44 resultados para Bifurcation diagram
Resumo:
This paper describes the design and development cycle of a 3D biochip separator and the modelling analysis of flow behaviour in the biochip microchannel features. The focus is on identifying the difference between 2D and 3D implementations as well as developing basic forms of 3D microfluidic separators. Five variants, based around the device are proposed and analysed. These include three variations of the branch channels (circular, rectangular, disc) and two variations of the main channel (solid and concentric). Ignoring the initial transient behaviour and assuming steady state flow has been established, the efficiencies of the flow between the main and side channels for the different designs are analysed and compared with regard to relevant biomicrofluidic laws or effects (bifurcation law, Fahraeus effect, cell-free phenomenon, bending channel effect and laminar flow behaviour). The modelling results identify flow features in microchannels, a constriction and bifurcations and show detailed differences in flow fields between the various designs. The manufacturing process using injection moulding for the initial base case design is also presented and discussed. The work reported here is supported as part of the UK funded 3D-MINTEGRATION project. © 2010 IEEE.
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Our society is addicted to steel. Global demand for steel has risen to 1.4 billion tonnes a year and is set to at least double by 2050, while the steel industry generates nearly a 10th of the world's energy related CO₂ emissions. Meeting our 2050 climate change targets would require a 75% reduction in CO₂ emissions for every tonne of steel produced and finding credible solutions is proving a challenge. The starting point for understanding the environmental impacts of steel production is to accurately map the global steel supply chain and identify the biggest steel flows where actions can be directed to deliver the largest impact. In this paper we present a map of global steel, which for the first time traces steel flows from steelmaking, through casting, forming, and rolling, to the fabrication of final goods. The diagram reveals the relative scale of steel flows and shows where efforts to improve energy and material efficiency should be focused.
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We study the Fe-catalyzed chemical vapor deposition of carbon nanotubes by complementary in situ grazing-incidence X-ray diffraction, in situ X-ray reflectivity, and environmental transmission electron microscopy. We find that typical oxide supported Fe catalyst films form widely varying mixtures of bcc and fcc phased Fe nanoparticles upon reduction, which we ascribe to variations in minor commonly present carbon contamination levels. Depending on the as-formed phase composition, different growth modes occur upon hydrocarbon exposure: For γ-rich Fe nanoparticle distributions, metallic Fe is the active catalyst phase, implying that carbide formation is not a prerequisite for nanotube growth. For α-rich catalyst mixtures, Fe3C formation more readily occurs and constitutes part of the nanotube growth process. We propose that this behavior can be rationalized in terms of kinetically accessible pathways, which we discuss in the context of the bulk iron-carbon phase diagram with the inclusion of phase equilibrium lines for metastable Fe3C. Our results indicate that kinetic effects dominate the complex catalyst phase evolution during realistic CNT growth recipes. © 2012 American Chemical Society.
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The ballistic performance of equi-mass plates made from (i) stainless steel (SS); (ii) carbon fibre/epoxy (CF) laminate and (iii) a hybrid plate of both materials has been characterised for a spherical steel projectile. The hybrid plate was orientated with steel on the impact face (SSCF) and on the distal face (CFSS). The penetration velocity (V 50) was highest for the SS plate and lowest for the CF plate. A series of double impact tests were performed, with an initial velocity V I and a subsequent velocity V II at the same impact site. An interaction diagram in (V I,V II) space was constructed to delineate penetration from survival under both impacts. The degree of interaction between the two impact events was greater for the CFSS plate than for the SSCF plate, implying that the distal face has the major effect upon the degree of interaction.
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A common approach to visualise multidimensional data sets is to map every data dimension to a separate visual feature. It is generally assumed that such visual features can be judged independently from each other. However, we have recently shown that interactions between features do exist [Hannus et al. 2004; van den Berg et al. 2005]. In those studies, we first determined individual colour and size contrast or colour and orientation contrast necessary to achieve a fixed level of discrimination performance in single feature search tasks. These contrasts were then used in a conjunction search task in which the target was defined by a combination of a colour and a size or a colour and an orientation. We found that in conjunction search, despite the matched feature discriminability, subjects significantly more often chose an item with the correct colour than one with correct size or orientation. This finding may have consequences for visualisation: the saliency of information coded by objects' size or orientation may change when there is a need to simultaneously search for colour that codes another aspect of the information. In the present experiment, we studied whether a colour bias can also be found in a more complex and continuous task, Subjects had to search for a target in a node-link diagram consisting of SO nodes, while their eye movements were being tracked, Each node was assigned a random colour and size (from a range of 10 possible values with fixed perceptual distances). We found that when we base the distances on the mean threshold contrasts that were determined in our previous experiments, the fixated nodes tend to resemble the target colour more than the target size (Figure 1a). This indicates that despite the perceptual matching, colour is judged with greater precision than size during conjunction search. We also found that when we double the size contrast (i.e. the distances between the 10 possible node sizes), this effect disappears (Figure 1b). Our findings confirm that the previously found decrease in salience of other features during colour conjunction search is also present in more complex (more 'visualisation- realistic') visual search tasks. The asymmetry in visual search behaviour can be compensated for by manipulating step sizes (perceptual distances) within feature dimensions. Our results therefore also imply that feature hierarchies are not completely fixed and may be adapted to the requirements of a particular visualisation. Copyright © 2005 by the Association for Computing Machinery, Inc.
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Demand for aluminum in final products has increased 30-fold since 1950 to 45 million tonnes per year, with forecasts predicting this exceptional growth to continue so that demand will reach 2-3 times today's levels by 2050. Aluminum production uses 3.5% of global electricity and causes 1% of global CO2 emissions, while meeting a 50% cut in emissions by 2050 against growing demand would require at least a 75% reduction in CO2 emissions per tonne of aluminum produced--a challenging prospect. In this paper we trace the global flows of aluminum from liquid metal to final products, revealing for the first time a complete map of the aluminum system and providing a basis for future study of the emissions abatement potential of material efficiency. The resulting Sankey diagram also draws attention to two key issues. First, around half of all liquid aluminum (~39 Mt) produced each year never reaches a final product, and a detailed discussion of these high yield losses shows significant opportunities for improvement. Second, aluminum recycling, which avoids the high energy costs and emissions of electrolysis, requires signification "dilution" (~ 8 Mt) and "cascade" (~ 6 Mt) flows of higher aluminum grades to make up for the shortfall in scrap supply and to obtain the desired alloy mix, increasing the energy required for recycling.
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This paper describes a novel approach to the analysis of supply and demand of water in California. A stochastic model is developed to assess the future supply of and demand for water resources in California. The results are presented in the form of a Sankey diagram where present and stochastically-varying future fluxes of water in California and its sub-regions are traced from source to services by mapping the various transformations of water from when it is first made available for use, through its treatment, recycling and reuse, to its eventual loss in a variety of sinks. This helps to highlight the connections of water with energy and land resources, including the amount of energy used to pump and treat water, the amount of water used for energy production, and the land resources that create a water demand to produce crops for food. By mapping water in this way, policy-makers can more easily understand the competing uses of water, through the identification of the services it delivers (e.g. sanitation, food production, landscaping), the potential opportunities for improving themanagement of the resource and the connections with other resources which are often overlooked in a traditional sector-based management strategy. This paper focuses on a Sankey diagram for water, but the ultimate aim is the visualisation of linked resource futures through inter-connected Sankey diagrams for energy, land and water, tracking changes from the basic resources for all three, their transformations, and the final services they provide.
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The finite element method (FEM) is growing in popularity over the pressure diagram/hand calculation method for analysis of excavation systems in general and deep soil mixing excavations in particular. In this paper, a finite element analysis is used to study the behavior of a deep mixed excavation. Through the use of Plaxis (a FEM software program), the construction sequence is simulated by following the various construction phases allowing for deflections due to strut or anchor installation to be predicted. The numerical model used in this study simulates the soil cement columns as a continuous wall matching the bending stiffness of the actual wall. Input parameters based on laboratory tests and modeling assumptions are discussed. An example of the approach is illustrated using the Islais Creek Transport/Storage Project in San Francisco, California. Copyright ASCE 2006.
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We use the qualitative insight of a planar neuronal phase portrait to detect an excitability switch in arbitrary conductance-based models from a simple mathematical condition. The condition expresses a balance between ion channels that provide a negative feedback at resting potential (restorative channels) and those that provide a positive feedback at resting potential (regenerative channels). Geometrically, the condition imposes a transcritical bifurcation that rules the switch of excitability through the variation of a single physiological parameter. Our analysis of six different published conductance based models always finds the transcritical bifurcation and the associated switch in excitability, which suggests that the mathematical predictions have a physiological relevance and that a same regulatory mechanism is potentially involved in the excitability and signaling of many neurons. © 2013 Franci et al.
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This paper studies the excitability properties of a generalized FitzHugh-Nagumo model. The model differs from the classical FitzHugh-Nagumo model in that it accounts for the effect of cooperative gating variables such as activation of calcium currents. Excitability is explored by unfolding a pitchfork bifurcation that is shown to organize five different types of excitability. In addition to the three classical types of neuronal excitability, two novel types are described and distinctly associated to the presence of cooperative variables. © 2012 Society for Industrial and Applied Mathematics.
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Several feedback control laws have appeared in the literature concerning the stabilization of the nonlinear Moore-Greitzer axial compression model. Motivated by magnitude and rate limitations imposed by the physical implementation of the control law, Larsen et al. studied a dynamic implementation of the S-controller suggested by Sepulchre and Kokotović. They showed the potential benefit of implementing the S-controller through a first-order lag: while the location of the closed-loop equilibrium achieved with the static control law was sensitive to poorly known parameters, the dynamic implementation resulted in a small limit cycle at a very desirable location, insensitive to parameter variations. In this paper, we investigate the more general case when the control is applied with a time delay. This can be seen as an extension of the model with a first-order lag. The delay can either be a result of system constraints or be deliberately implemented to achieve better system behavior. The resulting closed-loop system is a set of parameter-dependent delay differential equations. Numerical bifurcation analysis is used to study this model and investigate whether the positive results obtained for the first-order model persist, even for larger values of the delay.
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Mitigation plans to combat climate change depend on the combined implementation of many abatement options, but the options interact. Published anthropogenic emissions inventories are disaggregated by gas, sector, country, or final energy form. This allows the assessment of novel energy supply options, but is insufficient for understanding how options for efficiency and demand reduction interact. A consistent framework for understanding the drivers of emissions is therefore developed, with a set of seven complete inventories reflecting all technical options for mitigation connected through lossless allocation matrices. The required data set is compiled and calculated from a wide range of industry, government, and academic reports. The framework is used to create a global Sankey diagram to relate human demand for services to anthropogenic emissions. The application of this framework is demonstrated through a prediction of per-capita emissions based on service demand in different countries, and through an example showing how the "technical potentials" of a set of separate mitigation options should be combined.
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The ability of hydrodynamically self-excited jets to lock into strong external forcing is well known. Their dynamics before lock-in and the specific bifurcations through which they lock in, however, are less well known. In this experimental study, we acoustically force a low-density jet around its natural global frequency. We examine its response leading up to lock-in and compare this to that of a forced van der Pol oscillator. We find that, when forced at increasing amplitudes, the jet undergoes a sequence of two nonlinear transitions: (i) from periodicity to T{double-struck}2 quasiperiodicity via a torus-birth bifurcation; and then (ii) from T{double-struck}2 quasiperiodicity to 1:1 lock-in via either a saddle-node bifurcation with frequency pulling, if the forcing and natural frequencies are close together, or a torus-death bifurcation without frequency pulling, but with a gradual suppression of the natural mode, if the two frequencies are far apart. We also find that the jet locks in most readily when forced close to its natural frequency, but that the details contain two asymmetries: the jet (i) locks in more readily and (ii) oscillates more strongly when it is forced below its natural frequency than when it is forced above it. Except for the second asymmetry, all of these transitions, bifurcations and dynamics are accurately reproduced by the forced van der Pol oscillator. This shows that this complex (infinite-dimensional) forced self-excited jet can be modelled reasonably well as a simple (three-dimensional) forced self-excited oscillator. This result adds to the growing evidence that open self-excited flows behave essentially like low-dimensional nonlinear dynamical systems. It also strengthens the universality of such flows, raising the possibility that more of them, including some industrially relevant flames, can be similarly modelled. © 2013 Cambridge University Press.
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The development is described of a computer-controlled bowing machine that can bow a string with a range of gestures that match or exceed the capabilities of a human violinist. Example measurements of string vibration under controlled bowing conditions are shown, including a Schelleng diagram and a set of Guettler diagrams, for the open D string of a cello. For some results a rosin-coated rod was used in place of a conventional bow, to provide quantitative data for comparison with theoretical predictions. The results show qualitative consistency with the predictions of Schelleng and Guettler, but details are revealed that go beyond the limitations of existing models. © S. Hirzel Verlag · EAA.