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36 results

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  • A numerical implementation of the unified Fokas transform for evolution problems on a finite interval

  • EMINE KESICI, BEATRICE PELLONI, TRISTAN PRYER, DAVID SMITH
  • Journal:
    European Journal of Applied Mathematics / Volume 29 / Issue 3 / June 2018
    Published online by Cambridge University Press:
    23 November 2017, pp. 543-567
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  • We present the numerical solution of two-point boundary value problems for a third-order linear PDE, representing a linear evolution in one space dimension. To our knowledge, the numerical evaluation of the solution so far could only be obtained by a time-stepping scheme, that must also take into account the issue, generically non-trivial, of the imposition of the boundary conditions. Instead of computing the evolution numerically, we evaluate the novel solution representation formula obtained by the unified transform, also known as Fokas transform. This representation involves complex line integrals, but in order to evaluate these integrals numerically, it is necessary to deform the integration contours using appropriate deformation mappings. We formulate a strategy to implement effectively this deformation, which allows us to obtain accurate numerical results.

Polarons
  • David Emin
  • Published online:
    05 December 2012
    Print publication:
    29 November 2012
  • Emin provides experimental and theoretical graduate students and researchers with a distinctive introduction to the principles governing polaron science. The fundamental physics is emphasized and mathematical formalism is avoided. The book gives a clear guide to how different types of polaron form and the measurements used to identify them. Analyses of four diverse physical problems illustrate polaron effects producing dramatic physical phenomena. The first part of the book describes the principles governing polaron and bipolaron formation in different classes of materials. The second part emphasizes distinguishing electronic-transport and optical phenomena through which polarons manifest themselves. The book concludes by extending polaron concepts to address critical aspects of four multifaceted electronic and atomic problems: large bipolarons' superconductivity, electronic switching of small-polaron semiconductors, electronically stimulated atomic desorption and diffusion of light interstitial atoms.

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