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  • 1.
    Bordag, Ljudmila A.
    Halmstad University, School of Information Science, Computer and Electrical Engineering (IDE), Halmstad Embedded and Intelligent Systems Research (EIS), MPE-lab.
    Symmetry reductions and exact solutions for nonlinear diffusion equations2009In: International Journal of Modern Physics A, ISSN 0217-751X, E-ISSN 1793-656X, Vol. 24, no 8/9, p. 1713-1716Article in journal (Refereed)
    Abstract [en]

    The symmetry properties of nonlinear diffusion equations are studied using a Lie group analysis. Reductions and families of exact solutions are found for some of these equations.

    © 2009 World Scientific Publishing Company.

  • 2.
    Bordag, Michael
    et al.
    Univ Leipzig, Vor Hospitaltore 1, D-04103 Leipzig, Germany..
    Nikolaev, Vladimir
    Halmstad University, School of Information Technology, Halmstad Embedded and Intelligent Systems Research (EIS).
    Analytic corrections to the electromagnetic casimir interaction between a sphere and a plate at shortdistances2010In: International Journal of Modern Physics A, ISSN 0217-751X, E-ISSN 1793-656X, Vol. 25, no 11, p. 2171-2176Article in journal (Refereed)
    Abstract [en]

    For the vacuum interaction of a sphere in front of a plane, both obeying conductor boundary conditions, we consider the approximation of small separation. We derive the next-to-leading order of the asymptotic expansion in the separation-to-radius ratio epsilon. This correction is of order epsilon. In opposite to the scalar cases it contains also contributions proportional to logarithms in first and second order, epsilon In epsilon and e(ln epsilon)(2). We compare this result with the available findings of numerical and experimental approaches.

  • 3.
    Bordag, Michael
    et al.
    Leipzig University, Vor Dem Hospitaltore 1, D-04103 Leipzig, Germany.
    Nikolaev, Vladimir
    Halmstad University, School of Information Science, Computer and Electrical Engineering (IDE), Halmstad Embedded and Intelligent Systems Research (EIS).
    Analytic corrections to the electromagnetic casimir interaction between a sphere and a plate at shortdistances2010In: International Journal of Modern Physics A, ISSN 0217-751X, E-ISSN 1793-656X, Vol. 25, no 11, p. 2171-2176Article in journal (Refereed)
    Abstract [en]

    For the vacuum interaction of asphere in front of a plane,both obeying conductor boundary conditions, we consider the approximation of small separation. We derive the next-to-leading order of the asymptotic expansion in the separation-to-radius ratio epsilon. This correction is of order epsilon. In opposite to the scalar cases it contains also contributions proportional to logarithms in first and second order, epsilon ln epsilon and epsilon(ln epsilon)(2). We compare this result with the available findings of numerical and experimental approaches.

  • 4.
    Bordag, Michael
    et al.
    Leipzig University, Vor dem Hospitaltore 1, D-04103 Leipzig, Germany.
    Nikolaev, Vladimir
    Halmstad University, School of Information Science, Computer and Electrical Engineering (IDE), Halmstad Embedded and Intelligent Systems Research (EIS).
    Beyond proximity force approximation in the casimir effect2009In: International Journal of Modern Physics A, ISSN 0217-751X, E-ISSN 1793-656X, Vol. 24, no 8-9, p. 1743-1747Article in journal (Refereed)
    Abstract [en]

    We compare the analytical and numerical results for the Casimir force for the configuration of a plane and a cylinder in front of a plane. While for Dirichlet boundary conditions on both, plane and sphere or cylinder, agreement is found, for Neumann boundary conditions on either the plane or one of the two, cylinder or sphere, disagreement is found. This holds, for a sphere, also for different boundary conditions on the interacting surfaces. From recent, new numerical results for the cylinder, a general appearance of logarithmic contributions beyond PFA can be predicted.

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