Showing papers by "Jorge Eduardo Macías-Díaz published in 2009"
TL;DR: In this article, an implicit finite-difference scheme was proposed to approximate solutions of generalized Fermi-Pasta-Ulam systems defined on bounded domains which, amongst other features, include the presence of external and internal damping.
35 citations
TL;DR: It is established numerically that, under the presence of suitable initial conditions, there exists a threshold for the relaxation time with the property that solutions to the problems considered are nonnegative if and only if the relaxationTime is below a critical value.
28 citations
TL;DR: In this paper, the problem of controlling the propagation of moving breathers in semi-infinite discrete mechanical lattices in two dimensions is tackled, and nonlinear supratransmission is employed to show that an adequate modulation of the driving amplitude on two adjacent boundaries of the lattice yields an efficient transmission of binary information.
10 citations
TL;DR: In this article, the authors studied the nonlinear phenomena of supratransmission and bistability in harmonically forced arrays of anharmonic oscillators and employed a finite-difference scheme with multiple properties of consistency.
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.
7 citations
TL;DR: In this article, an explicit finite-difference method was developed to approximate solutions of modified Fermi-Pasta-Ulam media, which consider the presence of parameters, such as external damping, relativistic mass, a coefficient for the nonlinear term, and a coefficient of coupling in the case of discrete systems.
Abstract: We develop an explicit finite-difference method to approximate solutions of modified, Fermi–Pasta–Ulam media, which consider the presence of parameters, such as external damping, relativistic mass, a coefficient for the nonlinear term, and a coefficient of coupling in the case of discrete systems. We propose discrete expressions to approximate consistently the total energy of the system and the average energy flux, and prove that the discrete rate of change of energy is a consistent estimate of its continuous counterpart. The method is thoroughly tested in the energy domain, and our results show that the method gives an approximately constant energy in the case of conservative systems, which fluctuates within a narrow margin of error that may be attributed to truncation errors. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010
6 citations
TL;DR: In this article, the existence of nonlinear supratransmission in the simplest generalization of the classical β-Fermi-Pasta-Ulam chain to two-space dimensions, subject to harmonic boundary data in one end of the Dirichlet form, is established.
Abstract: In this work, we establish computationally the existence of the process of nonlinear supratransmission in the simplest generalization of the classical β-Fermi–Pasta–Ulam chain to two-space dimensions, subject to harmonic boundary data in one end of the Dirichlet form. Our simulations employ a finite-difference scheme with multiple properties of consistency in the domains of the solutions, the local energy density and the total energy of the system. Moreover, our results establish the presence of the phenomenon of nonlinear infratransmission or lower-transmission, thus proving the existence of a bistable region where a conducting and an insulating regimes coexist.
6 citations
TL;DR: In this article, the authors show that an adequate modulation of the driving amplitude in an anharmonic chain results in an efficient transmission of binary information, and the nonlinear processes of supratransmission and infratransmission are shown to be useful in the solution of the problem under investigation.
Abstract: In this work, we show that an adequate modulation of the driving amplitude in an anharmonic chain results in an efficient transmission of binary information. The nonlinear processes of supratransmission and infratransmission are shown to be useful in the solution of the problem under investigation. Numerical results are conducted using a finite-difference scheme with consistency properties in the energy domain, and the experiments show that localized nonlinear modes are propagated through the chain in a reliable and controlled manner.
2 citations