Biomedical subjects

Ramaz Khomeriki

Publications and source records attributed to Ramaz Khomeriki.

6 recordsLinked to original sources

PubMed2006

Coexistence of Josephson oscillations and a novel self-trapping regime in optical waveguide arrays.

Considering the coherent nonlinear dynamics between two weakly linked optical waveguide arrays, we find the first example of coexistence of Josephson oscillations with a novel self-trapping regime. This macroscopic bistability is explained by proving analytically the simultaneous existence of symmetric, antisymmetric, and asymmetric stationary solutions of the associated nonlinear Schrödinger equation. The effect is illustrated and confirmed by numerical simulations. This property allows us to conceive an optical switch based on the variation of the refractive index of the linking central waveguide.

Journal Article↗

PubMed2005

Nonadiabatic Landau-Zener tunneling in waveguide arrays with a step in the refractive index.

Landau-Zener tunneling is discussed in connection with optical waveguide arrays. Light injected in a specific band of the Bloch spectrum in the propagation constant can be transmitted to another band, changing its physical properties. This can be achieved using two coupled waveguide arrays with different refractive indices. The step in the refractive index causes wave "acceleration" and thus induces strongly nonadiabatic Landau-Zener tunneling. Theoretically, the analysis is performed by considering a Schrödinger equation in a periodic potential with a step. The region of physical parameters where this phenomenon can occur is analytically determined and a realistic experimental setup is suggested. Its application could allow the realization of light filters.

Journal Article↗

PubMed2005

The anti-FPU problem.

We present a detailed analysis of the modulational instability of the zone-boundary mode for one and higher-dimensional Fermi-Pasta-Ulam (FPU) lattices. Following this instability, a process of relaxation to equipartition takes place, which we have called the Anti-FPU problem because the energy is initially fed into the highest frequency part of the spectrum, at variance with the original FPU problem (low frequency excitations of the lattice). This process leads to the formation of chaotic breathers in both one and two dimensions. Finally, the system relaxes to energy equipartition on time scales which increase as the energy density is decreased. We show that breathers formed when cooling the lattice at the edges, starting from a random initial state, bear strong qualitative similarities with chaotic breathers.

Models, Statistical↗

PubMed2004

Nonlinear supratransmission and bistability in the Fermi-Pasta-Ulam model.

The recently discovered phenomenon of nonlinear supratransmission consists in a sudden increase of the amplitude of a transmitted wave triggered by the excitation of nonlinear localized modes of the medium. We examine this process for the Fermi-Pasta-Ulam chain, sinusoidally driven at one edge and damped at the other. The supratransmission regime occurs for driving frequencies above the upper band edge and originates from direct moving discrete breather creation. We derive approximate analytical estimates of the supratransmission threshold, which are in excellent agreement with numerics. When analyzing the long-time behavior, we discover that, below the supratransmission threshold, a conducting stationary state coexists with the insulating one. We explain the bistable nature of the energy flux in terms of the excitation of quasiharmonic extended waves. This leads to the analytical calculation of a lower-transmission threshold which is also in reasonable agreement with numerical experiments.

Journal Article↗

PubMed2004

Nonlinear band gap transmission in optical waveguide arrays.

The effect of nonlinear transmission in coupled optical waveguide arrays is theoretically investigated and a realistic experimental setup is suggested. The beam is injected in a single boundary waveguide, linear refractive index of which (n(0)) is larger than refractive indexes (n) of other identical waveguides in the array. Particularly, the effect holds if omega(n(0)-n)/c>2Q, where Q is a linear coupling constant between array waveguides, omega is a carrier wave frequency, and c is a light velocity. Numerical experiments show that the energy transfers from the boundary waveguide to the waveguide array above a certain threshold intensity of the injected beam. This effect is due to the creation and the propagation of gap solitons in full analogy with a similar phenomenon in sine-Gordon lattice [Phys. Rev. Lett. 89, 134102 (2002)]].

Journal Article↗

PubMed2002

Interaction of a kink soliton with a breather in a Fermi-Pasta-Ulam chain.

The collision process between a breather and moving kink soliton is investigated both analytically and numerically in Fermi-Pasta-Ulam (FPU) chains. As it is shown by both analytical and numerical consideration low amplitude breathers and soft kinks retain their shapes after interaction. Low amplitude breather only changes the location after collision and remains static. As the numerical simulations show, the shift of its position is proportional to the stiffness of the kink soliton, what is in accordance with the analytical predictions made in this paper. The numerical experiments are also carried out for large amplitude breathers and some interesting effects are observed: The odd parity large amplitude breather does not change position when colliding with a widely separated soft kink-antikink pair, while in the case of a closely placed kink-antikink pair the breather transforms into the moving one. Therefore it is suggested that the "harmless" objects similar to the kink solitons in FPU chains could be used in order to displace or move the strongly localized structures in realistic physical systems. In particular, the analogies with quasi-one-dimensional easy-plane-type spin structures are discussed.

Journal Article↗