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Bibliography: l. 102

Bibliography: l. 102

Consider a periodically forced nonlinear system which can be presented as a collection of smaller subsystems with pairwise interactions between them. Each subsystem is assumed to be a massive point moving with friction on a compact surface, possibly with a boundary, in an external periodic field. We present sufficient conditions for the existence of a periodic solution for the whole system. The result is illustrated by a series of examples including a chain of strongly coupled pendulums in a periodic field.

The propagation of dispersive nonlinear waves in continuous and discrete media is investigated. The small scale dispersive oscillations are averaged out and a complete set of modulation equations that describe the evolution of the macroscopic quantities are derived and in special cases solved. At the level of greater refinement. detailed information on the small scale structure is obtained in integrable models. This is made possible by the development of a powerful new technique that leads to the explicit asymptotic solution of Riemann-Hilbert problems. Other techniques employed include Liapounov-Schmidt decomposition, modulation theory, eigenvalue dynamics, stability analysis, and shock wave theory. Models analyzed include the integrable as well as the generalized nonitegrable Korteweg-de Vries equation, the (modulationally unstable) nonlinear Schroedinger equation, and particle chains under various types of forcing. Semiconductor instabilities are also investigated. which lead to the generation of time periodic waves in semiconductors upon appropriate dc voltage bias. The nature of the instability that drives such time periodic behavior is explained and the phenomena are analyzed and understood by the use of analytical and computational means.

The propagation of dispersive nonlinear waves in continuous and discrete media is investigated. The small scale dispersive oscillations are averaged out and a complete set of modulation equations that describe the evolution of the macroscopic quantities are derived and in special cases solved. At the level of greater refinement. detailed information on the small scale structure is obtained in integrable models. This is made possible by the development of a powerful new technique that leads to the explicit asymptotic solution of Riemann-Hilbert problems. Other techniques employed include Liapounov-Schmidt decomposition, modulation theory, eigenvalue dynamics, stability analysis, and shock wave theory. Models analyzed include the integrable as well as the generalized nonitegrable Korteweg-de Vries equation, the (modulationally unstable) nonlinear Schroedinger equation, and particle chains under various types of forcing. Semiconductor instabilities are also investigated. which lead to the generation of time periodic waves in semiconductors upon appropriate dc voltage bias. The nature of the instability that drives such time periodic behavior is explained and the phenomena are analyzed and understood by the use of analytical and computational means.

The propagation of dispersive nonlinear waves in continuous and discrete media is investigated. The small scale dispersive oscillations are averaged out and a complete set of modulation equations that describe the evolution of the macroscopic quantities are derived and in special cases solved. At the level of greater refinement. detailed information on the small scale structure is obtained in integrable models. This is made possible by the development of a powerful new technique that leads to the explicit asymptotic solution of Riemann-Hilbert problems. Other techniques employed include Liapounov-Schmidt decomposition, modulation theory, eigenvalue dynamics, stability analysis, and shock wave theory. Models analyzed include the integrable as well as the generalized nonitegrable Korteweg-de Vries equation, the (modulationally unstable) nonlinear Schroedinger equation, and particle chains under various types of forcing. Semiconductor instabilities are also investigated. which lead to the generation of time periodic waves in semiconductors upon appropriate dc voltage bias. The nature of the instability that drives such time periodic behavior is explained and the phenomena are analyzed and understood by the use of analytical and computational means.

The propagation of dispersive nonlinear waves in continuous and discrete media is investigated. The small scale dispersive oscillations are averaged out and a complete set of modulation equations that describe the evolution of the macroscopic quantities are derived and in special cases solved. At the level of greater refinement. detailed information on the small scale structure is obtained in integrable models. This is made possible by the development of a powerful new technique that leads to the explicit asymptotic solution of Riemann-Hilbert problems. Other techniques employed include Liapounov-Schmidt decomposition, modulation theory, eigenvalue dynamics, stability analysis, and shock wave theory. Models analyzed include the integrable as well as the generalized nonitegrable Korteweg-de Vries equation, the (modulationally unstable) nonlinear Schroedinger equation, and particle chains under various types of forcing. Semiconductor instabilities are also investigated. which lead to the generation of time periodic waves in semiconductors upon appropriate dc voltage bias. The nature of the instability that drives such time periodic behavior is explained and the phenomena are analyzed and understood by the use of analytical and computational means.

We study a fractional reaction-diffusion system with two types of variables: activator and inhibitor. The interactions between components are modeled by cubical nonlinearity. Linearization of the system around the homogeneous state provides information about the stability of the solutions which is quite different from linear stability analysis of the regular system with integer derivatives. It is shown that by combining the fractional derivatives index with the ratio of characteristic times, it is possible to find the marginal value of the index where the oscillatory instability arises. The increase of the value of fractional derivative index leads to the time periodic solutions. The domains of existing of periodic solutions for different parameters of the problem are obtained. A computer simulation of the corresponding nonlinear fractional ordinary differential equations is presented. It is established by computer simulation that there exists a set of stable spatio-temporal tructures of the one-dimensional system under the Neumann and periodic boundary condition. The features of these solutions consist in the transformation of the steady state dissipative structures to homogeneous oscillations or space temporary structures at a certain value of fractional index and the ratio of characteristic times of system.

The anharmonic response of charge-density wave (CDW) order to strong laser-pulse perturbations in 1T-TaS_2 and TbTe_3 is investigated by means of a multiple-pump-pulse time-resolved femtosecond optical spectroscopy. We observe remarkable anharmonic effects hitherto undetected in the systems exhibiting collective charge ordering. The efficiency for additional excitation of the amplitude mode by a laser pulse becomes periodically modulated after the mode is strongly excited into a coherently oscillating state. A similar effect is observed also for some other phonons, where the cross-modulation at the amplitude-mode frequency indicates anharmonic interaction of those phonons with the amplitude mode. By analyzing the observed phenomena in the framework of time-dependent Ginzburg-Landau theory we attribute the effects to the anharmonicity of the mode potentials inherent to the broken symmetry state of the CDW systems.

Journal of Research of the National Bureau of Standards

Journal of Research of the National Bureau of Standards