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Nonlinear Supratransmission And Nonlinear Bistability In A Forced Linear Array Of Anharmonic Oscillators: A Computational Study

Author

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  • J. E. MACÍAS-DÍAZ

    (Departamento de Matemáticas y Física, Universidad Autónoma de Aguascalientes, Avenida Universidad 940, Ciudad Universitaria, Aguascalientes 20100, Mexico)

  • I. E. MEDINA-RAMÍREZ

    (Departamento de Química, Universidad Autónoma de Aguascalientes, Avenida Universidad 940, Ciudad Universitaria, Aguascalientes 20100, Mexico)

Abstract

The nonlinear phenomena of supratransmission and bistability in harmonically forced arrays of anharmonic oscillators are studied in the present article. Employing a finite-difference scheme with multiple properties of consistency, we show that these processes are actually present in such nonlinear systems. We show that, for every frequency in the forbidden band-gap of the medium, there exists a critical forcing amplitude above which the propagation of energy into the system from the boundary is inevitable. We provide diagrams of total energy vs amplitude for several values of the parameters of the model studied in this work, as well as a graph establishing the relationship between the critical amplitude at which supratransmission starts vs frequency. Likewise, we establish the existence of a bistable region, where a conducting and an insulating regimes coexist.

Suggested Citation

  • J. E. Macías-Díaz & I. E. Medina-Ramírez, 2009. "Nonlinear Supratransmission And Nonlinear Bistability In A Forced Linear Array Of Anharmonic Oscillators: A Computational Study," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 20(12), pages 1911-1923.
    • Handle: RePEc:wsi:ijmpcx:v:20:y:2009:i:12:n:s0129183109014813
    DOI: 10.1142/S0129183109014813
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