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    ABSTRACT: We present a lattice QCD computation of η and η^{′} masses and mixing angles, for the first time controlling continuum and quark mass extrapolations. The results for M_{η}=551(8)_{stat}(6)_{syst} MeV and M_{η^{′}}=1006(54)_{stat}(38)_{syst}(+61)_{ex} MeV are in excellent agreement with experiment. Our data show that the mixing in the quark flavor basis can be described by a single mixing angle of ϕ=46(1)_{stat}(3)_{syst}° indicating that the η^{′} is mainly a flavor singlet state.
    Physical Review Letters 10/2013; 111(18). DOI:10.1103/PhysRevLett.111.181602
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    ABSTRACT: Using the framework of transformation optics, this paper presents a detailed analysis of a non-singular square cloak for acoustic, out-of-plane shear elastic and electromagnetic waves. Analysis of wave propagation through the cloak is presented and accompanied by numerical illustrations. The efficacy of the regularized cloak is demonstrated and an objective numerical measure of the quality of the cloaking effect is provided. It is demonstrated that the cloaking effect persists over a wide range of frequencies. As a demonstration of the effectiveness of the regularized cloak, a Young's double slit experiment is presented. The stability of the interference pattern is examined when a cloaked and uncloaked obstacle are successively placed in front of one of the apertures. This novel link with a well-known quantum mechanical experiment provides an additional method through which the quality of cloaks may be examined. In the second half of the paper, it is shown that an approximate cloak may be constructed using a discrete lattice structure. The efficiency of the approximate lattice cloak is analysed and a series of illustrative simulations presented. It is demonstrated that effective cloaking may be obtained by using a relatively simple lattice structure, particularly, in the low-frequency regime.
    Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences 09/2013; 469(2157):20130218. DOI:10.1098/rspa.2013.0218
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    ABSTRACT: Understanding models which represent the invasion of network-based systems by infectious agents can give important insights into many real-world situations, including the prevention and control of infectious diseases and computer viruses. Here we consider Markovian susceptible-infectious-susceptible (SIS) dynamics on finite strongly connected networks, applicable to several sexually transmitted diseases and computer viruses. In this context, a theoretical definition of endemic prevalence is easily obtained via the quasi-stationary distribution (QSD). By representing the model as a percolation process and utilising the property of duality, we also provide a theoretical definition of invasion probability. We then show that, for undirected networks, the probability of invasion from any given individual is equal to the (probabilistic) endemic prevalence, following successful invasion, at the individual (we also provide a relationship for the directed case). The total (fractional) endemic prevalence in the population is thus equal to the average invasion probability (across all individuals). Consequently, for such systems, the regions or individuals already supporting a high level of infection are likely to be the source of a successful invasion by another infectious agent. This could be used to inform targeted interventions when there is a threat from an emerging infectious disease.
    PLoS ONE 07/2013; 8(7):e69028. DOI:10.1371/journal.pone.0069028
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    ABSTRACT: For an integer b>1 let (ϕ b (n)) n≥0 denote the base b van der Corput sequence in [0,1). Answering a question of O. Strauch, C. Aisleitner and M. Hofer [On the limit distribution of consecutive elements of the van der Corput sequence. Unif. Distrib. Theory 8, No. 1, 89–96 (2013)] showed that the distribution function of (ϕ b (n),ϕ b (n+1),⋯,ϕ b (n+s-1)) n≥0 on [0,1) s exists and is a copula. In this note we show that this phenomenon extends to a broad class of subsequences of the van der Corput sequences.
    Indagationes Mathematicae 06/2013; 24(3):593–601. DOI:10.1016/j.indag.2013.03.006
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    ABSTRACT: The mortality patterns in human populations reflect biological, social and medical factors affecting our lives, and mathematical modelling is an important tool for the analysis of these patterns. It is known that the mortality rate in all human populations increases with age after sexual maturity. This increase is predominantly exponential and satisfies the Gompertz equation. Although the exponential growth of mortality rates is observed over a wide range of ages, it excludes early- and late-life intervals. In this work we accept the fact that the mortality rate is an exponential function of age and analyse possible mechanisms underlying the deviations from the exponential law across the human lifespan. We consider the effect of heterogeneity as well as stochastic factors in altering the exponential law and compare our results to publicly available age-dependant mortality data for Swedish and US populations. In a model of heterogeneous populations we study how differences in parameters of the Gompertz equation describing different subpopulations account for mortality dynamics at different ages. Particularly, we show that the mortality data on Swedish populations can be reproduced fairly well by a model comprising four subpopulations. We then analyse the influence of stochastic effects on the mortality dynamics to show that they play a role only at early and late ages, when only a few individuals contribute to mortality. We conclude that the deviations from exponential law at young ages can be explained by heterogeneity, namely by the presence of a subpopulation with high initial mortality rate presumably due to congenital defects, while those for old ages can be viewed as fluctuations and explained by stochastic effects.
    Experimental gerontology 05/2013; 48(8). DOI:10.1016/j.exger.2013.05.054
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    ABSTRACT: Localized defect modes generated by a finite line defect composed of several masses, embedded in an infinite square cell lattice, are analysed using the linear superposition of Green's function for a single mass defect. Several representations of the lattice Green's function are presented and discussed. The problem is reduced to an eigenvalue system and the properties of the corresponding matrix are examined in detail to yield information regarding the number of symmetric and skew-symmetric modes. Asymptotic expansions in the far field, associated with long wavelength homogenization, are presented. Asymptotic expressions for Green's function in the vicinity of the band edge are also discussed. Several examples are presented where eigenfrequencies linked to this system and the corresponding eigenmodes are computed for various defects and compared with the asymptotic expansions. The case of an infinite defect is also considered and an explicit dispersion relation is obtained. For the case when the number of masses within the line defect is large, it is shown that the range of the eigenfrequencies can be predicted using the dispersion diagram for the infinite chain.
    Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences 02/2013; 469(2150-2150). DOI:10.1098/rspa.2012.0579
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    ABSTRACT: We give a rather general recipe for constructing nonextremal black hole solutions to N=2, D=4 gauged supergravity coupled to abelian vector multiplets. This problem simplifies considerably if one uses the formalism developed in arXiv:1112.2876, based on dimensional reduction and the real formulation of special geometry. We use this to find new nonextremal black holes for several choices of the prepotential, that generalize the BPS solutions found in arXiv:0911.4926. Some physical properties of these black holes are also discussed.
    Journal of High Energy Physics 11/2012; 2013(1). DOI:10.1007/JHEP01(2013)053
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    ABSTRACT: It has often been observed that population heterogeneities can lead to outbreaks of infection being less frequent and less severe than homogeneous population models would suggest. We address this issue by comparing a model incorporating various forms of heterogeneity with a homogenised model matched according to the value of the basic reproduction number [Formula: see text]. We mainly focus upon heterogeneity in individuals' infectivity and susceptibility, though with some allowance also for heterogeneous patterns of mixing. The measures of infectious spread we consider are (i) the probability of a major outbreak; (ii) the mean outbreak size; (iii) the mean endemic prevalence level; and (iv) the persistence time. For each measure, we establish conditions under which heterogeneity leads to a reduction in infectious spread. We also demonstrate that if such conditions are not satisfied, the reverse may occur. As well as comparison with a homogeneous population, we investigate comparisons between two heterogeneous populations of differing degrees of heterogeneity. All of our results are derived under the assumption that the susceptible population is sufficiently large.
    Journal of Mathematical Biology 09/2012; 67(4). DOI:10.1007/s00285-012-0578-x
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    ABSTRACT: In still fluid, many phytoplankton swim in helical paths with an average upwards motion. A new mechanistic model for gravitactic algae subject to an intrinsic torque is developed here, based on Heterosigma akashiwo, which results in upwards helical trajectories in still fluid. The resultant upwards swimming speed is calculated as a function of the gravitactic and intrinsic torques. Helical swimmers have a reduced upwards speed in still fluid compared to cells which swim straight upwards. However a novel result is obtained when the effect of fluid shear is considered. For intermediate values of shear and intrinsic torque, a new stable equilibrium solution for swimming direction is obtained for helical swimmers. This results in positive upwards transport in vertical shear flow, in contrast to the stable equilibrium solution for straight swimmers which results in downwards transport in vertical shear flow. Furthermore, for strong intrinsic torque, when there is no longer a stable orientation equilibrium, we show that the average downwards transport of helical swimmers in vertical shear flow is greatly suppressed compared to straight swimmers. We hypothesise that helical swimming provides robustness for upwards transport in the presence of fluid shearing motions.
    Journal of Mathematical Biology 04/2012; 66(7). DOI:10.1007/s00285-012-0531-z
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    ABSTRACT: Generic singularities of envelopes of families of chords and bifurcations of affine equidistants defined by a pair of a curve and a surface in R3 are classified. The chords join pairs of points of the curve and the surface such that the tangent line to the curve is parallel to the tangent plane to the surface. The classification contains singularities of stable Lagrange and Legendre projections, boundary singularities and some less known classes appearing at the points of the surface and the curve themselves.
    Topology and its Applications 02/2012; 159(2). DOI:10.1016/j.topol.2011.09.031
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