995 resultados para 0101 Pure Mathematics


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Steady simulations were performed to investigate tip leakage flow and heat transfer characteristics on the rotor blade tip and casing in a single-stage gas turbine engine. A typical high-pressure gas turbine stage was modeled with a pressure ratio of 3.2. The predicted isentropic Mach number and adiabatic wall temperature on the casing showed good agreement with available experimental data under similar operating condition. The present numerical study focuses extensively on the effects of tip clearance heights and rotor rotational speeds on the blade tip and casing heat transfer characteristics. It was observed that the tip leakage flow structure is highly dependent on the height of the tip gap and the speed of the rotor. In all cases, the tip leakage flow was seen to separate and recirculate just around the corner of the pressure side of the blade tip. This region of re-circulating flow enlarges with increasing clearance heights. The separated leakage flow reattaches afterwards on the tip surface. Leakage flow reattachment was shown to enhance surface heat transfer at the tip. The interaction between tip leakage flow and secondary flows that is induced by the relative casing motion is found to significantly influence the blade tip and casing heat transfer distribution. A region of critical heat transfer exists on the casing near the blade tip leading edge and along the pressure-side edge for all the clearance heights that were investigated. At high rotation speed, the region of critical heat transfer tends to move towards the trailing edge due to the change in inflow angle.

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In conditional probabilistic logic programming, given a query, the two most common forms for answering the query are either a probability interval or a precise probability obtained by using the maximum entropy principle. The former can be noninformative (e.g.,interval [0; 1]) and the reliability of the latter is questionable when the priori knowledge isimprecise. To address this problem, in this paper, we propose some methods to quantitativelymeasure if a probability interval or a single probability is sufficient for answering a query. We first propose an approach to measuring the ignorance of a probabilistic logic program with respect to a query. The measure of ignorance (w.r.t. a query) reflects howreliable a precise probability for the query can be and a high value of ignorance suggests that a single probability is not suitable for the query. We then propose a method to measure the probability that the exact probability of a query falls in a given interval, e.g., a second order probability. We call it the degree of satisfaction. If the degree of satisfaction is highenough w.r.t. the query, then the given interval can be accepted as the answer to the query. We also prove our measures satisfy many properties and we use a case study to demonstrate the significance of the measures. © Springer Science+Business Media B.V. 2012

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The Irish Pavilion at the Venice Architecture Biennale 2012 charts a position for Irish architecture in a global culture where the modes of production of architecture are radically altered. Ireland is one of the most globalised countries in the world, yet it has developed a national culture of architecture derived from local place as a material construct. We now have to evolve our understanding in the light of the globalised nature of economic processes and architectural production which is largely dependent on internationally networked flows of products, data, and knowledge. We have just begun to represent this situation to ourselves and others. How should a global architecture be grounded culturally and philosophically? How does it position itself outside of shared national reference points?
heneghan peng architects were selected as participants because they are working across three continents on a range of competition-winning projects. Several of these are in sensitive and/or symbolic sites that include three UNESCO World Heritage sites, including the Grand Egyptian Museum in Cairo, the Giants Causeway Visitor Centre in Northern Ireland, and the new Rhine Bridge near Lorelei.
Our dialogue led us to discussing the universal languages of projective geometry and number are been shared by architects and related professionals. In the work of heneghan peng, the specific embodiment of these geometries is carefully calibrated by the choice of materials and the detailed design of their physical performance on site. The stone facade of the Giant’s Causeway Visitor Centre takes precise measure of the properties of the volcanic basalt seams from which it is hewn. The extraction of the stone is the subject of the pavilion wall drawings which record the cutting of stones to create the façade of the causeway centre.
We also identified water as an element which is shared across the different sites. Venice is a perfect place to take measure of this element which suggests links to another site – the Nile Valley which was enriched by the annual flooding of the River Nile. An ancient Egyptian rod for measuring the water level of the Nile inspired the design of the Nilometre - a responsive oscillating bench that invites visitors to balance their respective weights. This action embodies the ways of thinking that are evolving to operate in the globalised world, where the autonomous architectural object is dissolving into an expanded field of conceptual rules and systems. The bench constitutes a shifting ground located in the unstable field of Venice. It is about measurement and calibration of the weight of the body in relation to other bodies; in relation to the site of the installation; and in relation to water. The exhibit is located in the Artiglierie section of the Arsenale. Its level is calibrated against the mark of the acqua alta in the adjacent brickwork of the building which embodies a liminal moment in the fluctuating level of the lagoon.
The weights of bodies, the level of water, changes over time, are constant aspects of design across cultures and collectively they constitute a common ground for architecture - a ground shared with other design professionals. The movement of the bench required complex engineering design and active collaboration between the architects, engineers and fabricators. It is a kind of prototype – a physical object produced from digital data that explores the mathematics at play – the see-saw motion invites the observer to become a participant, to give it a test drive. It shows how a simple principle can generate complex effects that are difficult to predict and invites visitors to experiment and play with them.

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Silicon carbide (SiC) is a material of great technological interest for engineering applications concerning hostile environments where silicon-based components cannot work (beyond 623 K). Single point diamond turning (SPDT) has remained a superior and viable method to harness process efficiency and freeform shapes on this harder material. However, it is extremely difficult to machine this ceramic consistently in the ductile regime due to sudden and rapid tool wear. It thus becomes non trivial to develop an accurate understanding of tool wear mechanism during SPDT of SiC in order to identify measures to suppress wear to minimize operational cost.

In this paper, molecular dynamics (MD) simulation has been deployed with a realistic analytical bond order potential (ABOP) formalism based potential energy function to understand tool wear mechanism during single point diamond turning of SiC. The most significant result was obtained using the radial distribution function which suggests graphitization of diamond tool during the machining process. This phenomenon occurs due to the abrasive processes between these two ultra hard materials. The abrasive action results in locally high temperature which compounds with the massive cutting forces leading to sp3–sp2 order–disorder transition of diamond tool. This represents the root cause of tool wear during SPDT operation of cubic SiC. Further testing led to the development of a novel method for quantitative assessment of the progression of diamond tool wear from MD simulations.

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Oscillating wave surge converters (OWSCs) are a class of wave power technology that exploits the enhanced horizontal fluid particle movement of waves in the nearshore coastal zone with water depths of 10–20 m. OWSCs predominantly oscillate horizontally in surge as opposed to the majority of wave devices, which oscillate vertically in heave and usually are deployed in deeper water. The characteristics of the nearshore wave resource are described along with the hydrodynamics of OWSCs. The variables in the OWSC design space are discussed together with a presentation of some of their effects on capture width, frequency bandwidth response and power take-off characteristics. There are notable differences between the different OWSCs under development worldwide, and these are highlighted. The final section of the paper describes Aquamarine Power’s 315kW Oyster 1 prototype, which was deployed at the European Marine Energy Centre in August 2009. Its place in the OWSC design space is described along with the practical experience gained. This has led to the design of Oyster 2, which was deployed in August 2011. It is concluded that nearshore OWSCs are serious contenders in the mix of wave power technologies. The nearshore wave climate has a narrower directional spread than the offshore, the largest waves are filtered out and the exploitable resource is typically only 10–20% less in 10m depth compared with 50m depth. Regarding the devices, a key conclusion is that OWSCs such as Oyster primarily respond in the working frequency range to the horizontal fluid acceleration; Oyster is not a drag device responding to horizontal fluid velocity. The hydrodynamics of Oyster is dominated by inertia with added inertia being a very significant contributor. It is unlikely that individual flap modules will exceed 1MW in installed capacity owing to wave resource, hydrodynamic and economic constraints. Generating stations will be made up of line arrays of flaps with communal secondary power conversion every 5–10 units.

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This paper investigates the distribution of the condition number of complex Wishart matrices. Two closely related measures are considered: the standard condition number (SCN) and the Demmel condition number (DCN), both of which have important applications in the context of multiple-input multipleoutput (MIMO) communication systems, as well as in various branches of mathematics. We first present a novel generic framework for the SCN distribution which accounts for both central and non-central Wishart matrices of arbitrary dimension. This result is a simple unified expression which involves only a single scalar integral, and therefore allows for fast and efficient computation. For the case of dual Wishart matrices, we derive new exact polynomial expressions for both the SCN and DCN distributions. We also formulate a new closed-form expression for the tail SCN distribution which applies for correlated central Wishart matrices of arbitrary dimension and demonstrates an interesting connection to the maximum eigenvalue moments of Wishart matrices of smaller dimension. Based on our analytical results, we gain valuable insights into the statistical behavior of the channel conditioning for various MIMO fading scenarios, such as uncorrelated/semi-correlated Rayleigh fading and Ricean fading. © 2010 IEEE.

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The application of the shape memory alloy NiTi in micro-electro-mechanical-systems (MEMSs) is extensive nowadays. In MEMS, complex while precise motion control is always vital. This makes the degradation of the functional properties of NiTi during cycling loading such as the appearance of residual strain become a serious problem to study, in particular for laser micro-welded NiTi in real applications. Although many experimental efforts have been put to study the mechanical properties of laser welded NiTi, surprisingly, up to the best of our understanding, there has not been attempts to quantitatively model the laser-welded NiTi under mechanical cycling in spite of the accurate prediction required in applications and the large number of constitutive models to quantify the thermo-mechanical behavior of shape memory alloys. As the first attempt to fill the gap, we employ a recent constitutive model, which describes the localized SIMT in NiTi under cyclic deformation; with suitable modifications to model the mechanical behavior of the laser welded NiTi under cyclic tension. The simulation of the model on a range of tensile cyclic deformation is consistent with the results of a series of experiments. From this, we conclude that the plastic deformation localized in the welded regions (WZ and HAZs) of the NiTi weldment can explain most of the extra amount of residual strain appearing in welded NiTi compared to the bare one. Meanwhile, contrary to common belief, we find that the ability of the weldment to memorize its transformation history, sometimes known as ‘return point memory’, still remains unchanged basically though the effective working limit of this ability reduces to within 6% deformation.

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We consider the problem of self-healing in peer-to-peer networks that are under repeated attack by an omniscient adversary. We assume that, over a sequence of rounds, an adversary either inserts a node with arbitrary connections or deletes an arbitrary node from the network. The network responds to each such change by quick “repairs,” which consist of adding or deleting a small number of edges. These repairs essentially preserve closeness of nodes after adversarial deletions, without increasing node degrees by too much, in the following sense. At any point in the algorithm, nodes v and w whose distance would have been l in the graph formed by considering only the adversarial insertions (not the adversarial deletions), will be at distance at most l log n in the actual graph, where n is the total number of vertices seen so far. Similarly, at any point, a node v whose degree would have been d in the graph with adversarial insertions only, will have degree at most 3d in the actual graph. Our distributed data structure, which we call the Forgiving Graph, has low latency and bandwidth requirements. The Forgiving Graph improves on the Forgiving Tree distributed data structure from Hayes et al. (2008) in the following ways: 1) it ensures low stretch over all pairs of nodes, while the Forgiving Tree only ensures low diameter increase; 2) it handles both node insertions and deletions, while the Forgiving Tree only handles deletions; 3) it requires only a very simple and minimal initialization phase, while the Forgiving Tree initially requires construction of a spanning tree of the network.

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In 2000–2002 an innovative early years curriculum, the Enriched Curriculum (EC), was introduced
into 120 volunteer schools across Northern Ireland, replacing a traditional curriculum similar to
others across the UK at that time. It was intended by the designers to be developmentally appropriate
and play-based with the primary goal of preventing the experience of persistent early failure in
children. The EC was not intended to be a literacy and numeracy intervention, yet it did considerably
alter pedagogy in these domains, particularly the age at which formal reading and mathematics
instruction began. As part of a multi-method evaluation running from 2000–2008, the research
team followed the primary school careers of the first two successive cohorts of EC children, comparing
them with year-ahead controls attending the same 24 schools. Compared to the year-ahead control
group, the findings show that the EC children’s reading and mathematics scores fell behind in
the first two years but the majority of EC children caught up by the end of their fourth year. Thereafter,
the performance of the first EC cohort fell away slightly, while that of the second continued to
match that of controls. Overall, the play-based curriculum had no statistically significant positive
effects on reading and mathematics in the medium term. At best, the EC children’s scores matched
those of controls.