18 resultados para Multi-term time-fractional diffusion equations

em CentAUR: Central Archive University of Reading - UK


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In the UK, participation in higher education has risen over the past two decades, along with a shift of the costs of higher education onto the individual and a move to widening participation among previously underrepresented groups. This has led to changes in the way individuals fund their higher education, in particular a rise in the incidence of term time employment. Term time employment potentially plays a much bigger role than in the past, both as a means for individuals to fund their education and reduce debt, and as a way to gain valuable work experience and increase employability. With the increase in the number of graduates in the UK labour market it is now more important for individuals to be able to differentiate themselves in the labour market.

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We consider the time-harmonic Maxwell equations with constant coefficients in a bounded, uniformly star-shaped polyhedron. We prove wavenumber-explicit norm bounds for weak solutions. This result is pivotal for convergence proofs in numerical analysis and may be a tool in the analysis of electromagnetic boundary integral operators.

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In this paper, we extend to the time-harmonic Maxwell equations the p-version analysis technique developed in [R. Hiptmair, A. Moiola and I. Perugia, Plane wave discontinuous Galerkin methods for the 2D Helmholtz equation: analysis of the p-version, SIAM J. Numer. Anal., 49 (2011), 264-284] for Trefftz-discontinuous Galerkin approximations of the Helmholtz problem. While error estimates in a mesh-skeleton norm are derived parallel to the Helmholtz case, the derivation of estimates in a mesh-independent norm requires new twists in the duality argument. The particular case where the local Trefftz approximation spaces are built of vector-valued plane wave functions is considered, and convergence rates are derived.

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Recent UK changes in the number of students entering higher education, and in the nature of financial support, highlight the complexity of students’ choices about human capital investments. Today’s students have to focus not on the relatively narrow issue of how much academic effort to invest, but instead on the more complicated issue of how to invest effort in pursuit of ‘employability skills’, and how to signal such acquisitions in the context of a highly competitive graduate jobs market. We propose a framework aimed specifically at students’ investment decisions, which encompasses corner solutions for both borrowing and employment while studying.

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In homogeneous environments, by overturning the possibility of competitive exclusion among phytoplankton species, and by regulating the dynamics of overall plankton population, toxin-producing phytoplankton (TPP) potentially help in maintaining plankton diversity—a result shown recently. Here, I explore the competitive effects of TPP on phytoplankton and zooplankton species undergoing spatial movements in the subsurface water. The spatial interactions among the species are represented in the form of reaction-diffusion equations. Suitable parametric conditions under which Turing patterns may or may not evolve are investigated. Spatiotemporal distributions of species biomass are simulated using the diffusivity assumptions realistic for natural planktonic systems. The study demonstrates that spatial movements of planktonic systems in the presence of TPP generate and maintain inhomogeneous biomass distribution of competing phytoplankton, as well as grazer zooplankton, thereby ensuring the persistence of multiple species in space and time. The overall results may potentially explain the sustainability of biodiversity and the spatiotemporal emergence of phytoplankton and zooplankton species under the influence of TPP combined with their physical movement in the subsurface water.

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Much of the writing on urban regeneration in the UK has been focused on the types of urban spaces that have been created in city centres. Less has been written about the issue of when the benefits of regeneration could and should be delivered to a range of different interests, and the different time frames that exist in any development area. Different perceptions of time have been reflected in dominant development philosophies in the UK and elsewhere. The trickle-down agendas of the 1980s, for example, were criticised for their focus on the short-term time frames and needs of developers, often at the expense of those of local communities. The recent emergence of sustainability discourses, however, ostensibly changes the time focus of development and promotes a broader concern with new imagined futures. This paper draws on the example of development in Salford Quays, in the North West of England, to argue that more attention needs to be given to the politics of space-time in urban development processes. It begins by discussing the importance and relevance of this approach before turning to the case study and the ways in which the local politics of space-time has influenced development agendas and outcomes. The paper argues that such an approach harbours the potential for more progressive, far-reaching, and sustainable development agendas to be developed and implemented.

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Electrochemical determination of redox active dye species is demonstrated in indigo samples contaminated with high levels of organic and inorganic impurities. The use of a hydrodynamic electrode system based on a vibrating probe (250 Hz, 200 mu m lateral amplitude) allows time-independent diffusion controlled signals to be enhanced and reliable concentration data to be obtained under steady state conditions at relatively fast scan rates up to 4 V s-1In this work the indigo content of a complex plant-derived indigo sample (dye content typically 30%) is determined after indigo is reduced by addition of glucose in aqueous 0.2 M NaOH. The soluble leuco-indigo is measured by its oxidation response at a vibrating electrode. The vibrating electrode, which consisted of a laterally vibrating 500 mu m diameter gold disc, is calibrated with Fe(CN)(6) 3-/4- in 0.1 M KCl and employed for indigo determination at 55, 65, and 75 C in 0.2 M NaOH. Determinations of the indigo content of 25 different samples of plant-derived indigo are compared with those obtained by conventional spectrophotometry. This comparison suggests a significant improvement by the electrochemical method, which appears to be less sensitive to impurities.

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A one-dimensional shock-reflection test problem in the case of slab, cylindrical or spherical symmetry is discussed for multi-component flows. The differential equations for a similarity solution are derived and then solved numerically in conjunction with the Rankine-Hugoniot shock relations.

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An efficient numerical self-consistent field theory (SCFT) algorithm is developed for treating structured polymers on spherical surfaces. The method solves the diffusion equations of SCFT with a pseudospectral approach that combines a spherical-harmonics expansion for the angular coordinates with a modified real-space Crank–Nicolson method for the radial direction. The self-consistent field equations are solved with Anderson-mixing iterations using dynamical parameters and an alignment procedure to prevent angular drift of the solution. A demonstration of the algorithm is provided for thin films of diblock copolymer grafted to the surface of a spherical core, in which the sequence of equilibrium morphologies is predicted as a function of diblock composition. The study reveals an array of interesting behaviors as the block copolymer pattern is forced to adapt to the finite surface area of the sphere.

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This study examines the numerical accuracy, computational cost, and memory requirements of self-consistent field theory (SCFT) calculations when the diffusion equations are solved with various pseudo-spectral methods and the mean field equations are iterated with Anderson mixing. The different methods are tested on the triply-periodic gyroid and spherical phases of a diblock-copolymer melt over a range of intermediate segregations. Anderson mixing is found to be somewhat less effective than when combined with the full-spectral method, but it nevertheless functions admirably well provided that a large number of histories is used. Of the different pseudo-spectral algorithms, the 4th-order one of Ranjan, Qin and Morse performs best, although not quite as efficiently as the full-spectral method.

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The benefits of property in the mixed asset portfolio has been the subject of a number of studies both in the UK and around the world. The traditional way of investigating this issue is to use MPT with the results suggesting that Property should play a significant role in the mixed asset portfolio. These results are not without criticism and generally revolve around quality and quantity of the property data series. To overcome these deficiencies this paper uses cointegration methodology which examines the longer term time series behaviour of various asset markets using a very long run desmoothed data series. Using a number of different cointegration tests, both pair-wise and multivariate, the results show, in unambiguous terms, that there is no contemporous cointegration between the major asset classes Property, Equities and Bonds. The implications of which are that Property does indeed have a risk reducing place to play in the long-run strategic mixed-asset portfolio. A result of particular relevance to institutions such as pension funds and life insurance companies who would wish to hold investments for the long-term.

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The phase shift full bridge (PSFB) converter allows high efficiency power conversion at high frequencies through zero voltage switching (ZVS); the parasitic drain-to-source capacitance of the MOSFET is discharged by a resonant inductance before the switch is gated resulting in near zero turn-on switching losses. Typically, an extra inductance is added to the leakage inductance of a transformer to form the resonant inductance necessary to charge and discharge the parasitic capacitances of the PSFB converter. However, many PSFB models do not consider the effects of the magnetizing inductance or dead-time in selecting the resonant inductance required to achieve ZVS. The choice of resonant inductance is crucial to the ZVS operation of the PSFB converter. Incorrectly sized resonant inductance will not achieve ZVS or will limit the load regulation ability of the converter. This paper presents a unique and accurate equation for calculating the resonant inductance required to achieve ZVS over a wide load range incorporating the effects of the magnetizing inductance and dead-time. The derived equations are validated against PSPICE simulations of a PSFB converter and extensive hardware experimentations.

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South American seasonally-dry tropical forests (SDTF) are critically endangered, with only a small proportion of their original distribution remaining. This paper presents a 12,000 year reconstruction of climate change, fire and vegetation dynamics in the Bolivian Chiquitano SDTF, based upon pollen and charcoal analysis, to examine the resilience of this ecosystem to drought and fire. Our analysis demonstrates a complex relationship between climate, fire and floristic composition over multi-millennial time scales, and reveals that moisture variability is the dominant control upon community turnover in this ecosystem. Maximum drought during the early Holocene, consistent with regional drought reconstructions, correlates with a period of significant fire activity between 8,000 and 7,000 cal yr BP which resulted in a decrease in SDTF diversity. As fire activity declined, but severe regional droughts persisted through the mid-Holocene, SDTF, including Anadenanthera and Astronium, became firmly established in the Bolivian lowlands. The trend of decreasing fire activity during the last two millennia promotes the idea among forest ecologists that SDTF are threatened by fire. Our analysis shows that the Chiquitano seasonally dry biome has been more resilient to Holocene changes in climate and fire regime than previously assumed, but raises questions over whether this resilience will continue in the future under increased temperatures and drought coupled with a higher frequency anthropogenic fire regime.

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Decadal predictions on timescales from one year to one decade are gaining importance since this time frame falls within the planning horizon of politics, economy and society. The present study examines the decadal predictability of regional wind speed and wind energy potentials in three generations of the MiKlip (‘Mittelfristige Klimaprognosen’) decadal prediction system. The system is based on the global Max-Planck-Institute Earth System Model (MPI-ESM), and the three generations differ primarily in the ocean initialisation. Ensembles of uninitialised historical and yearly initialised hindcast experiments are used to assess the forecast skill for 10 m wind speeds and wind energy output (Eout) over Central Europe with lead times from one year to one decade. With this aim, a statistical-dynamical downscaling (SDD) approach is used for the regionalisation. Its added value is evaluated by comparison of skill scores for MPI-ESM large-scale wind speeds and SDD-simulated regional wind speeds. All three MPI-ESM ensemble generations show some forecast skill for annual mean wind speed and Eout over Central Europe on yearly and multi-yearly time scales. This forecast skill is mostly limited to the first years after initialisation. Differences between the three ensemble generations are generally small. The regionalisation preserves and sometimes increases the forecast skills of the global runs but results depend on lead time and ensemble generation. Moreover, regionalisation often improves the ensemble spread. Seasonal Eout skills are generally lower than for annual means. Skill scores are lowest during summer and persist longest in autumn. A large-scale westerly weather type with strong pressure gradients over Central Europe is identified as potential source of the skill for wind energy potentials, showing a similar forecast skill and a high correlation with Eout anomalies. These results are promising towards the establishment of a decadal prediction system for wind energy applications over Central Europe.