literature
Literature
Authors
Jobs
Seminars
Conferences
DataBETA

Computational Results for the Higgs Boson Equation in the de Sitter Spacetime

Mar 3, 2018
22 pages
e-Print:
View in:
pdf
reference search0 citations

Citations per year

0 Citations
Abstract: (arXiv)
High performance computations are presented for the Higgs Boson Equation in the de Sitter Space- time using explicit fourth order Runge-Kutta scheme on the temporal discretization and fourth order finite difference discretization in space. In addition to the fully three space dimensional equation its one space dimensional radial solutions are also examined. The numerical code for the three space di- mensional equation has been programmed in CUDA Fortran and was performed on NVIDIA Tesla K40c GPU Accelerator. The radial form of the equation was simulated in MATLAB. The numerical results demonstrate the existing theoretical result that under certain conditions bubbles form in the scalar field. We also demonstrate the known blow-up phenomena for the solutions of the semilinear Klein-Gordon equation with imaginary mass. Our numerical studies suggest several previously not known properties of the solution for which theoretical proofs do not exist yet: 1. smooth solution exists for all time if the initial conditions are compactly supported and smooth; 2. under some conditions no bubbles form; 3. solutions converge to step functions related to unforced, damped Duffing equations.
  • [1]
    Sobolev spaces, second ed., Pure and Applied Mathematics (Amsterdam), vol. 140 / Press, Amsterdam,. MR 2424078
    • Robert A. Adams
      ,
    • John J.F. Fournier
  • [2]
    Utkarsh Ayachit, The ParaView guide: A parallel visualization application, Kitware, Inc., USA
  • [3]
    Kartik Chandra Basak, Pratap Chandra Ray, and Rasajit Kumar Bera, Solution of non-linear Klein- Gordon equation with a quadratic non-linear term by adomian decomposition method
      • Commun.Nonlinear Sci.Numer.Simul. 14 (2009) 718-723
  • [4]
    The impossibility of free tachyons, Relativity and Gravitation C. G. Kuper and Asher Peres, eds.), New York Science Publishers,, pp. 41-46
    • A. Bers
      ,
    • R. Fox
      ,
    • C.G. Kuper
      ,
    • S.G. Lipson
  • [5]
    Christophe Bogey and Christophe family of low dispersive and low dissipative explicit schemes for flow and noise computations
    • A. Bailly
      • J.Comput.Phys. 194 (2004) 194-214
  • [6]
    Gary Cohen and Patrick Joly, Construction and analysis of fourth-order finite difference schemes for the acoustic wave equation in nonhomogeneous media
      • SIAM J.Numer.Anal. 33 (1996) 1266-1302
  • [7]
    Sidney Coleman, Aspects of symmetry: Selected Erice lectures, Cambridge University Press
  • [8]
    Mehdi Dehghan and Ali Shokri, Numerical solution of the nonlinear Klein-Gordon equation using radial basis functions
      • J.Comput.Appl.Math. 230 (2009) 400-410
  • [9]
    Stability of Runge-Kutta methods for stiff nonlinear differential equations Science Ltd Amsterdam
    • K. Dekker
      ,
    • J.G. Verwer
  • [10]
    Numerical study of the blowup/global existence dichotomy for the focusing cubic nonlinear Klein-Gordon equation
    • R. Donninger
      ,
    • W. Schlag
      • Nonlinearity 24 (2011) 2547
  • [12]
    Smooth bump functions and the geometry of banach spaces: A brief survey
    • R. Fry
      ,
    • S. McManus
      • Expo.Math. 20 (2002) 143-183
  • [13]
    Traveling wave analysis of partial differential equations: Numerical and analytical methods with Matlab and Maple Science
    • G. Griffiths
      ,
    • W.E. Schiesser
  • [14]
    Lars Hörmander, Lectures on nonlinear hyperbolic differential equations, Mathématiques & Applications (Berlin) [Mathematics & Applications], vol. 26 -Verlag, Berlin,. MR 1466700
  • [15]
    Salvador Jiménez and Luis Vázquez, Analysis of four numerical schemes for a nonlinear Klein-Gordon equation
      • Appl.Math.Comput. 35 (1990) 61-94
  • [16]
    Doˇgan Kaya and Salah M. El-Sayed, A numerical solution of the Klein-Gordon equation and convergence of the decomposition method
      • Appl.Math.Comput. 156 (2004) 341-353
  • [17]
    Symbolic generation of finite difference formulas MR 0494848
    • H.B. Keller
      ,
    • V. Pereyra
      • Math.Comput. 32 (1978) 955-971
  • [18]
    Andrew Liddle, An introduction to modern cosmology, 3 ed 7
  • [19]
    Particle physics and inflationary cosmology, Harwood Publishers, Chur Switzerland New York
    • A.D. Linde
  • [20]
    Two finite-difference schemes that preserve the dissipation of energy in a system of modified wave equations 22 REFERENCES
    • J.E. Macías-Díaz
      ,
    • S. Jerez-Galiano
      • Commun.Nonlinear Sci.Numer.Simul. 15 (2010) 552-563
  • [21]
    NVIDIA Corporation, CUDA Fortran programming guide and reference doc/pgicudaforug.pdf
  • [22]
    PGI CUDA Fortran compiler
  • [23]
    Numerical solution of the nonlinear Klein-Gordon equation
    • J. Rashidinia
      ,
    • M. Ghasemi
      ,
    • R. Jalilian
      • J.Comput.Appl.Math. 233 (2010) 1866-1878
  • [24]
    Gilbert Strang, Computational science and engineering, Wellesley-Cambridge Press, Wellesley, MA,. MR 2742791
  • [25]
    Inc. The MathWorks, MATLAB and Statistics Toolbox Releaseb
  • 1-25 of 30
  • 1
  • 2
  • 25 / page