Contracting bubbles in Hele-Shaw cells with a power-law fluid

The problem of bubble contraction in a Hele-Shaw cell is studied for the case in which the surrounding fluid is of power-law type. A small perturbation of the radially symmetric problem is first considered, focussing on the behaviour just before the bubble vanishes, it being found that for shear-thinning fluids the radially symmetric solution is stable, while for shear-thickening fluids the aspect ratio of the bubble boundary increases. The borderline (Newtonian) case considered previously is neutrally stable, the bubble boundary becoming elliptic in shape with the eccentricity of the ellipse depending on the initial data. Further light is shed on the bubble contraction problem by considering a long thin Hele-Shaw cell: for early times the leading-order behaviour is one-dimensional in this limit; however, as the bubble contracts its evolution is ultimately determined by the solution of a Wiener-Hopf problem, the transition between the long-thin limit and the extinction limit in which the bubble vanishes being described by what is in effect a similarity solution of the second kind. This same solution describes the generic (slit-like) extinction behaviour for shear-thickening fluids, the interface profiles that generalise the ellipses that characterise the Newtonian case being constructed by the Wiener-Hopf calculation.

Linear stern waves in finite depth channels

This paper formulates an analytically tractable problem for the wake generated by a long flat bottom ship by considering the steady free surface flow of an inviscid, incompressible fluid emerging from beneath a semi-infinite rigid plate. The flow is considered to be irrotational and two-dimensional so that classical potential flow methods can be exploited. In addition, it is assumed that the draft of the plate is small compared to the depth of the channel. The linearised problem is solved exactly using a Fourier transform and the Wiener-Hopf technique, and it is shown that there is a family of subcritical solutions characterised by a train of sinusoidal waves on the downstream free surface. The amplitude of these waves decreases as the Froude number increases. Supercritical solutions are also obtained, but, in general, these have infinite vertical velocities at the trailing edge of the plate. Consideration of further terms in the expansions suggests a way of canceling the singularity for certain values of the Froude number.

Minimising wave drag for free surface flow past a two-dimensional stern

Free surface flow past a two-dimensional semi-infinite curved plate is considered, with emphasis given to solving for the shape of the resulting wave train that appears downstream on the surface of the fluid. This flow configuration can be interpreted as applying near the stern of a wide blunt ship. For steady flow in a fluid of finite depth, we apply the Wiener-Hopf technique to solve a linearised problem, valid for small perturbations of the uniform stream. Weakly nonlinear results found using a forced KdV equation are also presented, as are numerical solutions to the fully nonlinear problem, computed using a conformal mapping and a boundary integral technique. By considering different families of shapes for the semi-infinite plate, it is shown how the amplitude of the waves can be minimised. For plates that increase in height as a function of the direction of flow, reach a local maximum, and then point slightly downwards at the point at which the free surface detaches, it appears the downstream wavetrain can be eliminated entirely.

Two-dimensional bow and stern flows in a finite-depth fluid with constant vorticity

This thesis is concerned with two-dimensional free surface flows past semi-infinite surface-piercing bodies in a fluid of finite-depth. Throughout the study, it is assumed that the fluid in question is incompressible, and that the effects of viscosity and surface tension are negligible. The problems considered are physically important, since they can be used to model the flow of water near the bow or stern of a wide, blunt ship. Alternatively, the solutions can be interpreted as describing the flow into, or out of, a horizontal slot. In the past, all research conducted on this topic has been dedicated to the situation where the flow is irrotational. The results from such studies are extended here, by allowing the fluid to have constant vorticity throughout the flow domain. In addition, new results for irrotational flow are also presented. When studying the flow of a fluid past a surface-piercing body, it is important to stipulate in advance the nature of the free surface as it intersects the body. Three different possibilities are considered in this thesis. In the first of these possibilities, it is assumed that the free surface rises up and meets the body at a stagnation point. For this configuration, the nonlinear problem is solved numerically with the use of a boundary integral method in the physical plane. Here the semi-infinite body is assumed to be rectangular in shape, with a rounded corner. Supercritical solutions which satisfy the radiation condition are found for various values of the Froude number and the dimensionless vorticity. Subcritical solutions are also found; however these solutions violate the radiation condition and are characterised by a train of waves upstream. In the limit that the height of the body above the horizontal bottom vanishes, the flow approaches that due to a submerged line sink in a $90^\circ$ corner. This limiting problem is also examined as a special case. The second configuration considered in this thesis involves the free surface attaching smoothly to the front face of the rectangular shaped body. For this configuration, nonlinear solutions are computed using a similar numerical scheme to that used in the stagnant attachment case. It is found that these solution exist for all supercritical Froude numbers. The related problem of the cusp-like flow due to a submerged sink in a corner is also considered. Finally, the flow of a fluid emerging from beneath a semi-infinite flat plate is examined. Here the free surface is assumed to detach from the trailing edge of the plate horizontally. A linear problem is formulated under the assumption that the elevation of the plate is close to the undisturbed free surface level. This problem is solved exactly using the Wiener-Hopf technique, and subcritical solutions are found which are characterised by a train of sinusoidal waves in the far field. The nonlinear problem is also considered. Exact relations between certain parameters for supercritical flow are derived using conservation of mass and momentum arguments, and these are confirmed numerically. Nonlinear subcritical solutions are computed, and the results are compared to those predicted by the linear theory.

Converse results to the Wiener attack on RSA

A well-known attack on RSA with low secret-exponent d was given by Wiener about 15 years ago. Wiener showed that using continued fractions, one can efficiently recover the secret-exponent d from the public key (N,e) as long as d < N 1/4. Interestingly, Wiener stated that his attack may sometimes also work when d is slightly larger than N 1/4. This raises the question of how much larger d can be: could the attack work with non-negligible probability for d=N 1/4 + ρ for some constant ρ > 0? We answer this question in the negative by proving a converse to Wiener’s result. Our result shows that, for any fixed ε > 0 and all sufficiently large modulus lengths, Wiener’s attack succeeds with negligible probability over a random choice of d < N δ (in an interval of size Ω(N δ )) as soon as δ > 1/4 + ε. Thus Wiener’s success bound d 1/4. The known attacks in this class (by Verheul and Van Tilborg and Dujella) run in exponential time, so it is natural to ask whether there exists an attack in this class with subexponential run-time. Our second converse result answers this question also in the negative.

A natural model for architecture : the nature of the evolutionary model 1995

John Frazer's architectural work is inspired by living and generative processes. Both evolutionary and revolutionary, it explores informatin ecologies and the dynamics of the spaces between objects. Fuelled by an interest in the cybernetic work of Gordon Pask and Norbert Wiener, and the possibilities of the computer and the "new science" it has facilitated, Frazer and his team of collaborators have conducted a series of experiments that utilize genetic algorithms, cellular automata, emergent behaviour, complexity and feedback loops to create a truly dynamic architecture. Frazer studied at the Architectural Association (AA) in London from 1963 to 1969, and later became unit master of Diploma Unit 11 there. He was subsequently Director of Computer-Aided Design at the University of Ulter - a post he held while writing An Evolutionary Architecture in 1995 - and a lecturer at the University of Cambridge. In 1983 he co-founded Autographics Software Ltd, which pioneered microprocessor graphics. Frazer was awarded a person chair at the University of Ulster in 1984. In Frazer's hands, architecture becomes machine-readable, formally open-ended and responsive. His work as computer consultant to Cedric Price's Generator Project of 1976 (see P84)led to the development of a series of tools and processes; these have resulted in projects such as the Calbuild Kit (1985) and the Universal Constructor (1990). These subsequent computer-orientated architectural machines are makers of architectural form beyond the full control of the architect-programmer. Frazer makes much reference to the multi-celled relationships found in nature, and their ongoing morphosis in response to continually changing contextual criteria. He defines the elements that describe his evolutionary architectural model thus: "A genetic code script, rules for the development of the code, mapping of the code to a virtual model, the nature of the environment for the development of the model and, most importantly, the criteria for selection. In setting out these parameters for designing evolutionary architectures, Frazer goes beyond the usual notions of architectural beauty and aesthetics. Nevertheless his work is not without an aesthetic: some pieces are a frenzy of mad wire, while others have a modularity that is reminiscent of biological form. Algorithms form the basis of Frazer's designs. These algorithms determine a variety of formal results dependent on the nature of the information they are given. His work, therefore, is always dynamic, always evolving and always different. Designing with algorithms is also critical to other architects featured in this book, such as Marcos Novak (see p150). Frazer has made an unparalleled contribution to defining architectural possibilities for the twenty-first century, and remains an inspiration to architects seeking to create responsive environments. Architects were initially slow to pick up on the opportunities that the computer provides. These opportunities are both representational and spatial: computers can help architects draw buildings and, more importantly, they can help architects create varied spaces, both virtual and actual. Frazer's work was groundbreaking in this respect, and well before its time.

Educating the Other: Standpoint and Theory on the 'Internationalisation' of Higher Education

How adequate are current theoretical standpoints, tools and categories for explaining the flows of international students to Anglo/American/European universities? This essay takes a different analytic tact and historical standpoint to the study of them and us, insiders and outsiders (cf. Foley, Levinson & Hurtig, 2001), in the internationalisation of education.

Bootstrap approaches for estimation and confidence intervals of long term memory processes

In this work, we investigate an alternative bootstrap approach based on a result of Ramsey [F.L. Ramsey, Characterization of the partial autocorrelation function, Ann. Statist. 2 (1974), pp. 1296-1301] and on the Durbin-Levinson algorithm to obtain a surrogate series from linear Gaussian processes with long range dependence. We compare this bootstrap method with other existing procedures in a wide Monte Carlo experiment by estimating, parametrically and semi-parametrically, the memory parameter d. We consider Gaussian and non-Gaussian processes to prove the robustness of the method to deviations from normality. The approach is also useful to estimate confidence intervals for the memory parameter d by improving the coverage level of the interval.

Chlorzoxazone, an SK-type potassium channel activator used in humans, reduces excessive alcohol intake in rats

Background Alcoholism imposes a tremendous social and economic burden. There are relatively few pharmacological treatments for alcoholism, with only moderate efficacy, and there is considerable interest in identifying additional therapeutic options. Alcohol exposure alters SK-type potassium channel (SK) function in limbic brain regions. Thus, positive SK modulators such as chlorzoxazone (CZX), a US Food and Drug Administration–approved centrally acting myorelaxant, might enhance SK function and decrease neuronal activity, resulting in reduced alcohol intake. Methods We examined whether CZX reduced alcohol consumption under two-bottle choice (20% alcohol and water) in rats with intermittent access to alcohol (IAA) or continuous access to alcohol (CAA). In addition, we used ex vivo electrophysiology to determine whether SK inhibition and activation can alter firing of nucleus accumbens (NAcb) core medium spiny neurons. Results Chlorzoxazone significantly and dose-dependently decreased alcohol but not water intake in IAA rats, with no effects in CAA rats. Chlorzoxazone also reduced alcohol preference in IAA but not CAA rats and reduced the tendency for rapid initial alcohol consumption in IAA rats. Chlorzoxazone reduction of IAA drinking was not explained by locomotor effects. Finally, NAcb core neurons ex vivo showed enhanced firing, reduced SK regulation of firing, and greater CZX inhibition of firing in IAA versus CAA rats. Conclusions The potent CZX-induced reduction of excessive IAA alcohol intake, with no effect on the more moderate intake in CAA rats, might reflect the greater CZX reduction in IAA NAcb core firing observed ex vivo. Thus, CZX could represent a novel and immediately accessible pharmacotherapeutic intervention for human alcoholism. Key Words: Alcohol intake; intermittent; neuro-adaptation; nucleus accumbens; SK potassium channel

Dopamine responsiveness is regulated by targeted sorting of D2 receptors

Abstract Aberrant dopaminergic signaling is a critical determinant in multiple psychiatric disorders, and in many disease states, dopamine receptor number is altered. Here we identify a molecular mechanism that selectively targets D2 receptors for degradation after their activation by dopamine. The degradative fate of D2 receptors is determined by an interaction with G protein coupled receptor-associated sorting protein (GASP). As a consequence of this GASP interaction, D2 responses in rat brain fail to resensitize after agonist treatment. Disruption of the D2-GASP interaction facilitates recovery of D2 responses, suggesting that modulation of the D2-GASP interaction is important for the functional down-regulation of D2 receptors.

Low rank Runge-Kutta methods, symplecticity and stochastic Hamiltonian problems with additive noise

In this paper we extend the ideas of Brugnano, Iavernaro and Trigiante in their development of HBVM($s,r$) methods to construct symplectic Runge-Kutta methods for all values of $s$ and $r$ with $s\geq r$. However, these methods do not see the dramatic performance improvement that HBVMs can attain. Nevertheless, in the case of additive stochastic Hamiltonian problems an extension of these ideas, which requires the simulation of an independent Wiener process at each stage of a Runge-Kutta method, leads to methods that have very favourable properties. These ideas are illustrated by some simple numerical tests for the modified midpoint rule.

A boundary preserving numerical algorithm for the Wright-Fisher model with mutation

The Wright-Fisher model is an Itô stochastic differential equation that was originally introduced to model genetic drift within finite populations and has recently been used as an approximation to ion channel dynamics within cardiac and neuronal cells. While analytic solutions to this equation remain within the interval [0,1], current numerical methods are unable to preserve such boundaries in the approximation. We present a new numerical method that guarantees approximations to a form of Wright-Fisher model, which includes mutation, remain within [0,1] for all time with probability one. Strong convergence of the method is proved and numerical experiments suggest that this new scheme converges with strong order 1/2. Extending this method to a multidimensional case, numerical tests suggest that the algorithm still converges strongly with order 1/2. Finally, numerical solutions obtained using this new method are compared to those obtained using the Euler-Maruyama method where the Wiener increment is resampled to ensure solutions remain within [0,1].

Pragmatics, perceptions and strategies in Chinese college English learning

This study investigated Chinese College English students. perceptions of pragmatics, their pragmatic competence in selected speech acts, strategies they employed in acquiring pragmatic knowledge, as well as their general approach to learning English as a foreign language. The research was triggered by a national curriculum initiative that prioritizes the need for College English students to enhance their ability to use English effectively in different social interactions (Chinese College English Education and Supervisory Committee, 2007). The traditional "grammar-translation" and "examination-oriented" method is believed to have reduced Chinese College English students to what is dubbed "mute" and "deaf" language learners (Zhang, 2008; Zhao, 2009). Many students lack pragmatic knowledge on how to interpret discourse by relating utterances to their meanings, understanding the intention of language users, and how language is used in specific settings (Bachman & Palmer, 1996, 2010). There is an increasing body of literature on awareness-raising of the importance of pragmatic knowledge and strategies for classroom instruction. However, to date, researchers have tended to focus largely on the teaching of pragmatics, rather than on how students acquire pragmatic competence (Bardovi-Harlig & Dornyei, 1998; Du, 2004; Hou, 2007; Ruan, 2007; Schauer, 2009). It is this gap in the research that this study fills, with a focus on different types of pragmatic knowledge, learner perceptions of such knowledge, and learning strategies that College English students employ in the process of learning English in general, and pragmatics in particular. Three strands of theories of second language acquisition (Ellis, 1985, 1994): pragmatics (Levinson, 1983; Mey, 2001; Yule, 1996), intercultural communications (Kramsch, 1998; Samovar & Porter, 1997; Samovar, Porter & McDaniel, 2009) and English as a lingua franca (ELF) (Canagarajah, 2006; Firth, 1996; Pennycook, 2010) were employed to establish a conceptual framework for data collection and analyses. Key constructs derived from the three related theories helped to form a typology for a detailed examination and theorization of the empirical evidence gathered from different sources. Four research instruments: a questionnaire (N=237), Discourse Completion Tasks (DCTs) (N=55), focus group interviews (N=18), and a textbook tasks analysis were employed to collect data for this systematic inquiry. Data collected by different instruments were analyzed and compared by way of a triangulation to enhance its validity and reliability. Major findings derived from different sources highlighted that, although College English students were grammatically advanced language learners, they displayed limited pragmatic knowledge and a highly restricted repertoire of language learning strategies. The majority of the respondents, however, believed that pragmatic knowledge was as important as linguistic knowledge in the process of developing communicative competence for interaction in different contexts. It was argued that a combination of a less than sufficient English proficiency, limited knowledge of pragmatics, inadequate language materials and tasks, and a small stock of language learning strategies, were a major hindrance to effective learning and communication, resulting in pragmatic failures in many intercultural communication situations. As the first systematic study of how Chinese College English students learned pragmatics, the research provided a solid empirical base for developing a tentative model for the learning of pragmatics in a College English classroom in China and similar educational contexts. The model was strengthened by a unique combination of theories of pragmatics, intercultural communication and ELF. Findings from this research provided insights into how Chinese College English students perceived pragmatics in the English as foreign language (EFL) curriculum, the processes of learning, as well as strategies they utilized in developing linguistic and pragmatic knowledge and competence.