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  Proceedings of the Estonian Academy of Sciences. Physics. Mathematics

 

ISSN 1406-0086

Published since 1952 to 2007

Proceedings of the Estonian Academy of Sciences. Physics. Mathematics

 

ISSN 1406-0086

Published since 1952 to 2007

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On the propagation of localized perturbations in media with microstructure; 84–92

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Authors

Lauri Ilison, Andrus Salupere, Pearu Peterson

Abstract

The propagation of solitary waves in dilatant granular materials is studied using the hierarchical Korteweg–de Vries type evolution equation. The model equation is solved numerically under localized initial conditions by the pseudospectral method. The behaviour of the solution is analysed over a wide range of material parameters (two dispersion parameters and one microstructure parameter). Five solution types are introduced. Special attention is paid to the solitonic character of solutions.

Keywords

dilatant granular materials, solitons, wave hierarchies, Korteweg–de Vries type evolution equations.

References

  1. Giovine , P. and Oliveri , F. Dynamics and wave propagation in dilatant granular materials. Meccanica , 1995 , 30 , 341–357.

 doi:10.1007/BF00993418

  2. Oliveri , F. Wave propagation in granular materials as continua with microstructure. Application to seismic waves in a sediment filled site. Rend. Circolo Matem. Palermo , 1996 , 45 , 487–499.

  3. Cataldo , G. and Oliveri , F. Nonlinear seismic waves: a model for site effects. Int. J. Non-Linear Mech. , 1999 , 34 , 457–468.

  4. Whitham , G. B. Linear and Nonlinear Waves. John Wiley & Sons , New York , 1974.

  5. Zabusky , N. J. and Kruskal , M. D. Interaction of “solitons” in a collisionless plasma and the recurrence of initial states. Phys. Rev. Lett. , 1965 , 15 , 240–243.

  6. Fornberg , B. A. Practical Guide to Pseudospectral Methods. Cambridge University Press , Cambridge , 1998.

  7. Salupere , A. , Engelbrecht , J. and Peterson , P. On the long-time behaviour of soliton ensembles. Math. Comput. Simul. , 2003 , 62 , 137–147.

  8. Jones , E. , Oliphant , T. , Peterson , P. et al. SciPy: Open Source Scientific Tools for Python. 2001 , available at http://www.scipy.org

  9. Frigo , M. and Johnson , S. G. The design and implementation of FFTW3. Proc. IEEE , 2005 , 93 , 216–231.

10. Peterson , P. Fortran to Python Interface Generator. 2005 , available at http://cens.ioc.ee/projects/f2py2e/

11. Hindmarsh , A. C. Odepack , a systematized collection of ODE solvers. In Scientific Computing (Stepleman , R. S. et al. , eds). North-Holland , Amsterdam , 1983 , 55–64.

12. Porubov , A. V. Amplification of Nonlinear Strain Waves in Solids. World Scientific , Singapore , 2003.

13. Christov , C. I. and Velarde , M. G. Dissipative solitons. Physica D , 1995 , 86 , 323–347.

 
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Current Issue: Vol. 56, Issue 4, 2007




Publishing schedule:
No. 1: 20 March
No. 2: 20 June
No. 3: 20 September
No. 4: 20 December