Presence Of Nonlinear Effects Research Articles

Nonlinear electrical response and breakdown of semicontinuous metal films

The weakly nonlinear electrical response, determined by 3rd harmonic generation, and the breakdown current I b of percolating systems are measured in real materials: semicontinuous Ag and Au films. The 3rd harmonic is interpreted as a direct measure of the 4th moment of the current distribution, and thus provides the critical exponent κ (normally determined by 1/ƒ noise measurements). Observations of higher harmonics (5th and 7th), corresponding to higher moments of the current distribution, provide an estimation of higher critical indices. The breakdown current I b was measured over three decades of film resistance. A new criterion for I b is suggested, defined as the current at which a hot spot reaches the melting temperature of the metallic grains T m. This criterion remains valid in the presence of nonlinear effects. The hot spot model yields a power law I b ∞ B - x , B=V 3ƒ/I 3 where the upper and lower bounds of x are found to be 0.5 (extreme case of continuum percolation) and 0.36 (lattice percolation lower bound), respectively, in excellent agreement with the measured data.

Electrical breakdown measurements of semicontinuous metal films.

The breakdown current ${\mathit{I}}_{\mathit{c}}$ of a percolating system is measured on real materials. We find that ${\mathit{I}}_{\mathit{c}}$\ensuremath{\propto}${\mathit{B}}^{\mathrm{\ensuremath{-}}\mathit{x}}$, B is the weakly nonlinear response determined by third-harmonic generation. A new criterion for ${\mathit{I}}_{\mathit{c}}$ is suggested, defined as the current at which a hot spot reaches the melting temperature of the metallic grains, ${\mathit{T}}_{\mathit{m}}$. This criterion remains valid in the presence of nonlinear effects. It is also consistent with the experimental observations: At ${\mathit{I}}_{\mathit{c}}$ the resistance either increases to infinity or decreases, i.e., the local geometry is changed at ${\mathit{T}}_{\mathit{m}}$. Modeling the breakdown by hot spots yields the above power law with 0.5\ensuremath{\ge}x\ensuremath{\ge}0.36, in excellent agreement with the measured data: x=0.48 and 0.41 for Ag and Au films.

Performance evaluation of single-channel coherent systems in presence of nonlinear effects

The combined effect is evaluated of instantaneous nonlinearity in both regions of chromatic dispersion on the bit error rate of high speed DPSK and ASK coherent optical systems. In particular it is shown that chromatic dispersion induced penalty can be either partially compensated for or enhanced by the nonlinear effect depending on the launched power level.

The shallow-water nonlinear Schrödinger equation in Lagrangian coordinates

The nonlinear Schrödinger equation in Lagrangian coordinates (LNLS) is derived from the Lagrangian form of the Korteweg–de Vries equation (LKdV) using a multiscale averaging approach. The resultant LNLS equation describes fluid particle motions for a small-amplitude, narrow-banded nonlinear wave field propagating in shallow water. Particle motion is discussed for LNLS in the context of the inverse scattering transform (IST) for both infinite-line and periodic boundary conditions and explicit expressions for the trajectories of fluid parcels are derived. It is demonstrated that, even in the presence of nonlinear effects, a particle trajectory can be orthogonally decomposed into nonlinear horizontal and vertical motions which, given the initial conditions, evolve independently of each other. It is shown how the presence of a long, slowly varying wave component, which is interpreted as radiation stress, influences the motion of fluid particles. Finally it is also shown how these results may be used in an experimental context for the study of data described approximately by the LNLS equation is discussed.

The nonlinear transfer problem in accreting pulsars - Stimulated scattering effects

The accreting pulsar radiative transfer problem in the presence of nonlinear effects in the radiation field, in particular those introduced by stimulated scattering, is solved. This leads to an extension of the Feautrier method in the strong magnetic case, which is solved by iterations. Relativistic cross sections are introduced and their effect is compared to the nonrelativistic approximation. This affects the cyclotron line shape and energy. It is found that stimulated scattering is important in determining the flux level in the continuum above the effective thermalization frequency and also in determining the cyclotron line flux.

Analysis of gas–surface reactions by surface temperature modulation: Theoretical formulation

The theoretical formulation of a frequency response technique, based on surface temperature modulation, for the study of surface reaction dynamics is described in detail. The formalism is developed for analyzing adsorption, desorption, and both unimolecular and bimolecular surface reactions. The evaluation of the activation barriers for the elementary surface reactions is straightforward even in the presence of strong nonlinearities and requires no knowledge of the composition or configuration (i.e., structure) of the adlayer. This capability provides a distinct advantage over competitive techniques such as modulated molecular beam reactive scattering. Although the evaluation of the preexponential factors of the rate coefficients is complicated by the presence of nonlinear effects (e.g., coverage-dependent rate parameters or a bimolecular reaction), in many cases the preexponential factors may also be evaluated in a straightforward manner.

BEACH GROUND-WATER OSCILLATIONS

Oscillations of ground-water table were measured in perforated piezometers distributed across the Baltic beach at the coastal research station of Lubiatowo, Prom spectral and correlation analysis it appears that the most pronounced wind-wave oscillations having a period of about 6 seconds have not been detected in the beach, while longwave oscillations, dominant in the beach spectrum, correlate well with nearshore long waves. Among the longwave oscillations, it is only those having periods about or slightly longer than 100 seconds that obey the Boussinesq law. However, some longer waves may also be generated by the interaction of shorter waves. Oscillations with periods from 50 to 100 s are very coherent throughout the beach. In the absence of stochastic noise and variety of inputs, low values of coherence for other periods indicate presence of nonlinear effects. More light should be shed on the origin of this nonlinearity and theoretical tools should be tried to complement the Boussinesq model.