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  • 1.
    Andersson, Anders
    et al.
    Jönköping University, School of Engineering, JTH, Physics and Mathematics and Chemical Engineering.
    Nilsson, Börje
    Linnaeus university, Vaxjö, Sweden.
    Biro, Thomas
    Jönköping University, School of Engineering, JTH, Physics and Mathematics and Chemical Engineering.
    Fourier methods for harmonic scalar waves in general waveguides2016In: Journal of Engineering Mathematics, ISSN 0022-0833, E-ISSN 1573-2703, Vol. 98, no 1, p. 21-38Article in journal (Refereed)
    Abstract [en]

    A set of semi-analytic techniques based on Fourier analysis is used to solve wave-scattering problems in variously shaped waveguides with varying normal admittance boundary conditions. Key components are the newly developed conformal mapping methods, wave splitting, Fourier series expansions in eigenfunctions to non-normal operators, the building block method or the cascade technique, Dirichlet-to-Neumann operators, and reformulation in terms of stable differential equations for reflection and transmission matrices. For an example, the results show good correspondence with a finite element method solution to the same problem in the low- and medium-frequency domains. The Fourier method complements finite element analysis as a waveguide simulation tool. For inverse engineering involving tuning of straight waveguide parts joining complicated waveguide elements, the Fourier method is an attractive alternative including time aspects. The prime motivation for the Fourier method is its added physical understanding primarily at low frequencies.

  • 2.
    Olofsson, Peter
    et al.
    Jönköping University, School of Engineering, JTH, Physics and Mathematics and Chemical Engineering. Department of Mathematics, Trinity University, United States.
    Livingstone, Kevin
    Department of Biology, Trinity University, United States.
    Humphreys, Joshua
    Department of Biology, Trinity University, United States.
    Steinman, Douglas
    Department of Mathematics, Trinity University, United States.
    The probability of speciation on an interaction network with unequal substitution rates2016In: Mathematical Biosciences, ISSN 0025-5564, E-ISSN 1879-3134, Vol. 278, p. 1-4Article in journal (Refereed)
    Abstract [en]

    Speciation is characterized by the development of reproductive isolating barriers between diverging groups. A seminal paper of a mathematical model of speciation was published by Orr (1995), extended by Livingstone et al. (2012) to incorporate interaction networks. Here, we further develop the model to take into account the possibility of different substitution rates for network nodes of different connectivity. Mathematically, this amounts to sampling nodes from an undirected graph where the inclusion probability for a given node depends on its degree (number of connecting edges). We establish formulas for the rate of speciation and identify a crucial parameter that is a measure of the deviation from simple random sampling.

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