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Search Results: 1 - 10 of 8525 matches for " Chris King "
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Fostering Self-directed Learning through Guided Tasks and Learner Reflection
Chris King
Studies in Self-Access Learning Journal , 2011,
Abstract: This article reports on the potential impact on learner attitudes and behaviour from the use of a set of guided self-directed learning worksheets. The study consisted of a before and after questionnaire with a portfolio of activities that became progressively less teacher directed. Each activity had a section for learner reflection. Final reflective comments were captured at the end of the portfolio. Data collected from both questionnaires and from reflective comments was analysed using a grounded theory approach (Strauss and Corbin, 1998). While it is recognised that this study is a classroom-based research project with a small number of participants, and that the data collected is learner-reported, the findings are nevertheless important and suggest that such portfolios can be successful both in promoting the use of self-access centres and in fostering learner autonomy.
Fractal Geography of the Riemann Zeta Function
Chris King
Mathematics , 2011,
Abstract: The quadratic Mandelbrot set has been referred to as the most complex and beautiful object in mathematics and the Riemann Zeta function takes the prize for the most complicated and enigmatic function. Here we elucidate the spectrum of Mandelbrot and Julia sets of Zeta, to unearth the geography of its chaotic and fractal diversities, combining these two extremes into one intrepid journey into the deepest abyss of complex function space.
A Dynamical Key to the Riemann Hypothesis
Chris King
Mathematics , 2011,
Abstract: We investigate a dynamical basis for the Riemann hypothesis (RH) that the non-trivial zeros of the Riemann zeta function lie on the critical line x = 1/2. In the process we graphically explore, in as rich a way as possible, the diversity of zeta and L-functions, to look for examples at the boundary between those with zeros on the critical line and otherwise. The approach provides a dynamical basis for why the various forms of zeta and L-function have their non-trivial zeros on the critical line. It suggests RH is an additional unprovable postulate of the number system, similar to the axiom of choice, arising from the asymptotic behavior of the primes as tends to infinity.
Broken discs: warp propagation in accretion discs
Chris Nixon,Andrew King
Physics , 2012, DOI: 10.1111/j.1365-2966.2011.20377.x
Abstract: We simulate the viscous evolution of an accretion disc around a spinning black hole. In general any such disc is misaligned, and warped by the Lense-Thirring effect. Unlike previous studies we use effective viscosities constrained to be consistent with the internal fluid dynamics of the disc. We find that nonlinear fluid effects, which reduce the effective viscosities in warped regions, can promote the breaking of the disc into two distinct planes. This occurs when the Shakura & Sunyaev dimensionless viscosity parameter alpha is <~ 0.3 and the initial angle of misalignment between the disc and hole is >~ 45 degrees. The break can be a long-lived feature, propagating outwards in the disc on the usual alignment timescale, after which the disc is fully co- or counter-aligned with the hole. Such a break in the disc may be significant in systems where we know the inclination of the outer accretion disc to the line of sight, such as some X-ray binaries: the inner disc, and so any jets, may be noticeably misaligned with respect to the orbital plane.
Do jets precess... or even move at all?
Chris Nixon,Andrew King
Physics , 2013, DOI: 10.1088/2041-8205/765/1/L7
Abstract: Observations of accreting black holes often provoke suggestions that their jets precess. The precession is usually supposed to result from a combination of the Lense-Thirring effect and accretion disc viscosity. We show that this is unlikely for any type of black hole system, as the disc generally has too little angular momentum compared with a spinning hole to cause any significant movement of the jet direction across the sky on short timescales. Uncorrelated accretion events, as in the chaotic accretion picture of active galactic nuclei, change AGN jet directions only on timescales \gtrsim 10^7 yr. In this picture AGN jet directions are stable on shorter timescales, but uncorrelated with any structure of the host galaxy, as observed. We argue that observations of black-hole jets precessing on timescales short compared to the accretion time would be a strong indication that the accretion disc, and not the standard Blandford-Znajek mechanism, is responsible for driving the jet. This would be particularly convincing in a tidal disruption event. We suggest that additional disc physics is needed to explain any jet precession on timescales short compared with the accretion time. Possibilities include the radiation warping instability, or disc tearing.
Warp propagation in astrophysical discs
Chris Nixon,Andrew King
Physics , 2015, DOI: 10.1007/978-3-319-19416-5_2
Abstract: Astrophysical discs are often warped, that is, their orbital planes change with radius. This occurs whenever there is a non-axisymmetric force acting on the disc, for example the Lense-Thirring precession induced by a misaligned spinning black hole, or the gravitational pull of a misaligned companion. Such misalignments appear to be generic in astrophysics. The wide range of systems that can harbour warped discs - protostars, X-ray binaries, tidal disruption events, quasars and others - allows for a rich variety in the disc's response. Here we review the basic physics of warped discs and its implications.
SMBH accretion & mergers: removing the symmetries
Andrew King,Chris Nixon
Physics , 2013, DOI: 10.1088/0264-9381/30/24/244006
Abstract: We review recent progress in studying accretion flows on to supermassive black holes (SMBH). Much of this removes earlier assumptions of symmetry and regularity, such as aligned and prograde disc rotation. This allows a much richer variety of effects, often because cancellation of angular momentum allows rapid infall. Potential applications include lower SMBH spins allowing faster mass growth and suppressing gravitational-wave reaction recoil in mergers, gas-assisted SMBH mergers, and near-dynamical accretion in galaxy centres.
AGN Flickering and Chaotic Accretion
Andrew King,Chris Nixon
Physics , 2015, DOI: 10.1093/mnrasl/slv098
Abstract: Observational arguments suggest that the growth phases of the supermassive black holes in active galactic nuclei have a characteristic timescale $\sim 10^5$ yr. We show that this is the timescale expected in the chaotic accretion picture of black hole feeding, because of the effect of self-gravity in limiting the mass of any accretion disc feeding event.
Notions of Equivalence in Software Design
David King,Chris Kimble
Computer Science , 2004,
Abstract: Design methods in information systems frequently create software descriptions using formal languages. Nonetheless, most software designers prefer to describe software using natural languages. This distinction is not simply a matter of convenience. Natural languages are not the same as formal languages; in particular, natural languages do not follow the notions of equivalence used by formal languages. In this paper, we show both the existence and coexistence of different notions of equivalence by extending the no-tion of oracles used in formal languages. This allows distinctions to be made between the trustworthy oracles assumed by formal languages and the untrust-worthy oracles used by natural languages. By examin-ing the notion of equivalence, we hope to encourage designers of software to rethink the place of ambiguity in software design.
Uncovering the epistemological and ontological assumptions of software designers
David King,Chris Kimble
Computer Science , 2004,
Abstract: The ontological and epistemological positions adopted by information systems design methods are incommensur-able when pushed to their extremes. Information systems research has therefore tended to focus on the similarities between different positions, usually in search of a single, unifying position. However, by focusing on the similari-ties, the clarity of argument provided by any one philoso-phical position is necessarily diminished. Consequently, researchers often treat the philosophical foundations of design methods as being of only minor importance. In this paper, we have deliberately chosen to focus on the differences between various philosophical positions. From this focus, we believe we can offer a clearer under-standing of the empirical behaviour of software as viewed from particular philosophical positions. Since the em-pirical evidence does not favour any single position, we conclude by arguing for the validity of ad hoc approaches to software design which we believe provides a stronger and more theoretically grounded approach to software design.
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