction, and innovation than other animal, physical or cybernetic systems. However, this analysis also reveals that language is interconnected with the economically and technologically mediated social sphere and hence is vulnerable to abstraction, objectification, reification, and therefore ideology – all of which are antithetical to its reflexive function, whilst paradoxically being a fundamental part of it. In particular, in capitalism, language is increasingly commodified within the social domains created and affected by ubiquitous communication technologies. The advent of the so-called ‘knowledge economy’ implicates exchangeable forms of thought (language) as the fundamental commodities of this emerging system. The historical point at which a ‘knowledge economy’ emerges, then, is the critical point at which thought itself becomes a commodified ‘thing’, and language becomes its “objective” means of exchange. However, the processes by which such commodification and objectification occurs obscures the unique social relations within which these language commodities are produced. The latest economic phase of capitalism – the knowledge economy – and the obfuscating trajectory which accompanies it, we argue, is destroying the reflexive capacity of language particularly through the process of commodification. This can be seen in that the language practices that have emerged in conjunction with digital technologies are increasingly non-reflexive and therefore less capable of self-critical, conscious change.

Butterpaper, sweat & tears : the affective dimension of engaging students during the architectural critique

Considering how dominant a feature of architectural education the critique has been, and continues to be, little has been written about the affective dimension of engaging students during this key final stage of the design or documentation process. For most students, the critique is unlike any previous educational or life experience that they have ever confronted, and the abrupt change in the instructor’s role, from tutor to judge, can be disconcerting at a time when the student is feeling their most vulnerable. The fact that the period immediately leading up to the critique habitually entails not only a focused and sustained effort, but also sleepless nights of intensive work, further exacerbates this. The purpose of this paper is to recognise the affective phenomena influencing student engagement, during the critique. The participants of this research were second to fourth year architecture students at a major Australian university. Following the implementation of trials in alternative modes of critique in architectural design and technology studios, qualitative data was obtained from students, through questionnaires and interviews. Six indicators of engagement were investigated through this research: motivation and agency, transactional engagement with staff, transactional engagement with students, institutional support, active citizenship, and non-institutional support. This research confirms that affective phenomena play a significant role in the events of the critique; the relationship between instructor and student influences student engagement, as does the choreography and spatial planning of the critique environment; and these factors ultimately have an impact on the depth of student learning.

An analytical solution for diffusion and nonlinear uptake of oxygen in a spherical cell

We develop a new analytical solution for a reactive transport model that describes the steady-state distribution of oxygen subject to diffusive transport and nonlinear uptake in a sphere. This model was originally reported by Lin (Journal of Theoretical Biology, 1976 v60, pp449–457) to represent the distribution of oxygen inside a cell and has since been studied extensively by both the numerical analysis and formal analysis communities. Here we extend these previous studies by deriving an analytical solution to a generalized reaction-diffusion equation that encompasses Lin’s model as a particular case. We evaluate the solution for the parameter combinations presented by Lin and show that the new solutions are identical to a grid-independent numerical approximation.