1,204 research outputs found

    Ground State Energy of the One-Dimensional Discrete Random Schr\"{o}dinger Operator with Bernoulli Potential

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    In this paper, we show the that the ground state energy of the one dimensional Discrete Random Schroedinger Operator with Bernoulli Potential is controlled asymptotically as the system size N goes to infinity by the random variable \ell_N, the length the longest consecutive sequence of sites on the lattice with potential equal to zero. Specifically, we will show that for almost every realization of the potential the ground state energy behaves asymptotically as π2N+1)2\frac{\pi^2}{\ell_N+1)^2} in the sense that the ratio of the quantities goes to one

    Asymptotic behaviour of the spectrum of a waveguide with distant perturbations

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    We consider the waveguide modelled by a nn-dimensional infinite tube. The operator we study is the Dirichlet Laplacian perturbed by two distant perturbations. The perturbations are described by arbitrary abstract operators ''localized'' in a certain sense, and the distance between their ''supports'' tends to infinity. We study the asymptotic behaviour of the discrete spectrum of such system. The main results are a convergence theorem and the asymptotics expansions for the eigenvalues. The asymptotic behaviour of the associated eigenfunctions is described as well. We also provide some particular examples of the distant perturbations. The examples are the potential, second order differential operator, magnetic Schroedinger operator, curved and deformed waveguide, delta interaction, and integral operator

    Change in the order of the melting transition with oxygen content in YBa2Cu3O7-δ

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    The vortex phase transition was systematically studied in twin-free YBa2Cu3O7-δ for various δ. For 7-δ>~6.94, the first order transition was evidenced by an abrupt jump and a hysteresis of magnetization in the field-cooled (FC) cooling-warming cycles, which indicates the coexistence of vortex crystallites and liquid. For 7-δ<6.89 the jump was not sharp and FC magnetization was reversible, suggesting a second order transition. The first and the second order transitions merge at a critical point (CP) which goes to zero field for 7-δ<6.89. Three-dimensional XY scaling satisfactorily fits the data at 1–7 T for 7-δ<6.94 and for 7-δ<6.89, but does not fit for 6.89<7-δ<6.94, where the CP passes through this field range

    Visualising and quantifying the variability of hydrological state in intermittent rivers

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    The hydrology of intermittent rivers has been characterised using either flow regimes, with limited spatial resolution, or network contraction, with limited temporal resolution. Exploration of the dynamic behaviour of these rivers, on which highly diverse biological communities depend, requires longitudinal, year-round observations with a more detailed classification of hydrological state than can be provided by gauging stations or wet/dry mapping alone. Observations of dry, ponded, moderate flow and high flow hydrological states spanning 20 years with approximately monthly frequency along ten chalk rivers in the south-east of England were visualised. There was slower transitioning between hydrological states and less spatial fragmentation on rivers with groundwater-dominated regimes than on those more influenced by superficial deposits. Seasonal patterns in both the composition and configuration of states were demonstrated using adapted landscape metrics. Responses to hydrological extremes and anthropogenic influences included drying downstream of the source and an artificially near-perennial reach. A framework is proposed for the categorisation of metrics of hydrological state and demonstrates that the classification and dimensional limitations of traditional approaches cannot fully characterise the hydrological behaviour of intermittent rivers. Such characterisation is an important step towards the tailored assessments required for effective management of these dynamic systems

    A Detailed Investigation into Low-Level Feature Detection in Spectrogram Images

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    Being the first stage of analysis within an image, low-level feature detection is a crucial step in the image analysis process and, as such, deserves suitable attention. This paper presents a systematic investigation into low-level feature detection in spectrogram images. The result of which is the identification of frequency tracks. Analysis of the literature identifies different strategies for accomplishing low-level feature detection. Nevertheless, the advantages and disadvantages of each are not explicitly investigated. Three model-based detection strategies are outlined, each extracting an increasing amount of information from the spectrogram, and, through ROC analysis, it is shown that at increasing levels of extraction the detection rates increase. Nevertheless, further investigation suggests that model-based detection has a limitation—it is not computationally feasible to fully evaluate the model of even a simple sinusoidal track. Therefore, alternative approaches, such as dimensionality reduction, are investigated to reduce the complex search space. It is shown that, if carefully selected, these techniques can approach the detection rates of model-based strategies that perform the same level of information extraction. The implementations used to derive the results presented within this paper are available online from http://stdetect.googlecode.com

    Nonlinear porous medium flow with fractional potential pressure

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    We study a porous medium equation, with nonlocal diffusion effects given by an inverse fractional Laplacian operator. We pose the problem in n-dimensional space for all t>0 with bounded and compactly supported initial data, and prove existence of a weak and bounded solution that propagates with finite speed, a property that is nor shared by other fractional diffusion models.Comment: 32 pages, Late

    Assessing the risk of bluetongue to UK livestock: uncertainty and sensitivity analyses of a temperature-dependent model for the basic reproduction number

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    Since 1998 bluetongue virus (BTV), which causes bluetongue, a non-contagious, insect-borne infectious disease of ruminants, has expanded northwards in Europe in an unprecedented series of incursions, suggesting that there is a risk to the large and valuable British livestock industry. The basic reproduction number, R0, provides a powerful tool with which to assess the level of risk posed by a disease. In this paper, we compute R0 for BTV in a population comprising two host species, cattle and sheep. Estimates for each parameter which influences R0 were obtained from the published literature, using those applicable to the UK situation wherever possible. Moreover, explicit temperature dependence was included for those parameters for which it had been quantified. Uncertainty and sensitivity analyses based on Latin hypercube sampling and partial rank correlation coefficients identified temperature, the probability of transmission from host to vector and the vector to host ratio as being most important in determining the magnitude of R0. The importance of temperature reflects the fact that it influences many processes involved in the transmission of BTV and, in particular, the biting rate, the extrinsic incubation period and the vector mortality rate

    Age Trajectories of the Structural Connectome in Child and Adolescent Offspring of Individuals With Bipolar Disorder or Schizophrenia

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    Background: Offspring of parents with severe mental illness (e.g., bipolar disorder or schizophrenia) are at elevated risk of developing psychiatric illness owing to both genetic predisposition and increased burden of environmental stress. Emerging evidence indicates a disruption of brain network connectivity in young offspring of patients with bipolar disorder and schizophrenia, but the age trajectories of these brain networks in this high-familial-risk population remain to be elucidated. Methods: A total of 271 T1-weighted and diffusion-weighted scans were obtained from 174 offspring of at least 1 parent diagnosed with bipolar disorder (n = 74) or schizophrenia (n = 51) and offspring of parents without severe mental illness (n = 49). The age range was 8 to 23 years; 97 offspring underwent 2 scans. Anatomical brain networks were reconstructed into structural connectivity matrices. Network analysis was performed to investigate anatomical brain connectivity. Results: Offspring of parents with schizophrenia had differential trajectories of connectivity strength and clustering compared with offspring of parents with bipolar disorder and parents without severe mental illness, of global efficiency compared with offspring of parents without severe mental illness, and of local connectivity compared with offspring of parents with bipolar disorder. Conclusions: The findings of this study suggest that familial high risk of schizophrenia is related to deviations in age trajectories of global structural connectome properties and local connectivity strength.</p

    Singularities in the Fermi liquid description of a partially filled Landau level and the energy gaps of fractional quantum Hall states

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    We consider a two dimensional electron system in an external magnetic field at and near an even denominator Landau level filling fraction. Using a fermionic Chern--Simons approach we study the description of the system's low energy excitations within an extension of Landau's Fermi liquid theory. We calculate perturbatively the effective mass and the quasi--particle interaction function characterizing this description. We find that at an even denominator filling fraction the fermion's effective mass diverges logarithmically at the Fermi level, and argue that this divergence allows for an {\it exact} calculation of the energy gaps of the fractional quantized Hall states asymptotically approaching these filling fractions. We find that the quasi--particle interaction function approaches a delta function. This singular behavior leads to a cancelation of the diverging effective mass from the long wavelength low frequency linear response functions at even denominator filling fractions.Comment: 46 pages, RevTeX, 5 figures included in a uuencoded postscript file. Minor revisions relative to the original version. The paper will be published in the Physical Review B, and can be retrieved from the World Wide Web, in http://cmtw.harvard.edu/~ster
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