NONLINEAR SUPRATRANSMISSION AND NONLINEAR BISTABILITY IN A FORCED LINEAR ARRAY OF ANHARMONIC OSCILLATORS: A COMPUTATIONAL STUDY

J. E. Macías-Díaz () and I. E. Medina-Ramírez ()
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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

International Journal of Modern Physics C (IJMPC), 2009, vol. 20, issue 12, 1911-1923

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.

Keywords: Forced anharmonic chains; β-Fermi–Pasta–Ulam systems; finite-difference schemes; nonlinear supratransmission; nonlinear bistability; 02.60.Lj; 02.70.Bf; 63.20.Ry (search for similar items in EconPapers)
Date: 2009
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DOI: 10.1142/S0129183109014813

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