The Experts below are selected from a list of 279 Experts worldwide ranked by ideXlab platform

S. C. Pandey - One of the best experts on this subject based on the ideXlab platform.

  • A unified elliptic-type Integral and associated recurrence relations
    Indian Journal of Pure and Applied Mathematics, 2013
    Co-Authors: S. C. Pandey
    Abstract:

    Elliptic-type Integrals have their importance or potential in certain problems in radiation physics and nuclear technology. A number of earlier works on the subject contains several interesting unifications and generalizations of some significant families of elliptic-type Integrals. Beside explicit Representations of certain families of unified elliptic-type Integrals, Contour Integral Representation, various recurrence relations are derived in the present investigation. The results derived in this article are of manifold generality and provide extensions and unification to the large number of known results established earlier.

  • On the new computable solution of the generalized fractional kinetic equations involving the generalized function for the fractional calculus and related functions
    Astrophysics and Space Science, 2008
    Co-Authors: V. B. L. Chaurasia, S. C. Pandey
    Abstract:

    In view of the usefulness and a great importance of the kinetic equation in certain astrophysical problems the authors develop a new and further generalized form of the fractional kinetic equation involving the G -function, a generalized function for the fractional calculus. This new generalization can be used for the computation of the change of chemical composition in stars like the Sun. The Mellin-Barnes Contour Integral Representation of the G -function is also established. The manifold generality of the G -function is discussed in terms of the solution of the above fractional kinetic equation. A compact and easily computable solution is established. Special cases, involving the generalized Mittag-leffler function and the R -function, are considered. The obtained results imply more precisely the known results.

  • On the new computable solution of the generalized fractional kinetic equations involving the generalized function for the fractional calculus and related functions
    Astrophysics and Space Science, 2008
    Co-Authors: V. B. L. Chaurasia, S. C. Pandey
    Abstract:

    In view of the usefulness and a great importance of the kinetic equation in certain astrophysical problems the authors develop a new and further generalized form of the fractional kinetic equation involving the G-function, a generalized function for the fractional calculus. This new generalization can be used for the computation of the change of chemical composition in stars like the Sun. The Mellin-Barnes Contour Integral Representation of the G-function is also established. The manifold generality of the G-function is discussed in terms of the solution of the above fractional kinetic equation. A compact and easily computable solution is established. Special cases, involving the generalized Mittag-leffler function and the R-function, are considered. The obtained results imply more precisely the known results.

Klaus Kirsten - One of the best experts on this subject based on the ideXlab platform.

  • Heat Kernel Coefficients for Laplace Operators on the Spherical Suspension
    Communications in Mathematical Physics, 2012
    Co-Authors: Guglielmo Fucci, Klaus Kirsten
    Abstract:

    In this paper we compute the coefficients of the heat kernel asymptotic expansion for Laplace operators acting on scalar functions defined on the so called spherical suspension (or Riemann cap) subjected to Dirichlet boundary conditions. By utilizing a Contour Integral Representation of the spectral zeta function for the Laplacian on the spherical suspension we find its analytic continuation in the complex plane and its associated meromorphic structure. Thanks to the well known relation between the zeta function and the heat kernel obtainable via Mellin transform we compute the coefficients of the asymptotic expansion in arbitrary dimensions. The particular case of a d -dimensional sphere as the base manifold is studied as well and the first few heat kernel coefficients are given.

  • Heat Kernel Coefficients for Laplace Operators on the Spherical Suspension
    Communications in Mathematical Physics, 2012
    Co-Authors: Guglielmo Fucci, Klaus Kirsten
    Abstract:

    In this paper we compute the coefficients of the heat kernel asymptotic expansion for Laplace operators acting on scalar functions defined on the so called spherical suspension (or Riemann cap) subjected to Dirichlet boundary conditions. By utilizing a Contour Integral Representation of the spectral zeta function for the Laplacian on the spherical suspension we find its analytic continuation in the complex plane and its associated meromorphic structure. Thanks to the well known relation between the zeta function and the heat kernel obtainable via Mellin transform we compute the coefficients of the asymptotic expansion in arbitrary dimensions. The particular case of a d-dimensional sphere as the base manifold is studied as well and the first few heat kernel coefficients are given explicitly.

Guglielmo Fucci - One of the best experts on this subject based on the ideXlab platform.

  • Heat Kernel Coefficients for Laplace Operators on the Spherical Suspension
    Communications in Mathematical Physics, 2012
    Co-Authors: Guglielmo Fucci, Klaus Kirsten
    Abstract:

    In this paper we compute the coefficients of the heat kernel asymptotic expansion for Laplace operators acting on scalar functions defined on the so called spherical suspension (or Riemann cap) subjected to Dirichlet boundary conditions. By utilizing a Contour Integral Representation of the spectral zeta function for the Laplacian on the spherical suspension we find its analytic continuation in the complex plane and its associated meromorphic structure. Thanks to the well known relation between the zeta function and the heat kernel obtainable via Mellin transform we compute the coefficients of the asymptotic expansion in arbitrary dimensions. The particular case of a d -dimensional sphere as the base manifold is studied as well and the first few heat kernel coefficients are given.

  • Heat Kernel Coefficients for Laplace Operators on the Spherical Suspension
    Communications in Mathematical Physics, 2012
    Co-Authors: Guglielmo Fucci, Klaus Kirsten
    Abstract:

    In this paper we compute the coefficients of the heat kernel asymptotic expansion for Laplace operators acting on scalar functions defined on the so called spherical suspension (or Riemann cap) subjected to Dirichlet boundary conditions. By utilizing a Contour Integral Representation of the spectral zeta function for the Laplacian on the spherical suspension we find its analytic continuation in the complex plane and its associated meromorphic structure. Thanks to the well known relation between the zeta function and the heat kernel obtainable via Mellin transform we compute the coefficients of the asymptotic expansion in arbitrary dimensions. The particular case of a d-dimensional sphere as the base manifold is studied as well and the first few heat kernel coefficients are given explicitly.

V. B. L. Chaurasia - One of the best experts on this subject based on the ideXlab platform.

  • On the new computable solution of the generalized fractional kinetic equations involving the generalized function for the fractional calculus and related functions
    Astrophysics and Space Science, 2008
    Co-Authors: V. B. L. Chaurasia, S. C. Pandey
    Abstract:

    In view of the usefulness and a great importance of the kinetic equation in certain astrophysical problems the authors develop a new and further generalized form of the fractional kinetic equation involving the G -function, a generalized function for the fractional calculus. This new generalization can be used for the computation of the change of chemical composition in stars like the Sun. The Mellin-Barnes Contour Integral Representation of the G -function is also established. The manifold generality of the G -function is discussed in terms of the solution of the above fractional kinetic equation. A compact and easily computable solution is established. Special cases, involving the generalized Mittag-leffler function and the R -function, are considered. The obtained results imply more precisely the known results.

  • On the new computable solution of the generalized fractional kinetic equations involving the generalized function for the fractional calculus and related functions
    Astrophysics and Space Science, 2008
    Co-Authors: V. B. L. Chaurasia, S. C. Pandey
    Abstract:

    In view of the usefulness and a great importance of the kinetic equation in certain astrophysical problems the authors develop a new and further generalized form of the fractional kinetic equation involving the G-function, a generalized function for the fractional calculus. This new generalization can be used for the computation of the change of chemical composition in stars like the Sun. The Mellin-Barnes Contour Integral Representation of the G-function is also established. The manifold generality of the G-function is discussed in terms of the solution of the above fractional kinetic equation. A compact and easily computable solution is established. Special cases, involving the generalized Mittag-leffler function and the R-function, are considered. The obtained results imply more precisely the known results.

Ivan B Bazhlekov - One of the best experts on this subject based on the ideXlab platform.

  • Nonsingular boundary Integral method for deformable drops in viscous flows
    Physics of Fluids, 2004
    Co-Authors: Ivan B Bazhlekov, Patrick Patrick Anderson, Han E. H. Meijer
    Abstract:

    A three-dimensional boundary Integral method for deformable drops in viscous flows at low Reynolds numbers is presented. The method is based on a new nonsingular Contour-Integral Representation of the single and double layers of the free-space Green's function. The Contour integration overcomes the main difficulty with boundary-Integral calculations: the singularities of the kernels. It also improves the accuracy of the calculations as well as the numerical stability. A new element of the presented method is also a higher-order interface approximation, which improves the accuracy of the interface-to-interface distance calculations and in this way makes simulations of polydispersed foam dynamics possible. Moreover, a multiple time-step integration scheme, which improves the numerical stability and thus the performance of the method, is introduced. To demonstrate the advantages of the method presented here, a number of challenging flow problems is considered: drop deformation and breakup at high viscosity ratios for zero and finite surface tension; drop-to-drop interaction in close approach, including film formation and its drainage; and formation of a foam drop and its deformation in simple shear flow, including all structural and dynamic elements of polydispersed foams.

  • Contour Integral Representation of single and double layer potentials for axisymmetric problems
    Lecture Notes in Computer Science, 2003
    Co-Authors: Emilia Bazhlekova, Ivan B Bazhlekov
    Abstract:

    Based on recently proposed non-singular Contour-Integral Representations of single and double layer potentials for 3D surfaces, formulas in the axisymmetric case are derived. They express explicitly the singular layer potentials in terms of elliptic Integrals. The presented expressions are non-singular, satisfy exactly very important conservation principles and directly take into account the multivaluedness of the double layer potential. The results are compared with another method for calculating the single and double layer potentials. The comparison demonstrates higher accuracy and better performance of the presented formulas.

  • Numerical Methods and Application - Contour-Integral Representation of Single and Double Layer Potentials for Axisymmetric Problems
    Numerical Methods and Applications, 2002
    Co-Authors: Emilia Bazhlekova, Ivan B Bazhlekov
    Abstract:

    Based on recently proposed non-singular Contour-Integral Representations of single and double layer potentials for 3D surfaces, formulas in the axisymmetric case are derived. They express explicitly the singular layer potentials in terms of elliptic Integrals. The presented expressions are non-singular, satisfy exactly very important conservation principles and directly take into account the multivaluedness of the double layer potential. The results are compared with another method for calculating the single and double layer potentials. The comparison demonstrates higher accuracy and better performance of the presented formulas.